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The use of conditionals in argumentation : a proposal for the analysis and evaluationof argumentatively used conditionalsGerlofs, J.M.

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Citation for published version (APA):Gerlofs, J. M. (2009). The use of conditionals in argumentation : a proposal for the analysis and evaluation ofargumentatively used conditionals

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Download date: 18 May 2018

THEUSE OF CONDITIONALS IN

ARGUMENTATIONA proposal for the analysis and evaluation of

argumentatively used conditionals

Academisch proefschrift ter verkrijging van de graad

van doctor aan de Universiteit van Amsterdam op gezag

van de Rector Magnificus prof. dr. D.C. van den Boom

ten overstaan van een door het college van promoties

ingestelde commissie, in het openbaar te verdedigen in

de Agnietenkapel der Universiteit op dinsdag 16 juni

2009, te 14.00 u.

door Janne Maaike Gerlofsgeboren te Alkmaar

Use Argumentation

THE USE OF CONDITIONALS IN ARGUMENTATION

A proposal for the analysis and evaluation of argumentatively used conditionals

ACADEMISCH PROEFSCHRIFTter verkrijging van de graad van doctor

aan de Universiteit van Amsterdamop gezag van de Rector Magnificus

prof. dr. D.C. van den Boomten overstaan van een door het college van promoties ingestelde

commissie, in het openbaar te verdedigen in deAgnietenkapel der Universiteit

op dinsdag 16 juni 2009, te 14.00 uur

door Janne Maaike Gerlofsgeboren te Alkmaar

Promotiecommissie:

Promotores: prof. dr. F.H. Van Eemeren prof. dr. E.C.W. Krabbe

Co-promotor: dr. M. A. van Rees

Overige leden: prof. dr. T. van Haaften prof. dr. F.J.M.M. Veltman dr. A.F. Snoeck Henkemans

Faculteit der Geesteswetenschappen

1. Introduction

2 Logical approaches to conditionals2.1 Introduction2.2 Problems associated with the definition of material implication2.3 Solutions to the problems associated with material implication2.4 Conclusion

3 Classifications of conditionals3.1 Introduction3.2 Degrees of hypotheticality3.3 Types of connection between the antecedent and the consequent3.4 Conclusion

4 Conditionals functioning as a connecting premise4.1 Introduction4.2 The role connecting premises play4.3 Characteristics of conditionals that function as connecting premise4.4. The evaluation of connecting premises4.5 Conclusion

5 Conditionals functioning as a standpoint5.1 Introduction5.2 Conditional standpoints5.3 Conditional defence5.4 Hypothetical standpoints5.5 Conclusion

6 Conditionals functioning as a constituent of an argument scheme6.1 Introduction6.2 Conditionals as a a constituent of pragmatic argumentation6.3 Conditionals as a constituent of a dilemma6.4 Conditionals as a constituent of an argument from authority6.5 Conditionals as a constituent of an argument from example6.6 Conclusion

7. Summary and conclusions

Bibliography

Index

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1. Introduction

In argumentation, speakers often make use of conditionals. When someone wants to defend the claim that a certain course of action must be followed, he may support his claim by applying a conditional sentence to sketch the beneficial consequences that this course of action will have, as in example 1:

1 We should buy that house. If we move there, we will haveplenty of space for everyone, you will finally be able to have the garden you always wanted and we won’t have to escort the children to school, they can walk by themselves.

Alternatively, a speaker could use a conditional to indicate that he only wants to be committed to his point of view under certain conditions, as in 2:

2 I don’t know whether I will be able to join you on that trip.But if we go together, we could go by car. I am sure my parents won’t mind me using my mom’s car.

Or a speaker could use a conditional to ponder on scenarios that were once within reach but are now ruled out, as in 3:

3 If only I had accepted that job as a masseuse with Google,then I would not have to worry about anything anymore. They offered me shares, and those would have been worth a fortune by now.

As early as 1989, Alec Fischer called on argumentation theorists to pay attention to suppositions. In his article ‘Suppositions in Argumenta-tion’ he pointed out that the use of suppositions had been neglected, since attention had been merely directed toward assertions: sentences in which propositions are presented as true. In suppositions, Fisher argues, propositions are typically not presented as true, they are merely supposed ‘for the sake of argument’. They are supposed to be true for the purpose of considering their implications. Fisher alerts argumen-tation theorists to a rather undesirable consequence of the negligence of the use of suppositions in argumentation: very common ways of arguing a case remain undiscussed. Suppositions play an important

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role in mathematics, theology, philosophy and science, where a claim can be proven to be false by supposing it to be true and showing that this supposition would eventually lead to a falsity or even a contra-diction. But also in more ‘everyday’ reasoning, suppositions can be employed, as is represented by the following example of Fisher (1989: 403), whereby the police are attempting to solve a case:

4 Suppose Smith was the burglar. In that case his finger-printswill be on the stolen jewelry.

It is for this reason that Fisher had dedicated an entire chapter to suppositions in his book The Logic of Real Arguments (1988) and he challenges fellow argumentation theorists to do the same. I think Fisher’s call can be seen as an attempt to place more empha-sis on the use of conditionals in argumentation. I would not hesitate to put on par what Fisher calls suppositions with antecedents of conditionals, since typically the proposition expressed in the antece-dent of a conditional also is not asserted. If we take a look at example 1, the speaker does not assert that ‘we move there’, he just supposes this proposition for the sake of drawing out the consequences. In a similar manner, in example 2 it is supposed that ‘we go together’ and furthermore in example 3 that ‘I had accepted that job as a masseuse with Google’. What suppositions and the antecedents of conditionals have in common is that the consequent (or consequences, in case of suppositions) is only ‘asserted’ conditionally: it should be considered within the scope of the situation sketched in either the antecedent, or the initial supposition. That is why I would place together suppositi-ons and their expressed implications with conditionals (although I might thereby be stretching the meaning of the word ‘conditional’).

Despite Fisher’s plea, the field of argumentation theory has not of-fered a systematic approach for the analysis and evaluation of con-ditionals used in argumentation. This does not mean, however, that conditionals have been deprived of scholarly attention. In the field of logic, discussion about the meaning of the connective ‘if-then’ and the circumstances under which an if-then-statement is true began toward the end of the 4th century BC. During that period, Philo of Megara tried to capture the essence of the ‘if-then’ connective in his statement that a true conditional is one that does not begin with a truth and end with a falsehood. This view immediately gave rise to a variety of critical responses. Interestingly enough, when during a later period (1879)

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Frege described the circumstances under which an ‘if-then-sentence’ is true – without having studied and without having known the clas-sical approaches to conditionals – this description turned out to be equal to the one offered by Philo of Megara and incited the same kind of criticism Philo of Megara’s statement received. Logical approaches to conditionals can be seen as alternative ways of coping with this criticism. A second field in which if-then-sentences have been studied thorou-ghly is linguistics. In this area, the study of conditionals primarily centered on the question of how conditionality is expressed in langu-age. Linguists do not only describe and categorize different ways to express conditionality, but they also try to explain why at times condi-tional markers are used in cases where there seems to be no conditio-nality involved. A famous example of such usage of the conditionality marker ‘if’ is the so-called Austin conditional: ‘If you are hungry, there are biscuits on the sideboard’. Here ‘there being biscuits on the sideboard’ is made conditional on ‘you being hungry’, although the biscuits will be there whether the addressee is hungry or not.

Given the support of these two longstanding traditions in the study of conditional sentences, I now want to answer Fisher’s appeal and take up the gauntlet by giving an outline of a model for the analysis and evaluation of argumentatively used conditionals. In this underta-king, I take a pragma-dialectical approach to argumentation. Characte-ristic of this approach – developed by Van Eemeren and Grootendorst – is that argumentation is seen as a means to resolve a difference of opinion between interlocutors (Van Eemeren&Grootendorst 1992, 2004). In their view, argumentation comes about when one interlo-cutor puts forward a standpoint and another interlocutor questions whether this standpoint is correct or disagrees with it. It is through argumentation that the participants in the discussion try to resolve this difference of opinion.1

In the study of argumentation, pragma-dialectics aims at the sociali-zation, dialectification, functionalization and externalization of the

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1 These interlocutors take upon themselves the roles of protagonist and antago-nist of the standpoint under discussion. They do not need to represent ‘real people’ – but should be seen as roles that need to be fulfilled in order to let a discussion take place. One person can both fulfil the role of protagonist and antagonist, for instance in a ‘dialogue intérieur’ regarding a certain point of view (Van Eemeren & Grootendorst 2004: 120).

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subject matter. Socializing the subject matter of the study of argumen-tation is realized by taking argumentation to be part of a dialogue between a protagonist – defending a point of view – and an antagonist – questioning this point of view. As a result, successive argumentative moves by the protagonist (for instance in a written piece of argumen-tation) are regarded as responses to (expressed or expected) criticism from the antagonist, aimed at resolving the difference of opinion by convincing the antagonist of the acceptability of the standpoint that is under consideration. Dialectifying the subject matter is achieved by specifying which moves are prohibited, which are allowed and which moves are even compulsory in the process of resolving the difference of opinion. As a result, the discussion – the complex of moves executed by the pro-tagonist and antagonist – can be regarded as a rational way to resolve a dispute concerning a specific point of view. In pragma-dialectics, the moves needed or prohibited are specified in the rules for a criti-cal discussion. For instance, regarding the closing stage of a discus-sion, rule 14 states that if the antagonist has conclusively attacked the protagonist’s inititial standpoint, the protagonist then has to retract this standpoint. If the protagonist succeeds in conclusively defen-ding his point of view, the antagonist in turn has to retract his doubt (2004:154). What counts as a conclusive defence or a conclusive attack is specified by other rules, and further rules specify the moves in other stages of the discussion. Functionalizing the subject matter is achieved not by just reflecting on the various contributions to the discussion as sentences, but also taking into account how those sentences contribute to some specific aim. The sentences uttered in the process of argumentation are taken to fulfil a function in the resolution process. For instance, the sentence ‘It is a beautiful day today’ could function as the main standpoint under discussion, if someone utters ‘It is a beautiful day today! The sun is shining and it is not too cold.’ The same sentence could also function as an argument in support of a standpoint, as in ‘We should go out, because it is a beautiful day today’. It could even function as an argument and a (sub)standpoint at the same time, as in ‘We should go out, because it is a beautiful day today. The sun is shining and it is not too cold.’ Essential to the determination of the function that different senten-ces expressed in a discussion fulfil, is to treat them as speech acts. The notion ‘speech act’, introduced by John Searle, conveys the idea that through language a speaker does not just express a proposition,

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but simultaneously expresses his stance towards this proposition. The proposition ‘the window is open’ can, for instance, be expressed in an assertion – ‘[I think] the window is open’– or in a question – ‘Is the window open?’. The difference between the two lies in the commitments the speaker has incurred by uttering either speech act. In the case of an assertion, the speaker can be committed to the truth of the proposition ‘the window is open’, whereas in the case of a question this commitment is absent (be it that the speaker becomes committed to other things, like ‘being genuinely interested in the answer’).2 Functionalization of the subject matter results therefore in focusing on the commitments the participants in the discussion are subject to. The commitments of the participants in a discussion play an impor-tant role as well in the externalization of the subject matter of the study of argumentation. The pragma-dialectician is not so much interested in the state of mind of the interlocutors, rather the focus is on what the interlocutors have expressed through language. ‘Acceptance’, for in-stance, is not studied as a psychological state, but rather is something taken to be achieved when an interlocutor expresses his agreement with – and hence commits himself to – a certain proposition (irrespec-tive of the actual state of belief of this interlocutor).

The theoretical background provided by the pragma-dialectical theory of argumentation allows me to specify the conditionals that will be the subject of this thesis. As is indicated in the subtitle, I shall not strive for an exhaustive overview of conditional sentences that may fulfil a role in a discussion. A conditional like ‘If you don’t mind, I would like to finish my line of reasoning before you come up with your remarks’ may be very useful to let the discussion run smoothly, but that kind of conditional will not be discussed here. I shall limit the discussion to ‘argumentatively used’ conditionals, that is, to conditionals that

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2 Of course, I provide here just a very rough and strongly simplified sketch of speech act theory. For a complete overview of Searle’s theory see his book Speech Acts (1969).

3 Since the terms ‘standpoint’ and ‘argument’ – although clearly defined in pragma-dialectics – are not so commonly known and are not easily understood by individuals who are not familiar with the field, I have decided to use more colloquial terms to indicate ‘something in need of defence’ (claim, point of view) and ‘some-thing put forward in defence of another statement’ (premise, reason, ground).

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function either as a standpoint or as an argument: as something that is in need of defence or as something put forward in defence of another statement.3

In the search for a model for the analysis and evaluation of argumen-tatively used conditionals, I start with what may have been the first known stipulation about the soundness of if-then-sentences, namely the statement by Philo of Megara. In chapter 2, I describe how this sti-pulation – that some time after Frege’s ‘re-invention’ became known as the definition of material implication – formulates the circumstances under which an if-then-sentence is true. The chapter continues with the main problems that have traditionally been associated with the de-finition of material implication and the logical operations of ‘contrapo-sition’, ‘hypothetical syllogism’ and ‘strengthening the antecedent’, all of which are strongly linked to this definition. What then folllows is a description of the different logical approaches to conditionals that have been formulated in response to the above mentioned problems. The question is then raised as to whether the definition of material impli-cation should be discarded as a tool for the evaluation of conditionals because of these problems, or whether its use should just be restricted to the unproblematic instances. Chapter 3 aims to find a way to differentiate between conditionals that are and conditionals that are not problematic with regard to the definition of material implication. The starting point in making this distiction revolves around the various classifications of conditionals, all of which stem from the linguistic tradition. These classifications are grouped under two more or less commonly acknowledged variables: the degree of hypotheticality of the antecedent and the type of connec-tion between the antecedent and the consequent of a conditional. After a description of the different classifications, I discuss whether these classifications make it possible to unequivocally distinguish between conditionals that are unproblematic and conditionals that are proble-matic with regard to the definition of material implication. In chapter 4, the definition of material implication and the logical operations that are associated with it, are placed within the context of argumentation. It will be argued that this definition and these logical operations are unproblematic if their use is restricted to one particular category of conditionals: conditionals that function as a connecting premise in an application of either the modus ponendo ponens or the modus tollendo tollens type of reasoning. Furthermore, it will then be explained that conditionals can only function as such if they possess certain characteristics and will only be applied in this way if it does not

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lead to clashing commitments for the protagonist. The problems as-sociated with the definition of material implication can all be explained by showing that the conditionals used in the counter-examples either do not possess the necessary characteristics or will lead to clashing commitments when put to use. The chapter finishes with a proposal for the evaluation of conditionals functioning as a connecting premise. In chapter 5 and 6 other argumentative functions that conditionals can fulfil are discussed. Chapter 5 lists various ways to put forward a standpoint under a certain condition and then explains what a reasona-ble follow-up would be on such conditionalized standpoints. Chapter 6 deals with conditionals that are a constituent of an argument scheme. In the field of argumentation theory there is no consensus about the precise description of the various argument schemes nor is there agreement about the number of argument schemes to be discerned. The discussion in this chapter is therefore only tentative. It is res-tricted to conditionals as constituents of pragmatic argumentation, of dilemma’s, of arguments from authority and of arguments from example. Hopefully, the analysis and evaluation of conditionals which function as a premise in those schemes will give an indication as to how conditionals can be treated which function as constituents of other argument schemes. Before ending this introduction a few terminological remarks are in order. The term ‘conditional’ or ‘conditional sentence’ will be used in the broadest sense of the word; I do not restrict the usage of this term to a particular class of ‘sentences under a certain provision’ – as some theorists in the field of conditionals tend to do.4 I prefer to use the term conditional over the term ‘if-sentence’ because in the English language (as well as in many others) there are more ways to express conditionality and such sentences can be used argumentatively just as well. For the same reason, I prefer the term ‘antecedent’ to the term ‘if-clause’ and the term ‘consequent’ to the term ‘main clause’, although I do realize that the proposition expressed in the antecedent need not chronologically precede the proposition expressed in the consequent. The terms ‘protasis’ and ‘apodosis’ are not used because they are less commonly applied. —————

4 Dudman for instance exclusively uses the term conditional for sentences like ‘If she misses the bus this evening, the countess will walk home’, calling sentences like ‘If Socrates is a man, he is mortal’ compounds (see section 3.2 of this thesis for an explanation of those different categories).

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2 Logical approaches to conditionals

2.1 Introduction

In the search for a model to analyse and evaluate argumentatively used conditionals, let us start with the Stoics, who were the first to thorou-ghly discuss the nature of conditionals. Their interest in conditionals probably was prompted by two issues. First of all, they were not so interested in demonstration – the principal topic of Aristotelian syl-logistic logic – but more in every day, dialectical arguments.5 One of the prevailing dialectical arguments was of the form ‘If p then q’ and ‘if p then not-q’, therefore ‘not p’, which seems to make an interest in conditionals inevitable (Kneale&Kneale 1984: 128). Secondly, in their logic the validity of an argument was closely connected to the truth of the corresponding conditional. If the premises are taken together as the antecedent and the conclusion as the consequent, a valid inference schema would yield a conditional that is true under all circumstances. In order to explain the difficult notion of validity, one had to explain the notion of the truth of a conditional (which was perhaps just as dif-ficult) (Sanford 1992: 19). One of the contributors to this dicussion was Philo of Megara, pupil of Diodorus Cronos (end of the 4th century BC). His stance on the na-ture of conditionals is conveyed by Sextus Empiricus in his Pyrrhoneiae Hypotyposes (ii, 110-112):

[1] Philo says that a sound conditional is one that does not begin with a truth and end with a falsehood, e.g. when it is day and I am conversing, the statement ‘If it is day, I am conversing’. (Kneale&Kneale 1984: 128)

Philo’s definition can be seen as an early representation of the defini-tion of material implication.6 It is referred to as the truth-functional

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5 This is not to say that Aristotle failed to discuss hypotheticals altogether. He discerned two types of hypothetical syllogism, modus ponendo ponens and modus tol-lendo tollens. His pupil Theophrastus developed Aristotle’s initial ideas.

6 The term ‘material implication’ was first used by Russell and Whitehead in Principia Mathematica (1962: 7).

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definition, since for establishing the truth of the conditional one only needs to know the truth values of the atomic propositions. A condi-tional is not true if the antecedent is true and the consequent is false, in all other situations the conditional is true. Or, to use the truth-table notation developed in the beginning of the 20th century:

p q p→q

1 t t t

2 t f f

3 f t t

4 f f t

The only situation in which the conditional is false, is the situation where the antecedent is true and the consequent is false (the situation depicted in line 2 of the truth-table). In all other situations the condi-tional is true. Ever since the truth-functional definition of conditionals was presen-ted, various authors have argued that this definition is problematic. The problems associated with it can be seen as difficulties that arise when the definition of material implication is applied to ordinary lan-guage conditionals. The definition does not lack something needed for dealing with the logical properties of conditionals within the frame-work of propositional logic. On the contrary, this definition renders commonly accepted argument forms like modus ponens en modus tollens valid.7 In that sense, it performs exactly as can be expected of it. It is only when this definition is applied to particular instances of if-then-sentences that it yields undesirable or ‘counterintuitive’ results.8

The problems that have been associated with the definition of mate-rial implication can be divided into two broad categories: problems as-sociated with the definition itself, and problems associated with logical operations that are valid for material implications but render unaccep-

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7 If the if-then connective is interpreted according to the definition of material implication, and the conjunction of both premises is taken as the antecedent and the conclusion is taken as the consequent of a conditional sentence, one arrives at a conditional that is true under all circumstances. This means it is impossible for the premises to be true while the conclusion is false – the argument is therefore valid.

8 For instance, Sanford writes (1992: 58): ‘The success of Frege’s programme for propositional logic is uncontroversial. About the suitability of material con-ditionals for representing conditionals in ordinary language, on the other hand, controversies have raged.’

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table results when applied to (some) ordinary language conditionals. In the first part of this chapter I will describe these problems in detail. The second part will describe solutions developed by various modern logical approaches to conditionals.

2.2 Problems associated with the definition of material implication

To start with problems associated with the definition itself, let us look at the first line of the truth-table. According to the material implication definition of conditionals, a conditional is true when both the antece-dent and the consequent are true. If this interpretation of conditionals is correct, the conditional in 5 is true:

5 If 2 times 2 is 4, then Paris is the capital of France.

The capital of France is Paris, 2 times 2 is 4, therefore both the antece-dent and the consequent are true. But it is doubtful whether speakers not trained in propositional logic would find this conditional accep-table, since the antecedent and the consequent seem to be unrelated. Apart from being sound in a truth-functional sense, ordinary language conditionals seemingly have to possess another property: between the antecedent and the consequent there must be some sort of connection. A similar difficulty seems to arise when we look at the 3rd and 4th line of the truth-table. Both 6 and 7 are true according to the truth-functional definition of conditionals, simply because the antecedent is false:

6 If Philo of Megara had died at the age of one, he would havebeen the first to formulate a truth-functional definition of con-ditionals.

7 If Philo of Megara had died at the age of one, his contribution to the study of conditionals would have been nil.

In 6 the antecedent is false while the consequent is true (as far as we know), in 7 the antecedent is false and the consequent is false as well. 6 represents line 3 of the truth-table, 7 line 4. Although according to the truth-functional definition both 6 and 7 are true, 6 seems to be unacceptable, while 7 seems to pose no problem.

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The definition of material implication does not only render conditio-nals with a false antecedent true that seem to be false to an ordinary language user. Sometimes it even attaches a truth-value to a conditio-nal in a situation where it is rather akward to do so. Take the conditio-nal in 8:

8 If Susan takes an aspirin, her headache will disappear.

This conditional is true when Susan takes an aspirin and her headache disappears. It is false when she takes an aspirin and her headache does not disappear. But what if Susan does not take an aspirin at all? In that situation it seems to make more sense to leave the truth of the conditional undecided, whereas according to the definition of material implication it would be true because the antecedent is false. Example 5, 6 and 8 can be seen as instances of the paradoxes of ma-terial implication (Blumberg 1967: 15). From the definition of material implication it follows that a conditional is true when the consequent is true or the antecedent is false. That implies one can infer (A→B) from either not-A or B. In the case of ordinary language conditionals, for a conditional to be sound it does not seem to suffice that either the consequent is true or the antecedent false. Seemingly, there has to be a connection between the antecedent and the consequent as well. If Philo of Megara had died at the age of one, he would not have been the first to come up with a truth-functional account of conditionals, simply because he wouldn’t have lived long enough to do so. Which makes it acceptable to say that as a consequence of his dying young, his contribution to the study of conditionals would have been nil. Although line 1, 3, and 4 have been discussed frequently, line 2 of the truth-table has escaped such treatment. There seems to be a wide-spread consensus that a conditional with a true antecedent and a false consequent is false. In fact, this is seen as part of the core meaning of conditionals. Kahane, for instance, writes in the introduction to Logic and Philosophy:

So all that a material conditional affirms not to be the case is what any conditional affirms not to be the case, namely that it is not the case that its antecedent is true and its consequent false (1995:25).

Nevertheless, even regarding this undisputed line of the truth table, problematic instances can be formulated. Take for instance the fol-lowing example given by Mackie:

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...let us test it [the definition of material implication – jmg] further by considering four cases. All four begin with a father saying to a child ‘If you poke your finger into that monkey’s cage, you will get it nipped off’ and with the child poking its finger into the cage nonetheless.(...) In the fourth case the monkey snarls, snaps at the finger, but just at that moment a large object falls from the roof of the cage and deflects the monkey’s attack (1973: 107).

Is the conditional in this case true or false? The antecedent is true, the child has poked its finger in the cage. The consequent is false, since the finger is not nipped off. So strictly speaking the conditional is fal-se. But to call this conditional false seems rather far-fetched. The con-ditional expresses a prediction on the basis of a generalized conditio-nal, and to reject this conditional on the basis of one counter-example that can easily be explained away, would be rather premature.9

To sum up, for line 1, 3 and 4 of the truth-table, examples can be formulated that comply with the truth-functional definition of condi-tionals but seem to be unacceptable anyway. And for line 2 an example can be thought of where the truth of the antecedent and the falsity of the consequent do not suffice for the falsity of the conditional.

Apart from the problems associated with the definition of material implication, various authors discern problems when conditionals are submitted to logical operations that are valid for material conditionals. The discussion of this subject has been concentrated on ‘contraposi-tion’, ‘transitivity’ and ‘antecedent-strengthening’, but this does not mean that these operations are the only three raising difficulties. Contraposition is the name given to the logical operation whereby both the antecedent and the consequent are negated and the order is reversed. That is, ‘A→B’ is converted into ‘¬B→¬A’. In classical propositional logic ‘A→B’ is equivalent with ‘¬B→¬A’− whenever the first is true (or false), the second is true (or false) as well − as a consequence contraposition is valid. From the conditional ‘If Thomas

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9 According to Mackie this conditional is false (1973: 107): ‘As long as we stand firm on attending what was said, we must say the same about the fourth [that it is false-jmg]: there the father would be presumably withdraw to claiming that all he meant was that there was a serious risk of the finger’s being bitten off, and this has been thoroughly confirmed.’ At least this example shows that also with reference to the 2nd line of the truth table a conditional can mean something more (or less?) than is captured in the definition of material implication.

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is a vegetarian, he does not eat steaks’ one can infer that ‘If Thomas does(not not) eat steaks, he is not a vegetarian’. However, if one consi-ders some natural language conditionals, this operation doesn’t seem to be acceptable. First of all, contraposition is problematic for conditionals where the antecedent forms some kind of condition for a speech act expressed in the consequent, as in 9:

9 If you would appreciate it, I could ask the manager for a special discount.

In 9 the antecedent expresses a condition that must be fulfilled in order for the offer in the consequent to become ‘uttered’, which me-ans no one has offered to do anything as long as the condition in the antecedent is not satisfied. If contraposition is applied to 9, one arrives at 9’:

9’ If I could not ask the manager for a special discount, youwould not appreciate it.

Although 9’ might be true as well, it cannot be inferred from the con-ditional in 9. Sometimes conditionals of this type don’t lend themsel-ves to contraposition at all. It is hard to see for instance what contrapo-sition would amount to when applied to ‘If you don’t mind me asking, why did you move out of Amsterdam anyway.’ The second category of conditionals that do not allow contraposition are conditionals like the example in 10 given by Jackson (1987: 48):

10 If it rains, it will not rain heavily.

The antecedent of 10 conveys some sort of concession. If this proposi-tion is put on a scale, it would occupy a less extreme position than the proposition expressed in the consequent. These relative positions on a scale can be externalised by adding ‘at least’ to the consequent. (If it rains, at least it will not rain heavily). Contraposition in this example results in 10’, which is clearly not acceptable:

10’ If it rains heavily, it will not rain.

The third category of conditionals that do not comply with contraposi-tion are conditionals like the one in 11: 10

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11 If the U.S. halts the bombing, then North Vietnam will not agree to negotiate.

In 11 the antecedent of the conditional depicts a certain course of ac-tion, while the consequent shows what happens if this course of action is taken. Contraposition of this conditional results in:

11’ If North Vietnam agrees to negotiate, then the U.S. will nothave halted the bombing.

The strange thing about 11’ is that the course of action for the U.S. now seems to be the dependent on the willingness to negotiate. Contraposition is not the only logical operation that yields undesi-rable results when applied to certain ordinary language conditionals, transitivity poses problems as well. The principle of transitivity is ex-pressed in an argument form called ‘hypothetical syllogism’. In logic, ‘A→B’ and ‘B→C’ together justify the conclusion ‘A→C’. For instance, if one accepts that Theodore did not murder Philip if he was in jail at the time of the murder, and one accepts that he was in jail at the time of the murder if the prison records show this, one can conclude that if the prison records show that Theodore was in jail at the time of the murder, he did not commit the murder. A well-known example of ordinary language conditionals that do not allow transitivity is the following example given by Cooper (1978: 183):

12 If Brown wins the election, Smith will retire to private life. If Smith dies before the election, Brown will win it. So if Smith dies before the election, Smith will retire to private life.

Transitivity is not only problematic when applied to conditionals con-cerning the future, it can be at times just as problematic in the case of so called subjunctive conditionals, which is demonstrated by the following example given by Jackson (1987:80):

13 If it had snowed, I would have gone skiing.If there had been a blizzard, it would have snowed.So: If there had been a blizzard, I would have gone skiing.

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10 Examples (11) and (11’) are given by Stalnaker (1975: 173-174)

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Hypothetical syllogism is closely connected to another argument form that sometimes leads to unacceptable outcomes when applied to ordinary conditionals, namely, the operation called ‘strengthening the antecedent’. An example of strengthening the antecedent is given under 14:

14 If Max is a bat, Max can fly.So: If Max is a bat and has been born this morning, Max can fly.

Although the premise of this argument is acceptable, the conclusion certainly is not because newly-born bats cannot fly yet. That the reaso-ning is valid becomes clear when the underlying hypothetical syllo-gism is made explicit, as in 14’:

14’ If Max is a bat and has been born this morning, then Max is a bat.If Max is a bat, then Max can fly.So: If Max is a bat and has been born this morning, then Max can fly.

A and B taken together imply A, moreover, A implies C, therefore A and B taken together imply C. This means that from two acceptable premises, using the valid argument form of hypothetical syllogism, one may arrive at a conclusion that is clearly unacceptable.

In summation: apparently one runs into serious problems when the definition of material implication is taken as the definition of all ordi-nary language conditionals. This definition gives rise to the paradoxes of material implication: from something false anything can follow, and something true can follow from anything. Moreover, when ordinary language conditionals are applied in logically valid operations like con-traposition, hypothetical syllogism and strengthening the antecedent, unacceptable outcomes may occur. The most common explanation for these problems and paradoxes is that the meaning expressed in the truth-functional definition must not be seen as the ‘whole’ meaning of conditionals. As Kahane puts it:

The connective ‘⊃‘ has been defined so as to capture the bare mi-nimum in truth-functional terms that is asserted by a conditional. (...) When symbolizing conditionals of ordinary English, it must be remembered that most everyday conditionals are not merely

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truth-functional. Thus, when they are symbolized by ‘⊃‘, only part of their meaning is captured (namely, the part they share with all conditionals), the other part being lost (1995: 25).

In response, various logics have been developed in order to capture the parts of meaning that have been lost.

2.3 Solutions to the problems associated with material implication

One of the first (modern) reactions to the definition of material impli-cation came from C.I. Lewis. In an article in Mind, ‘Implication and the Algebra of Logic’, he introduces his concerns about this definition in the following manner:

The development of the algebra of logic brings to light two some-what startling theorems: (1) a false proposition implies any pro-position, and (2) a true proposition is implied by any proposition (1912: 522).’

The theorems Lewis refers to were first made explicit by Whitehead and Russell in their Principia Mathematica and are currently known as the paradoxes of material implication. It has been suggested that these paradoxes only appear to be pa-radoxical, due to confusion, which apparently began when Russell and Whitehead used the term ‘implication’ to refer to the conditional construction. In his article ‘External and Internal Relations’, Moore discusses the unusual meaning given to the word ‘implies’:

And these results, it seems to me, appear to be paradoxical, solely because, if we use ‘implies’ in any ordinary sense, they are quite certainly false. Why logicians should have thus chosen to use the word ‘implies’ as a name for a relation, for which it never is used by any one else, I do not know (1922:295).

But the confusion only seems to have started there. According to the Encyclopaedia of Philosophy a second shift in meaning has taken place.

Second, the meaning of ‘materially implied by’ is shifted from that of ‘if-then’ to that of ‘follows logically from’ (that is, from the truth-

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functional connective ‘→’ to the relation of deducibility or logical consequence). Once this shift is made, the results are indeed ‘pa-radoxical’: a true sentence follows logically from any sentence, and any sentence follows logically from a false sentence. However, such consequences follow not from the definition of ‘P→Q’ but from a confusion between ‘P→Q’ and ‘P; therefore Q’. The first set of symbols represents a truth-functional compound, the second an (obviously invalid) argument form (...) (Blumberg 1967: 16).

This second shift of meaning could well have been caused by the close connection between the truth of a conditional and the validity of an argument form. The premises and conclusion of a valid argument can be expressed in a conditional sentence which is true under all circum-stances. Consider for example the following argument:

15 Either John or Mary is coming to the conferenceJohn is not coming so: Mary is coming to the conference

can be expressed in the corresponding conditional ‘If either John or Mary is coming to the conference and John is not coming, then Mary is coming.’ Conditionals such as these can be seen as expressing logical consequence or ‘if..., then’ in the sense of ‘following logically from’.

While some attribute the paradoxical nature of the theorems to con-fusion, others have contended that these theorems rather are merely pragmatically akward. Grice for instance argues that ‘the other parts of meaning’ that are lost in the definition of material implication are not parts of the meaning of the conditional, but are in fact conversational implicatures (1989: 83). He discusses two ways in which these implica-tures can emerge. 11

The first explanation Grice offers is accomplished by an analysis based on the Cooperative principle and the maxims of conversation. If someone asserts ‘if p then q’– according to Grice – he asserts some-thing that is logically weaker than the negation of p or the assertion of q. This amounts to an infringement of the first maxim of Quantity: if a more informative statement is of interest to the interlocutor, the speaker is expected to assert this statement. Grice considers the more

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11 For an explanation of the main concepts of Grice’s theory of conversation, see Grice 1989: 22-40.

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informative statement ‘not-p’ or ‘q’ to be of interest, since:

No one would be would be interested in knowing that a particular relation (...) holds between two propositions without being inte-rested in the truth-value of at least one of the propositions con-cerned, unless his interest were of an academic or theoretical kind (...). Either because we know (...) that the use of language for prac-tical purposes is more fundamental than (...) its use for theoretical purposes, or because it is simply a well-known fact about human nature that practical interests are commoner than theoretical in-terests (...), we are justified in assuming, in the absence of any special contextual information, that an interest is practical more than theoretical (1989: 61).

The interlocutor, assuming that the speaker observes the Cooperative Principle, can explain this infringement of the maxim of Quantity by supposing that asserting the more informative ‘not-p’ or ‘q’ would amount to an infringement of the second maxim of Quality (which states that you must have adequate evidence for what you say). There-fore, whenever ‘if p..., then q’ is asserted under normal circumstances, the interlocutor concludes that the speaker does not put forward this assertion because he knows / has evidence that not-p, or that q (that is, he does not assert ‘if p then q’ on the basis of one of the paradoxes of material implication). To be sure, that is exactly what makes the paradoxes of material implication pragmatically odd. The second way an implicature might come about is closely con-nected to the role conditionals fulfil in discourse. Grice argues that conditionals might be fitted for the special role of presenting cases:

...in which a passage of thought, or inferential passage, is envi-saged from antecedent to consequent, and possibly to a further consequent with respect to which the first consequent occupies the position of antecedent (1989: 77).

If such a function can be ascribed to conditionals, a speaker might in asserting a conditional ‘implicate’ that he is using the conditional in this way. Furthermore, if it is a precondition for this use that the spea-ker’s knowledge of this conditional is not founded on his knowing that not-p or that q (but for instance rather on a strong connection between the antecedent and the consequent), then this information might be implicated as well

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Whether they ascribe the paradoxical nature of ‘q → ( p→ q)’ and ‘not-p → (p → q)’ to confusion or to pragmatic factors, the above mentioned authors agree that the definition of material implication does reflect the meaning of ‘if..., then’. Many other authors however have disputed just that. The paradoxes of material implication and the strange or counterintuitive results of applying contraposition, hypothe-tical syllogism and antecedent strengthening to ordinary conditionals, have led them to abandon the definition of material implication and to formulate an alternative definition that precludes such conundrums. C.I. Lewis for instance found the abovementioned theorems not only somewhat startling, but even went on to dispute the fact that the defi-nition of material implication reflected the true meaning of ‘to imply’. This definition states that a proposition materially implies another proposition if it is not the case that the antecedent is true and the consequent is false. Suppose someone says: ‘If it is sunny, then John is in the garden’. According to the definition, this sentence would be true if it is in fact sunny and John is in fact in the garden, no matter where John would be the next sunny day. From Lewis’ point of view, a proposition only truly implies another proposition if it is not just ‘not the case’ that the antecedent is true and the consequent false, but ‘impossible’ for the consequent to be false while the antecedent is true. In order to develop a logic of conditionals that reflects this quality, he introduced a symbol for what he called ‘strict implication’ and developed logical systems in which the para-doxes of material implication cannot be proven. Since these logical systems make use of modal terms like ‘necessary’ and ‘possibly’, they are commonly known as modal logics.12

Unfortunately, logical theories based on strict implication do have paradoxes of their own. If the consequent of a conditional is formed by a proposition that is necessarily true, this conditional will be true, irrespective of the truth or falsity of the antecedent. Something similar applies to a conditional of which the antecedent is necessarily false: such a conditional will always be true, whether the consequent is true or not. Lewis was not overly concerned by these results having nevert-heless held onto his definition of strict implication. Other logical theo-ries like possible world semantics and probability theory have elabora-ted on this basic notion of strict implication since then. But relevance

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12 For an overview of the different systems of modal logic and the discussions associated with them, see Bull & Segerberg 2001.

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logicians see the occurrence of the paradoxes of strict implication as a sign that strict implication doesn’t capture the true meaning of ‘to imply’ and have set themselves the task of improving this definition.

Relevance logicians are concerned with the formal analysis of the notion of ‘logical implication’.13 They contest the view that material implication has anything to do with implication, since ‘implication’ must be seen as:

...’entailment,’ or ‘the converse of deducibility’(...), expressed in such logical locutions as ‘if... then –,’ ‘implies,’ ‘entails,’ etc., and answering to such conclusion-signalling logical phrases as ‘there-fore,’ ‘it follows that,’ ‘hence,’ ‘consequently,’ and the like (Anderson & Belnap 1975: 5).14

Therefore, material implication is not a kind of implication, implica-tion is not yet formally analysed, while relevance logic aims at doing just that. As a starting point for their analysis, relevance logicians use natural deduction. Relevance logicians wish to interpret A→B as ‘A entails B’ or ‘B is deducible from A’. In a system of natural deduction this me-ans that – by the rules of derivation of the system – B can somehow be deduced from the hypothesis A. However, in most systems of natural deduction the paradoxes of material implication are deducible as well. That is why relevance logicians eventually reject this (official) natural deduction concept of proof from hypotheses as a basis for proper implication and propose two adjustments: the addition of the notion of necessity and of relevance.

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13 Dunn and Restall (2002) claim that relevance logicians are not exlusively concerned with the notion of logical implication. However, given that their article is not quite clear as to what relevance logicians are exactly concerned with, and since Anderson’s and Belnap’s books Entailment: the Logic of Relevance and Necessity (volume I, 1975; volume II, 1992) are still seen as the standard work on the subject, this discussion of relevance logic will mainly be based on these earlier works.

14 Judging from this exposition, relevance logicians seem to be subjected to the confusion mentioned before: ‘p materially implies q’ is taken to mean ‘p, therefore q’. However, they vehemently disagree with the view that the paradoxes of material implication are based on this confusion and consider ‘If p, then if q, then p’ to be just as objectionable as ‘p implies (q implies p)’ (Anderson & Belnap 1975: 13).

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That necessity must be added to arrive at a definition of implication is motivated by the basic assumption in logic that the validity of an in-ference depends on formal considerations alone. According to Ander-son and Belnap, this:

...amounts to saying that the validity of a valid inference is no acci-dent of nature, but rather a property a valid inference has necessa-rily. Still more accurately: an entailment, if true at all, is necessarily true (1975: 14).

Anderson and Belnap argue that this means that truths deduced from necessary truths are necessary truths as well. The paradoxes of material implication do not fulfil this condition, since an example can be developed whereby a statement that is not necessarily true can be deduced from a necessarily true statement. For instance, if it is true that John is in the garden, then one can deduce that ‘If a bachelor is an unmarried man, John is in the garden’. In this implication, a neces-sarily true statement implies a statement that is not necessarily true, which is in direct conflict with the condition mentioned above . Yet the logical system Anderson and Belnap devise to include the no-tion of necessity, suffers from the same trouble as C.I. Lewis’s modal logic: the paradoxes of strict implication. An arbitrary proposition p implies q when q is necessarily true. This means that the implication A→(B→B) is valid: since it is impossible for (B→B) to be false, it is impossible that the antecedent is true while the consequent is false. Anderson and Belnap conclude from this that a logical system that includes the notion of necessity still cannot capture the true meaning of ‘to imply’. According to Belnap and Anderson, the deduction of the necessary proposition (B→B) from an ordinary proposition A is unacceptable because A is irrelevant to (B→B). Anyone putting forward this deduc-tion would be guilty of a fallacy of relevance. Although Anderson and Belnap do not provide a definition of relevance, they claim that for a proposition A to be relevant in the deduction of another proposition B, proposition A must actually be used in deducing B. To keep track of the propositions used in a deduction, they propose a subscripting device and develop logical systems that comply with this notion of relevance. Only if the conclusion of a deduction contains the same subscript as an hypothesis earlier introduced, can this hypothesis be relevant for the conclusion of the deduction. And only if a proposition B follows necessarily from a proposition A with the same subscript, can one conclude that A implies B.

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Both strict implication and it’s combinations with the notion of rele-vance are advanced as a way to circumvent the paradoxes of material implication. Yet the paradoxes of material implication are not the only problems connected to a truth-functional definition of ‘if-then’. Some logical operations that are valid in propositional logic produce unac-ceptable outcomes when applied to ordinary conditionals. Conditio-nal logics, like possible world semantics and probability theory, are aimed at solving this problem: they try to explain why contraposition, hypothetical syllogism and strengthening the antecedent yield such undesirable results.

Possible world semantics was aimed originally at providing a seman-tics for logical systems based on the notion of strict implication. Since truth tables cannot be used for determining the truth of sentences that contain words like ‘possible’ or ‘necessary’, these logical systems ne-cessitate a different way of evaluating the truth of a sentence. Possible world semantics provides such a semantics by introducing the notion of an accessible possible world. Stalnaker introduces the main concepts of possible world semantics by examining how one proceeds in evaluating a certain conditional sentence. He presents the hypothetical situation of a true/false poli-tical opinion survey in which one is confronted with the statement ‘If the Chinese enter the Vietnam conflict, the United States will use nuclear weapons’. How does one go about determining whether one believes this statement or not? According to Stalnaker, the evaluation moves along the following lines:

First, add the antecedent (hypothetically) to your stock of beliefs; second, make whatever adjustments are required to maintain con-sistency (without modifying your belief in the antecedent); finally, consider whether or not the consequent is then true (1975: 169).

This procedure is now known as the Ramsey test. From these belief conditions, the transition to truth conditions is made by introducing the concept of a possible world: a world in which the antecedent of the conditional is true and which has been adjusted so that no contradictions arise. ‘Necessity’ is defined as ‘true in all ac-cessible possible worlds’, while ‘possibility’ is defined as ‘true in some accessible possible world’. Worlds are accessible when they comply with a restriction associated with the type of necessity or possibility under consideration. For instance, in the case of physical necessity /

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possibility, the worlds accessible are those in which the same laws of nature hold (D. Lewis 1973: 5). Although providing a semantics for logical systems based on the notion of strict implication triggered the research in the field of pos-sible world semantics, some logicians working in this field abandoned the notion of strict implication as a way to treat ordinary conditionals. After all, ordinary conditionals often cannot be submitted to the logical operations of contraposition, transitivity and strengthening the ante-cedent, while strict conditionals even in very weak modal logics allow for these logical operations. As a result conditionals are not treated as strict conditionals, although possible world semantics is still viewed as a valuable tool in evaluating ordinary conditionals. As Nute and Cross put it:

The basic intuition, that a conditional is true just in case its conse-quent is true at every member of some set of worlds at which its an-tecedent is true, may be yet salvageable. We can avoid Transitivity, etc. if we allow that the set of worlds involved in the truth conditi-ons for different conditionals may be different (2001: 9).

Possible world semantics explains the failure of contraposition, transi-tivity and strengthening the antecedent by referring to two crucial con-cepts in this theory: the selection of worlds and the relative closeness of worlds. In possible world semantics, a selection function is defined in order to decide on the set of worlds significant for the evaluation of the conditional. The relative closeness relates to the position of one world in relation to other worlds and the actual world. If one takes the-actual world as a starting point, all possible worlds can be positioned as either close to or further away from the actual world, depending on the similarity / dissimilarity that exists between the actual and the pos-sible world. When a possible world is very similar to the actual world, this world is close to it, when there are many differences, this world is ‘far’ away from it. In order to evaluate a conditional, one has to check whether the consequent of this conditional is true in the possible worlds in which the antecedent is true and that are closest to the actual world.15 If the consequent is true in those worlds, the conditional is true, if not, the conditional is false. Failures of contraposition, transitivity and streng-thening the antecedent arise when the conditional(s) that form the premise of the argument are true according to these truth conditions, whereas the conditional that forms the conclusion is false.

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A situation where contraposition fails is given in the following: sup-pose a father with two children says ‘If we had more than two child-ren, we would not have had more than ten children’.16 This conditional is true when in the possible worlds closest to the actual world in which the father has more than two children, he does not have more than ten children. Since worlds close to the actual world can be thought of where the father has three, four or in any case less than eleven children, this conditional is true. However, contraposition yields a conditional that is false. ‘If we would have had more than ten children, we would not have had more than two children’ is false since in the worlds closest to the actual world in which the statement ‘we would have had more than ten children’ is true, the statement ‘we would not have had more than two children’ is false. Transitivity fails in situations where the antecedent of the first pre-mise is more far-fetched than the antecedent of the second premise. As a result, the worlds closest to the actual world where the antecedent of the first premise holds, differ from the worlds closest to the actual worlds where the antecedent of the second premise holds. That is why the consequent of the second premise can be false in the nearest world where the antecedent of the first premise holds. Both Stalnaker (1975: 173) and D. Lewis (1973: 33) use the following example to make this point clear:

16 If J. Edgar Hoover had been born a Russian, then he would have been a communist.If he had been a communist, he would have been a traitor.Therefore: If he had been born a Russian, he would have been a traitor.

Both Stalnaker and Lewis consider the world in which Edgar J. Hoover is born a Russian to be less like the actual world than the world in which he is a communist. In the world closest to the actual world where he is born a Russian, J. Edgar Hoover would not be an Ameri-can citizen (whereas he would be an American citizen in the closest world in which he is a communist). As a result, the consequent ‘he would have been a traitor’ is not true in this world.

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15 One of the most difficult questions possible world semantics has to answer is ‘how does one decide which worlds are closest to the actual world?’ For an overview of the different viewpoints on this issue see Nute & Cross 2001: 9-28.

16 This is an example from Sanford (1992: 109).

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The failure of strengthening the antecedent is closely related to that of transitivity. Suppose someone says ‘If the cherries would have been cheap, Martha would have bought them’. This conditional would be true when in the possible worlds with cheap cherries closest to the actual world Martha would indeed have bought the cherries. Along the same line of reasoning, the conditional ‘If the cherries would have been rotten, they would have been cheap’ would be true. However, if these two conditionals are used as premises in a hypothetical syllo-gism, the conclusion ‘If the cherries would have been rotten, Martha would have bought then’ would be false. Similarly, the antecedent cannot be strengthened to ‘If the cherries would have been cheap and would have been rotten’, since in the world closest to the actual world where this antecedent would be true (which is different from the closest world with cheap cherries), the consequent ‘Martha would have bought them’ would be false. In cases like these, antecedent strengthe-ning fails. When one starts from the truth conditions for conditionals as descri-bed by possible world semantics, situations can be thought of where contraposition, transitivity and strengthening the antecedent lead to an argument with true premises and a false conclusion. Therefore, these argument forms are invalid and the formal systems of possible world semantics are designed in such a way that contraposition, transitivity and strengthening cannot be proven within these logical systems.

Just as with possible world semantics, probability theory provides an explanation for unacceptable inferences that may obtain when contraposition, transitivity and strengthening the antecedent are ap-plied to everyday conditionals, albeit this is achieved from a different starting point. According to probability theorists, the truth-functional soundness criterion does not always suffice for establishing whether a certain deduction is sound. Adams gives the following example of the failure of orthodox truth-functional logic:

Imagine a man about to eat some very good and non-poisonous mushrooms who is informed ‘if you eat these mushrooms, you will be poisoned’, which leads the man not to eat the mushrooms while making the statement ‘true’ (i.e. materially true) at the same time. Obviously the man would have been better off not to have arrived at this allegedly ‘true’ conclusion, and this type of example should make it questionable that reasoners should want to be gui-ded in their reasoning by the principles of orthodox logic, if those

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are designed to lead them to conclusions which are ‘true’ in this unwanted sense (1975:x).

Adams claims that orthodox truth-functional logic fails because it is designed for reasoning from certainties to other certainties. However, in everyday reasoning one often doesn’t start from absolute certainties (or rather, at least the truth of the premises often cannot be established at the time the reasoning takes place) and therefore the conclusion is no certainty either. Probability theory is designed to provide a soundness criterion that can be applied in such circumstances. The key to probability theories is that they do not start from the truth of propositions but from the probability of propositions. Reasoning should not just be evaluated by a truth conditional soundness criterion, but also by a ‘probabilistic soundness criterion’, according to which reasoning is sound if it is impossible for the premises of an inference to be probable while its conclusion is improbable. Or to be more precise: in a probabilistically valid argument the uncertainty of the conclusion cannot exceed the sum of the uncertainties of the premises (Adams 1975:2). Contraposi-tion, hypothetical syllogism and strengthening the antecedent in some instances fail to meet the probabilistic soundness criterion, and are therefore not endorsed in probability theory. An important question probability theory has to answer is: ‘what counts as the probability of a proposition?’ In the case of assertions like ‘it rains’, the answer to this question is simple: the probability of this proposition equals the probability of its truth. The probability of conditional sentences is less easy to establish. Just as in possible world semantics, the Ramsey test generally is taken as a starting point for the evaluation of if-then-sentences. In evaluating the sentence ‘If it rains, the birthday party will be cancelled’, one adds ‘It rains’ to one’s stock of beliefs, adjusts those beliefs so that this assumption is accommodated and then assesses how probable it is that ‘the birthday party will be cancelled’. The probability of a conditional is therefore

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17 No matter how convincing this definition of the probability of a conditional might seem at first glance, closer inspection reveals the complexity at hand. David Lewis showed that the definition leads to the so-called ‘triviality result’ when taken in combination with the axioms of probability logic (Lewis 1976: 131-134). One way out of this is to abandon the idea that indicative conditionals have truth-values. For more on this subject , see Bennett 2003 (especially chapters 4 and 5).

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a conditional probability: the probability that the consequent holds given the antecedent.17 If in 10 out of 20 situations when it rains, the birthday is cancelled, the probability of ‘If it rains, the birthday party will be cancelled’ is 10/20 = 1⁄2 (50%).18

Given this definition of the probability of conditionals and the pro-babilistic soundness criterion, one can show that contraposition, hypo-thetical syllogism and strengthening the antecedent are unsound. An example of contraposition failing to meet the probabilistic soundness criterion is given by Sanford (1989: 93-94). Take the two propositions S and T:

A roll of dice comes up 6. At least one of the dice comes up 3.

There are 36 equipossible ways for two dice to fall. In 11 of those 36 cases, (T) is true: at least one of the two dice comes up 3. In the remai-ning 25 cases (T) is false. (S) is true in 5 of the 36 cases, in 31 cases it is false. The distribution of truth and falsity is represented in the fol-lowing table (black indicates false, white indicates true)19:

From this table, it can easily be seen that ‘If S, then T’ and ‘If not-T, then not-S’ are not equally probable. The probability of ‘If S, then T’ is 1/5: out of the five situations in which S is true, there is one situation in which T is true as well. The probability of ‘If not-T, then not-S’ is much higher, out of 25 situations in which not-T is true, there are 21 in which not-S is true as well (probability is 21/25). This makes the

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18 From this definition it becomes apparent that probability theory can only say something about indicative conditionals, not about counterfactuals. If the antece-dent of a conditional is known-to-be false, there would be no situations in which the proposition expressed in the antecedent is true, and therefore the conditional probability would be n/0.

19 This table is taken from Sanford as well.

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argument ‘If not-T, then not-S; therefore, if S, then T’ probabilistically unsound, since the probability of the conclusion is much lower than that of the premise. That this hypothetical syllogism is probabilistically unsound is il-lustrated by the following example of Bennett (2003: 145). Imagine a farmer who believes that the gate to the turnip field is closed and that his cows are not in the turnip field. This farmer would accept the fol-lowing conditional:

17 If the cows are in the turnip field, the gate has been left open.

He would accept it because if he adds the antecedent to his stock of beliefs and adjusts his belief system, his belief in ‘the gate is closed’ would drop (making the proposition ‘the gate has been left open’ more probable). Furthermore, the farmer would accept the following conditional:

18 If the gate to the turnip field has been left open, the cows havenot noticed the gate’s condition.

The farmer accepts this consequent, given the antecedent, because he thinks the cows are not in the turnip field. Combining the two condi-tionals in a hypothetical syllogism, we are left with ‘If the cows are in the turnip field, they have not noticed the gate’s condition’, and this is clearly absurd. That this instance of hypothetical syllogism is probabilistically un-sound can be illustrated with the following table:

The conditional ‘If the cows are in the turnip field, the gate to the tur-nip field has been left open’ receives the probability 1: the a-segment lies completely within the c-segment. The probability of the second conditional is reasonably high as well: out of 14 situations in which the gate is open, the cows have not noticed it in 9. The conclusion of the hypothetical syllogism however, has the probability of 0: there is no

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situation in which the cows are in the turnip field, but have not noticed the gate’s condition. Here again, just as in the case of the role of dice, a situation can be thought of where the probabilities of the premises are high, whereas the probability of the conclusion is low. Therefore hypothetical syllogisms are not always probabilistically sound. Since the logical operations of hypothetical syllogism and antecedent strengthening are closely related, the table used to show that hypothe-tical syllogism can be probabilistically unsound can be also used for proving the probabilistically unsoundness of strengthening the antece-dent. Take for instance the following argument:

19 If the gate to the turnip field has been left open, the cows havenot noticed it. Therefore, if the gate to the turnip field has been left open, and the cows are in the turnip field, the cows have not noticed that the gate is open.

The probability of the premise is high (9/14), while the probability of the conclusion is zero, which makes the argument probabilistically invalid. The soundness criterion provided by probability theory renders contraposition, hypothetical syllogism and antecedent strenghtening invalid. Therefore, just as in the case of possible world semantics, pro-bability theory is devised in such a way that these three logical operati-ons are excluded.

A final group of logics that have been initiated by the counterintuitive results brought forth by the logical operation of strengthening the antecedent cannot remain unmentioned in a chapter about logical approaches to conditionals. These are the non-monotonic logics or logics for defeasible argumentation. The concept of defeasibility was first introduced by Hart, who worked in the field of legal philosophy (Prakken&Vreeswijk 2001: 229). He noted that in law, a case is not closed if the plaintiff can show that all conditions mentioned in the antecedent of the rule of law are met. The other party can acknowledge all the facts that the plaintiff came up with, and still argue that the conclusion drawn by the plaintiff must be rejected. In a similar man-ner, the conclusion drawn by a judge can be reversed by a higher court. Logical conclusions drawn in a judicial context are not definite but only tentative. Conclusions are drawn tentatively not only in judicial contexts but in everyday contexts as well. For instance, a person about to meet his

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friends and confronted with the fact that their car is not on the drive-way, might conclude from this that his friends are out and drive on. But if he comes to learn that the car is being serviced, he will retract his conclusion and ring their doorbell after all.20

Standard logic cannot deal with this kind of reasoning. In standard propositional logic a conclusion once reached on the basis of particu-lar premises remains true, irrespective of other premises that might be added. This makes standard propositional logic monotonic: it’s (deductively valid) inferences never can be undone by new informa-tion. This characteristic of logical reasoning is reflected in the logical operation called ‘strenghtening the antecedent’: from ‘A→C’ one can deduce ‘(A∧B) → C’. Strenghtening the antecedent seems to be invalid in the ‘car-not-on-the-driveway’-example. The original conditional ‘If the car is not on the driveway (A), my friends are out (C)’ cannot be expanded to ‘If the car is not on the driveway (A) and the car is being serviced (B), my friends are out (C)’; the new information makes it necessary to retract the original conclusion C. Inferences corresponding to conditionals like these are non-monotonic and various non-monotonic logics are devised to handle them.21

One way to formalize inferences with tentative conclusions is to reinterpret the conditional used in this type of reasoning. Whereas in monotonic logic the truth of the antecedent of a conditional guaran-tees the truth of the consequent, in non-monotonic logics no such gu-arantee is given. The conditional is qualified: if the antecedent holds, normally the consequent holds as well. Such a defeasible conditional is called a default: when there are no exceptional circumstances, the consequent can be derived. On the other hand, if at a later stage one can show that exceptional circumstances obtained, the consequent may have to be retracted. The default character of conditionals can be formalized in different ways. One possibility is to add an extra ‘normality’ condition to the antecedent of the conditional. Instead of ‘If their car is not on the driveway, my friends are out’ the conditional reads ‘If their car is not on the driveway and there is no abnormal situation with respect to the car, my friends are out’. The car being serviced would count as

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20 See for an elaborate non-judicial example Prakken & Vreeswijk 2001: 219-221.

21 For a clear and insightful overview of different systems for defeasible reaso-ning see Prakken & Vreeswijk 2001.

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an abnormal situation, and therefore in that case the consequent ‘my friends are out’ cannot be derived.22 Another possibility would be to re-interpret the meaning of the conditional operator. According to these accounts – that resemble possible world semantics – default conditio-nals are taken to mean something like ‘In all most normal worlds in which p holds, q holds as well.’ The world in which the car is serviced would not count as a ‘most normal world’ and therefore the truth of ‘my friends are out’ is not guaranteed. But one does not have to reinterpret the conditionals in first order logic as defeasible conditionals in order to handle non-monotonic inferences. In some systems of non-monotonic reasoning the logical language is expanded in such a way that the expression of ‘defeasible generalizations’ or rules of thumb is made possible. The conditional connective is only used for non-defeasible inferences, hence it need not be adjusted or reinterpreted. The sentence ‘If the car is being serviced, then the car is not on the driveway’ can therefore be expres-sed as an ‘ordinary’ non-defeasible conditional (since no exceptions to this rule are possible), whereas the sentence ‘If the car is not on the driveway, my friends are out’ is expressed in a new vocabulary.23

A fourth and final way to deal with non-monotonic reasoning is to comprehend defeasibility as a characteristic not of conditionals but of the arguments in which these conditionals occur. In order for defeasi-bility to emerge there must be a conflict between two arguments. ‘My friends are out, because their car is not on the driveway’ is for instance in conflict with the argument ‘My friends are in, because I just saw John through the window’, since the conclusions cannot both be true. In situations like this, an argument is defeated when one argument is preferred over the other (i.e. when direct proof ‘I saw him’ is preferred over indirect proof ‘their car is not on the driveway’. In a similar fa-shion, the statement ‘their car is being serviced’ defeats the argument in support of the conclusion that the friends are out. In the original argument, one infers from the effect (the car is not on the driveway) the occurrence of the cause (my friends are out). ‘Their car is being serviced’ successfully undercuts this inference by supplying an alter-

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22 Systems that make use of an additional condition in the antecedent of the conditional are in fact somewhat more complex: apart from the extra condition, an assumption is added that the situation is normal when there is no evidence to the contrary.

23 An example of such a theory is Reiter’s ‘Default logic’ (1980).

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native cause for the absence of the car.24 The defeasibility of arguments is captured in various logics for defeasible argumentation. Such logical systems consist not only of a logical language, but also define what an argument is, what it means to have a conflict between arguments and under what circumstances an argument can be said to have defeated another. Furthermore, such logical systems give a definition of the status of arguments, for only when arguments are placed in a hierarchy, can one decide which of the two competing arguments defeats the other.25

An important difference between logics for defeasible argumentation and propositional logic or possible world semantics is that logics for defeasible argumentation are not concerned with the truth or falsity of propositions. Instead, they are aimed at specifying under what circum-stances it is justified to accept a proposition as true. Conditionals that form part of an argument are therefore not defined with reference to the circumstances under which they are true but are subjected to the same criteria as other, non-conditional propositions: they are justified when not undercut or defeated.

2.4 Conclusion

One way of evaluating conditionals is to see whether a conditional is true according to the definition of material implication: when the an-tecedent is true and the consequent is false, the conditional is false; in all other situations it is true. Many authors have pointed out that this definition creates several problems when applied to ordinary conditio-nals. This chapter contains a discussion of these problems, as well as a discussion of logical theories that offer ways to solve them.26 I short, one can discern two ways of handling this matter. Either one retains the definition of material implication and tries to explain away

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24 An argument that defeats another argument and leads to the opposite conclusion is called a ‘rebuttal’. The original conclusion is rejected and the opposite conclusion is taken to be true. ‘The car is being serviced’ is said to ‘undercut’ the original argument. The argument is rejected but the truth of the conclusion still remains undecided (Prakken&Vreeswijk 2001: 231).

25 Consult for an overview of systems of defeasible argumentation, Prakken & Vreeswijk (2001: 230)

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the difficulties that arise, or one rejects this definition and replaces it by one that does not give rise to these difficulties. An author following the first strategy is Nieuwint. He argues that the failure of the hypothe-tical syllogism in 12 is not caused by a flaw in the definition of material implication, but rather results from neglecting the ‘ceteris paribus’-condition:

12 If Brown wins the election, Smith will retire to private life. If Smith dies before the election, Brown will win it. So if Smith dies before the election, Smith will retire to private life.

According to Nieuwint, the Brown that won in the first sentence took part in elections in which Smith took part as well, while the Brown in the second sentence didn’t. As a result, the the proposition ‘Brown wins the election’ that is expressed in the antecedent of the first condi-tional sentence is not the same as the one expressed in the consequent of the second conditional (1992: 195). That contraposition fails for a sentence like ‘If you are thirsty, there is beer in the fridge’ Nieuwint ex-plains by pointing out that the consequent ‘there is beer in the fridge’ is not the ‘real consequent’. The sentence is elliptical and should read ‘you will be interested to hear that there is beer in the fridge’. Contra-position would then yield ‘If you are not interested to hear that there is beer in the fridge, you are not thirsty’, which is unproblematic. Although Nieuwint manages to give explanations for common counter-examples to the definition of material implication, these are ad hoc and not always fortunate. Adding a ceteris paribus-condition to the antecedent of conditionals means for instance that modus tollendo tol-lens becomes more complicated. From a mere denial of the consequent one cannot deduce denial of the antecedent, since it could just as well be that the ceteris paribus-condition is not met. 27 Nieuwint’s explana-tion for the failure of contraposition makes sense as it stands, but it is not clear why in this example the consequent is elliptical and in others it isn’t. Where Nieuwint explains the difference between theory and practice in a rather unsystematic way, others take a more systematic approach. Just like Nieuwint, Grice sees the definition of material implication as

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26 Not all logical theories try to explain conditional sentences: relevance logic is for instance not so much occupied with the if-then connective as with formalizing what it means ‘to imply’.

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the correct description of the meaning of conditionals. Extra features added to ordinary conditionals, like the connection between the antece-dent and consequent, are not a part of the meaning of conditionals, but are conversational implicatures. They are a result of the way in which conditionals are commonly used. Grice uses his theory of conversation to explain how such conversational implicatures can come about. The failure of contraposition, strengthening the antecedent and hypothe-tical syllogism for ordinary conditionals might be explainable in a similar way.

By far the largest part of this chapter is dedicated to authors that fol-low not the first but the second path: they dispose of the definition of material implication altogether and replace it with a new one. All these theories are based on the assumption that the evaluation criteria offered by the definition of material implication are inadequate. New evaluation criteria are proposed and it is shown that the problematic cases are questionable because they fail to meet these new criteria. Unfortunately, the solutions offered suffer from problems of their own. In replacing material implication with strict implication, C.L. Lewis found a solution for the paradoxes of material implication, but his solution itself gave rise to the paradoxes of strict implication. Furthermore, modal logic does not provide an explanation for the strange outcomes that may occur when the logical operations of con-traposition, hypothetical syllogism and strengthening the antecedent are applied to ordinary conditionals. Relevance logic circumvents the paradoxes of strict implication by adding an extra ‘relevance-criterion’, but in the system devised to accommodate this, the inference ‘If A or B and not-A, so B’, which up to this point remained unproblematic, has to be rejected as well (Anderson & Belnap 1975: 165). Conditional logics like probability theory and possible world seman-tics for counterfactuals are designed in such a way that contraposition, hypothetical syllogism and strengthening the antecedent can not be proved within the logical system. However, the explanations provided by these theories give rise to new difficulties. Possible world seman-tics has to address the difficult question of the relative closeness of worlds,which has not been satisfactorily answered. Probability theory solves the problems at the very high cost of abandoning the idea that

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27 If one does deduce the denial of the antecedent, one is guilty of the fallacy of treating a non cause as a cause (Hamblin 1970:78).

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conditionals can be either true or false. As a result, probability theory works for simple conditional constructions but falls short when ap-plied to compounds with conditionals (Gibbard 1980: 213). Further-more, probability theory cannot be used to evaluate counterfactuals. Finally, the various non-monotonic logics have their own difficulties. For instance, if the default character of conditionals is formalized by adding an extra ‘normality’ condition to the antecedent of the condi-tional, one runs into the same problem as Nieuwint: such conditionals cannot be used in simple applications of modus tollendo tollens, since one may not be able decide whether it is the condition expressed in the antecedent or the normality condition that is not met. When defeasi-bility is conceived as a characteristic of not the conditionals but of the arguments in which these conditionals occur, it becomes unclear as to how the possible strange outcomes in the case of the logical operation of strenghtening the antecedent can be explained. To be sure, from the conflict between ‘My friends are out, because their car is not on the driveway’ and ‘My friends are in, because I just saw John through the window’ it follows that one should decide which argument is to be preferred. But this does not explain why ‘If their car is not on the driveway, then my friends are out’ cannot be strengthened to ‘If their car is not on the driveway and I just saw John through the window, then my friends are out’.

One could conclude that the difficulties associated with these different approaches to the evaluation of conditionals are only minor, and will be solved through further investigation. However, this way of per-ceiving the problems of the truth functional definition has a distinct disadvantage. By disposing of the definition of material implication on grounds of inadequacy, one might run the risk of disposing of some-thing valuable. As was mentioned in the introduction, the definition of material implication forms a connection between the logical truth of a conditional sentence and the validity of an argument. Although the validity of arguments could be established in a different way, perhaps one should not forfeit this approach. Furthermore, does one want to be rid of the logical operations of contraposition, hypothetical syllogism and strengthening the ante-cedent? While these logical operations do fail when applied to some ordinary conditionals, they are appropriate when applied to others. Take sentence 20:

20 If the bottle of olive oil is leaking, you have not closed it properly.

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Contraposition yields ‘If you have closed the bottle of olive oil pro-perly, it is not leaking’, a statement which makes perfect sense. If sentence 20 is combined with ‘If the bag is greasy, the bottle of olive oil is leaking’, the conclusion of this hypothetical syllogism would be ‘If the bag is greasy, you have not closed the bottle of olive oil properly’, which is unproblematic as well. Finally, one could devise examples of antecedent strengthening that pose no problem, such as ‘If the bottle of olive oil is leaking, and you are the one that put it in the bag, you have not closed it properly.28

Not only are these logical operations acceptable when applied to ordi-nary conditionals, they also retain their value when they are discerned mainly as patterns of reasoning. If A implies B, and B implies C, then the conclusion that A implies C seems inevitable; hypothetical syllogism indeed makes sense. The same conclusion can be drawn for contraposition: when B holds if A holds (if ‘If A, then B’ is true), then not-B indeed must mean that not-A; exactly what we are informed by contraposition. Finally, a similar plea could be made for strengthening the antecedent. If one really thinks that B holds if A holds, one might be committed to the statement that it does so under all circumstances, i.e. whatever circumstance added to the antecedent, it will not affect the consequent. If the reasons given above are convincing regarding the value of the definition of material implication and the logical operations related to it, perhaps we should not dispose of it too hastily. That leaves us in

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28 One could say that in this example strengthening the antecedent is unproble-matic because the proposition added to the antecedent can be interpreted as having influence on the truth / falsity of the consequent. Examples where this is not the case are possible as well, as can be witnessed from the following dialogue:

A: You haven’t closed the bottle of olive oil properly.

B: What do you mean?

A: It is leaking

B: You put it in the bag

A: If the bottle of olive oil is leaking, you have not closed it properly,

whether I put it in the bag or not.

This last sentence can be rewritten as ‘If the bottle of olive oil is leaking and I put it in the bag, you have not closed it properly and if the bottle of olive oil is leaking and I didn’t put it in the bag, you have not closed it properly’.

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the following situation: on the one hand we have a group of conditio-nal sentences to which the application of the definition of material implication together with the logical operations yields undesirable outcomes. At this point we have no satisfactory approach which would remove these undesirable outcomes. On the other hand, we have a definition that we don’t want to give up. We appear to be in deadlock. Fortunately, there is a way out. As we have seen, the definition of material implication is not problematic for all ordinary conditionals. Why not restrict the truth functional definition to the unproblematic cases? We could then maintain this definition and have one group of conditionals for which evaluation criteria are formulated. Fur-thermore, we will no longer be bothered by problematic cases, since ‘problematic conditionals’ are not subjected to the evaluation criteria provided by the definition of material implication. The solution appears to be rather simple, but difficulties remain that must be overcome. First of all, dividing conditional sentences into two categories – ones to which the definition of material implication is applicable and ones to which it is not – means we have to give up the idea of a unified theory for all conditional sentences. Secondly, we shall have to find a means to discriminate between these two kinds of conditionals. Only then can we decide whether a particular conditional sentence belongs either to the first or the second category. Finally, the decision that the definition of material implication is not applicable to conditionals belonging to the second category means that, for now, this category is deprived of evaluation criteria. If we want to evaluate all argumentatively used conditionals, we shall have to find out what evaluation criteria could be used for conditionals in this second cate-gory. Giving up the idea of a unified theory of conditionals is something that has been already proposed by some logicians. D. Lewis (1973) for instance has argued that indicative and subjunctive conditionals need different accounts. Also Gibbard argues that one should differentiate between two types of conditionals: epistemic and nearness conditio-nals. He argues that possible world semantics is concerned with the former while probability theory refers to the latter (1980: 211). The step to differentiate between various types of conditionals is easily made. But a fundamental question remains: how can we differentiate between conditionals in an easy and univocal way?

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3 Classifications of conditionals

3.1 Introduction

Whereas abandoning the search for an unified theory is rather uncom-mon amongst logicians, many linguists never even were concerned with the development of an unified approach. To the contrary, as Dan-cygier puts it in Conditionals and Prediction:

‘One solution fits all’ kind of approaches are not common amongst linguists, because a linguistic analysis cannot fail to notice the sig-nificant differences between types of conditionals (1998: 4).

For instance, most authors differentiate between the following three conditional sentences:

21 If it rains, Charley’s birthday party will be cancelled.

22 If it had rained, Charley’s birthday party would have beencancelled.

23 If you feel like coming, you are invited to Charley’s birthdayparty.

Sentences 21 and 23 are considered to be different from sentence 22 since the ‘knowledge status’ of their antecedent differs.29 In 21 the question ‘will it rain or not’ remains open: the conditional sentence does not give any indication of truth or falsity, or the degree of proba-bility of the antecedent. The sentence can be read as ‘Should it be the case that it rains – which it may or may not – then the birthday party

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29 The term ‘knowledge status of the antecedent’ is used in The Encyclopedia Brittanica to differentiate between three types of conditionals. ‘The knowledge sta-tus of this antecedent (...) may be problematic (unknown), or known-to-be-true, or known-to-be-false. In these three cases, one obtains, respectively (a) the problematic conditional: ‘should it be the case that p – which it may or may not be –, then q’; (b) the factual conditional: ‘Since p, then q.’ and (c) the counterfactual conditional: ‘If it were the case that p – which it is not –, then q would be the case’ (1998, vol 23: 260, 2nd column).”

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will be cancelled’. Similarly, in 23 the question whether the listener‘-feels like coming or not’ is left open. In 22 however, the situation des-cribed in the antecedent is presented as contrary-to-fact. This sentence reads most naturally as ‘If it had been the case that it rained – which it did not – then the birthday party would have been cancelled.’ Sentence 23 is seen as different from 21 and 22 because of a differen-ce in the status of their consequent. In 21 and 22 the truth / fulfilment of the consequent seems to be dependent on the truth / fulfilment of the antecedent. Whether the birthday party is cancelled is dependent on the weather conditions: rain leads to cancellation.30 In 23 the con-sequent is independent of the condition described in the antecedent: whether the listener feels like coming or not, he is invited.31

These and other differences between conditional sentences have given rise to various classifications. The proposed classifications differ in many respects. First of all, there is a big difference in the number of classes discerned: some authors have delineated only two classes of conditionals, others as many as six. Secondly and more importantly, the criteria used in differentiating between classes vary considerably. Some authors take as a starting point the linguistic characteristics of the different conditional sentences. Dancygier (1998) for instance makes a distinction between predictive and non-predictive conditionals on the basis of the linguistic phenomenon of ‘backshift’. She considers 21 and 22 to belong to the same category of predictive conditionals since in both antecedents the time indicated by the verb that is used is ‘backshifted’ from the time the sentence refers to. In 21 the present tense is used although the birthday party will take place in the fu-ture, in 22 the past perfect is used although there is no reference to a pre-past situation. The verb in the antecedent of 23 is not backshifted, therefore this conditional belongs to the class of non-predictive condi-tionals. Other classifications do not take linguistic characteristics into account but rather characteristics of the content of the conditional sentence. Nieuwint (1992) for instance differentiates between condi-

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30 In these examples some authors feel justified in concluding that the birthday party will not be cancelled if it doesn’t rain. The conditional is interpreted as a biconditional: ‘If p, q and if not-p, not-q’. This phenomenon is commonly called ‘conditional perfection’.

31 Sentences like 23 are sometimes called ‘Austin’s conditionals’, since Austin was the first to focus on this kind of conditional.

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tionals on the basis of the type of connection that exists between the antecedent and the consequent. This connection can be free – as in 24 – or unfree – as in 25 and 26:

24 If you do the dishes tonight, I will do them tomorrow.

25 If the ball hits the window, the window breaks.

26 If 6 x 5 = 30, then 30 / 5 = 6.

In these examples, there are no linguistic clues for deciding what kind of connection is expressed in a specific conditional sentence. Know-ledge of the world is needed to decide whether the connection is free (when the antecedent is fulfilled, it is up to the speaker whether the situation described in the consequent will occur) or unfree (the occur-rence of the consequent is independent of the speaker) (1992:141). No matter how different the various proposed classifications may be, they do indeed have some things in common as well. First of all, in all of the classifications something is said about the status of the proposi-tion expressed in the antecedent, i.e. conditionals like 21 and 22 are put into different categories since the ‘epistemic status’ of the antecedent differs in these cases.32

Secondly, it is generally accepted that in conditional sentences the antecedent and the consequent are somehow connected. These two characteristics are taken in this chapter as a starting point for the discussion of several classifications of conditional sentences: the dif-ference in status of the antecedent is discussed in 3.2 and the type of connection between the antecedent and the consequent in 3.3.

3.2 Degrees of hypotheticality

The first characteristic that most authors who are envolved with the classification of conditionals consider to be basic, is the degree of hypotheticality that can be expressed in the antecedent of a conditional sentence.

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32 Eventually, Dancygier differentiates between 21 and 22 as well. Within the category of ‘predictive conditionals’ she distinguishes conditionals (sentences like 21) and – weak or strong – hypotheticals (sentences like 22).

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The degree of hypotheticality can be seen as the relationship between the propositions expressed in the antecedent (and the consequent) of a conditional sentence and a state of affairs in ‘the world’. According to Johnson-Laird, three major classes of states of affairs can be discerned: actual states, real possibilities and hypothetical states (1986:65). One would then expect that these three classes of states of affairs could give rise to three types of conditional sentences, namely sentences like 27, 21 and 22:

27 Tom: I’m leaving now Harry: If you’re leaving now, I won’t be able to come with you.33

21 ’If it rains, Charley’s birthday party will be cancelled.

22 If it had rained, Charley’s birthday party would have beencancelled.

In 27, the antecedent refers to an actual state, since Tom has just an-nounced that he is leaving now. In 21 the antecedent refers to a real possibility: at the moment of speech, it is not known whether it will rain or not and there is a real chance that it will. In 22 the antecedent refers to a hypothetical state. Apparently, it didn’t rain, and in this sentence one ponders upon the hypothetical situation in which things would have been different. In the literature on conditionals a division in ‘actual’, ‘possible’ and ‘hypothetical’ conditional sentences is not at all common.34 Sentences like 27 remain largely undiscussed. Even Johnson-Laird himself does not formulate a class of ‘actual’ conditionals, judging contingent asser-

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33 Example given by Comrie (1986: 79).

34 Dangygier discusses ‘traditional philosophical approaches’ that make a dis-tinction between ‘realis’, ‘potentialis’ and ‘irrealis’ (1998: 29). This division seems to coincide with actual states, real possibilities and hypothetical states, but this coincidence is only apparent. The terms realis, potentialis and irrealis do not refer to states of affairs in the world, but to the speaker’s expectation as to the fulfilment of the condition expressed in the antecedent. The speaker can express no opinion towards fulfilment, as in ‘If two times two makes four, then two is an even number’ (realis), he can express that fulfilment is impossible, as in ‘If it rained, the match would be cancelled’ and ‘If it had rained, the match would have been cancelled’ (ir-realis) or he can express that fulfilment is possible, as in ‘If it rains, the match will be cancelled’ (potentialis) (1998: 29).

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tions to be the only type of sentence referring to an actual state (1986: 65). Others who are involved in this kind of analysis do acknowledge that in some conditionals the antecedent contains a proposition that is ‘actual’ and discern a class of factual conditionals consisting of senten-ces that can be paraphrased as ‘since p, then q’ (Encyclopedia Brit-tanica 2000: 260:2). Yet other authors have argued that conditionals with an ‘actual’ antecedent are in fact no conditionals after all. Bennett for instance made the following remark on conditionals such as 27:

When my colleague hears me say that I have applied for leave, he may say ‘If you have applied, I am going to apply too’. This is not a conditional, either. My colleague means ‘Because you have applied, I am going to apply’, and he uses ‘if’ because he is still digesting the news about my application (2003:5).

Whereas actual conditionals are not generally acknowledged, it is more common to make a distinction between possible and hypothe-tical conditionals. One could even say that the traditional ‘standard division’ is one between sentences 21 and 22. Sentences like 21, expres-sing a real possibility, have been called indicative, open,or real condi-tionals as opposed to subjunctive, closed, hypothetical or counterfactual conditionals like 22, where the antecedent refers to a hypothetical state. The terminological differences reflect differences in focus: the terms ‘indicative’ and ‘subjunctive’ refer to grammatical categories, the other notions refer to a relationship between the propositions expressed in the conditional clauses and the actual state of affairs in the world. Furthermore, they reflect a difference of opinion about the meaning of conditional sentences. A term like ‘counterfactual’ implies that ‘it didn’t rain’ is part of the meaning of sentence 22 whereas a term like ‘closed’ does not have this implication.

Although the division between sentences 21 and 22 is commonly called the standard division, it is not acknowledged by all authors on conditionals. Comrie (1986) for instance questions whether there exists such a clear-cut distinction between open and closed conditio-nals or between real and hypothetical or counterfactual conditionals. He proposes that hypotheticality should be seen on a continuum: sentences can express a higher or lower degree of hypotheticality. He defines ‘hypotheticality’ as ‘the degree of probability of realization of the situations referred to in the conditional, and more especially in the protasis [antecedent–jmg] (1986: 88)’. The lower the probability, the

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higher the hypotheticality and vice versa. The degree of hypotheticality can therefore vary from very low (in a factual statement) to very high (in a counterfactual one).

Whereas Comrie explicitly distances himself from the standard divi-sion, other authors have been less explicit in rejecting it. By speaking of ‘open’ and ‘closed’ conditionals, Funk (1985) for example, seems to comply with the distinction commonly made. However, a closer look reveals that he does deviate from the standard division since he uses the terms ‘open’ and ‘closed’ in a rather different way. Funk claims a speaker uses a conditional when it is uncertain as to whether the situation sketched in the antecedent holds. In that sense, sentences 28 and 29 have something in common:

28 If he submitted his paper to a journal, we won’t include it in our book.

29 If he submits his paper to a journal, we won’t include it in our book.

According to Funk, both in 28 and 29 the situation sketched in the antecedent is presented as uncertain: from these sentences one cannot tell whether the paper is / will be submitted to a journal. But senten-ces 28 and 29 differ as well, since the uncertainty comes from different sources. As Funk puts it:

In the case of (4) [29 – jmg] the uncertainty is largely due to the fact that the state-of-affairs described and predicated, does not yet exist, i.e. is still subject to manifestation (so that it cannot be affirmed or denied – it is unverifiable) at the moment of the sentence being uttered. In (1) [28 – jmg] however, the state-of-affairs does exist at the time of speaking (either in the positive or negative sense – it is manifested and could thus be verified), but the speaker does not have enough information (or is otherwise not disposed) to be sure about it and hence to affirm or deny it (1985: 375-376).

In 29, the uncertainty is objective: ‘he’ may or may not submit his paper to a journal; we don’t know what he will do. The state of affairs depicted in the antecedent did not yet manifest itself and as a result is not yet verifiable. In 28, the uncertainty is subjective. The relevant state of affairs is manifested. That the question as to whether ‘he’ did or did

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not submit his paper to a journal cannot be answered, is due to lack of knowledge. The difference between 28 and 29 is illustrated by Funk where he shows that 28 should be paraphrased as ‘If it is true that he submitted the paper to a journal’, whereas 29 should be paraphrased as ‘If it happens that he submits the paper to a journal’. Funk uses the term ‘closed’ for sentences like 28 and the term ‘open’ for sentences like 29. Reasoning along these same lines, Funk would consider 30 to be a closed conditional as well:

30 If it is raining, we won’t go to the playground.

Funk would paraphrase 30 as ‘If it is true that it is raining, we won’t go to the playground’ because, after all, the situation depicted in the antecedent can be verified. He therefore does break with the standard division, whereby a conditional like 30 would be classified not as a closed but as an open (indicative) conditional.

An author that explicitly and strongly opposes the standard division between indicative and subjunctive conditionals is Dudman.35 He argues that this distinction is not only mistaken, but complicates the discussion of if-sentences and as a consequence has steered especially logicians to positions that are untenable from a grammatical point of view. First of all, Dudman points out that it is wrong to confine the dis-cussion of if-sentences to sentences. One should rather be concerned with the messages those sentences express. Dudman uses examples 31 and 32 to make his point clear (1988: 1)36:

31 If she misses the last bus, the countess will walk home.

32 If she missed the last bus, the countess would walk home.

Sentences 31 and 32 can receive two different interpretations: they are interpreted either as generalisations (..’she will / would often walk home) or as particular claims about the future (if she misses / missed

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35 Dudman has written several articles in which he formulates his criticism on the standard division in theories on conditionals.

36 The pagenumbers in the references to Dudman refer to the pages of the actual article, not to the pagenumbers of the journals in which these articles were published.

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the bus this evening...). Dudman calls these different interpretations messages and claims that a theory of if-sentences should be aimed at such messages (1989: 1). As a result, instead of merely being concerned with 31 and 32, we should rather direct our attention to messages 31a-32b:

31a If she misses the bus, the countess will often walk home.

31b If she misses the bus this evening, the countess will walk home.

32a If she missed the bus, the countess would often walk home.

32b If she missed the bus this evening, the countess would walkhome.

The question then arises as to how those messages are classified ac-cording to the standard distinction between indicative and subjunctive conditionals. According to Dudman, logicians tend to place the gene-ralisations 31a and 32a together with a particular claim about the future 31b in one class: that of indicative conditionals. The particular claim about the future 32b is put in the class of subjunctives. Although the way in which the messages are placed into the diffe-rent classes is already peculiar, according to Dudman matters become even more enigmatic when other members of the class of indicative conditionals are taken into account. In the standard division, 33 and 34 would be part of the class of indicative conditionals as well:

33 If Socrates is a man, Socrates is mortal.

34 If Tom is fat, his sister is immense.

Dudman claims that from a grammatical point of view, this classificati-on could not be more mistaken. He argues that 31a and 32a differ from 31b which in turn differs from 33, whereas 34 differs from all sentences mentioned earlier. As a result, Dudman rejects the standard division. According to Dudman, the study of if-sentences would greatly benefit if the standard classification is replaced by a classification based on the way if-sentences are generated grammatically. Dudman discerns four categories, because in English, if-sentences can be generated in basically four different ways: compounds, like 33, habituals, like 31a and 32a, conditionals, like 31b and 32b and a remaining category which he

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calls ‘totally egregious if-sentences’, like 34 (1989: 9). Compounds, the first category of if-sentences, are formed from two prior messages. The compound 33 is for instance composed of the independent sentence ‘Socrates is mortal’ and what Dudman calls a ‘subsidiary string’ ‘If Socrates is a man’. This subsidiary string is in turn composed of the conjunction ‘if’ and the dependent sentence ‘Socrates is a man’.37 When ‘if’ is prefixed to a sentence, the message expressed receives the status of an hypothesis: it is announced that it is being treated as true or accepted, regardless of whether it actually is. Adding a subsidiary string containing ‘if’ to an independent message, signals that the independent sentence is ‘presumptively affirmed’: it is affirmed unless there is rational reason to believe otherwise (1991: 227). A speaker can have different reasons for presumptively affirming an independent sentence. In what Dudman calls ‘hypotheticals’ the ante-cedent is hypothesized so that the consequent can be concluded from it. The conditional in 33 is an example of a hypothetical:

33 If Socrates is a man, Socrates is mortal.

According to Dudman, hypotheticals are condensed arguments. The premise of the condensed argument in 33 is expressed in the depen-dent sentence ‘Socrates is a man’. Together with some further ground like ‘Men are generally mortal’, this premise justifies the conclusion that ‘Socrates is mortal’, which is expressed in the independent sen-tence (1986:15). A speaker can also decide to assert the independent sentence only presumptively when he is in doubt about either the propriety of it, or some detail of it, as in 35 and 36 (1989: 7).

35 If the Mayor is married, his wife did not accompany him.

36 The dog, if it was a dog, ran off

In 35, the speaker is in principle willing to commit himself to the as-sertion that the Mayor was not accompanied by his wife, for instance

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37 This analysis inspires Dudman to reject the traditional ‘ternary analysis’ of if-sentences, where an if-sentence is analysed as being built up from three compo-nents: the antecedent, the consequent and a ‘binary connective’ (‘if’) (1986: 3).

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on the ground that the Mayor was not accompanied by any woman, be it that he is not quite sure whether the Mayor is married and hence whether the phrase ‘his wife’ refers to anything. In order to confirm the message expressed in the independent sentence, he adds a subsi-diary string to it in which the presupposition is explicitly taken to be true. In 36 the speaker asserts the independent sentence only presump-tively because he is in doubt about some detail. Whatever reason a speaker has for asserting the independent sen-tence presumptively, the ‘if’-sentence that results, consists of two prior messages. In that sense, compounds differ from the second category of ‘if’-sentences that Dudman discerns: the category of ‘habituals’. This category contains ‘messages’ 31a and 32a as well as 37:

31a If she misses the bus, the countess will often walk home.

32a If she missed the bus, the countess would often walk home.

37 If she missed the bus, the countess often walked home.

Dudman argues that in habituals, ‘if’ is not prefixed to a sentence, but must be seen as the first word of a subordinate clause (1988:3). In that respect ‘if she misses the last bus’ is similar to ‘on Wednesdays’ in 38:

38 On Wednesdays the Countess walked home.

A sentence like 38 is analysed as a subject-predicate sentence where ‘the countess’ is the subject and ‘walked home on Wednesdays’ the (complex) predicate. Sentences 31a, 32a, and 37 must be analysed in the same way. In those sentences ‘the countess’ is the subject and ‘will often walk home if she misses the bus’, ‘would often walk home if she missed the bus’ and ‘often walked home if she missed the bus’ are the complex predicates respectively. Conditionals, the third category of ‘if’-sentences Dudman discerns, resemble habituals in that they also are not composed of two prior messages. Examples of conditionals are 31b and 32b:

31b If she misses the bus this evening, the countess will walk home.

32b If she missed the bus this evening, the countess would walk home.

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Conditionals are subject-predicate sentences with a rather elaborate and complex predicate as well. In sentences 31b and 32b, the subject is ‘the countess’ and the predicates are ‘will walk home if she mis-ses the bus this evening’ and ‘would walk home if she missed the bus this evening’ respectively. The difference between habituals and conditionals is that in habituals the ‘if’-clause governs the verb phrase, whereas in conditionals the ‘if’-clause governs the modal ‘will / would’ (1988:5). It is characteristic for the third category, that the time registered in the message is always later than the time registered by the form of the verb. In 31b for instance, the present tense is used, whereas the mes-sage refers to a situation in the future. In 32b this gap is even wider: the message still refers to a situation in the future while the past tense is used. Dudman explains this phenomenon by pointing out that conditionals express “judgements arrived at by imaginatively thinking futurewards from historical realities of some time whose location as present, past or past past is registred by the form”(1988: 7). What he means by this can be illustrated by comparing sentences 39 and 40:

39 If the auditors come tomorrow, they will find our books inperfect order.

40 If the auditors had come tomorrow, they would have found ourbooks in perfect order.

In 39 the imagined developments start at the moment of speech (hence the present tense). In 40 the imagined developments start at a time before the auditors came for their surprise visit. In this way, the speaker can set aside this historical fact and ‘imaginatively think futurewards’ how things could have been different. The fourth and final category of ‘if’-sentences seems to be brought up by Dudman for completeness’ sake only. This category of what Dudman calls ‘totally egregious if-sentences’ bears a great deal of simi-larity to the first category of compounds, since ‘if’-sentences in this category also are composed of two prior messages. Sentence 34 is for instance composed of an independent sentence ‘His sister is immen-se’ and a dependent sentence ‘Tom is fat’.

34 If Tom is fat, his sister is immense.

Still, sentences like (34) differ from compounds. Whereas in com-

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pounds the speaker can choose to change the order of the indepen-dent and dependent sentence, in conditionals belonging to the fourth category this is not possible. It is perfectly acceptable to say ‘Socrates is mortal, if he is a man’, but one cannot say ‘Tom’s sister is immense, if he is fat.’ In ‘if’-sentences like 34 the dependent sentence necessarily precedes the independent sentence and that is why Dudman assigns a separate category to them.

Finally, yet another author who has challenged the standard division between indicatives and subjunctive conditionals is Dancygier. Like Dudman, Dancygier is of the opinion that in the standard distinction, conditionals are grouped together that do not belong together, while simultaneously conditionals are put in different categories when they should be in the same. To illustrate her point, Dancygier uses the fol-lowing examples (1998:25):

41 If it rains, the match will be cancelled.

42 If it rained , the match would be cancelled.

43 If it had rained, the match would have been cancelled.

In the standard division, 42 and 43 are grouped together on the basis that both sentences signal – by means of the subjunctive mood – that the speaker does not want to commit himself to the propositions expressed. In 41 no such message is signalled, therefore 41 does belong to a different class. According to Dancygier, all verb forms – including indicative forms – do contribute to the interpretation of the conditional construction. She argues that 41, 42 and 43 do belong to the same class, since in all three sentences the tense of the verb used in the antecedent does not coincide with the time actually referred to. In 41 the present tense is used to refer to the future, in 42 the past tense is used to refer to either the present or the future and in 43 the past perfect is used although there is no reference to a pre-past situation. As was already mentioned in section 3.1, Dancygier calls this phenomenon ‘backshift’ and takes its presence or absence as the main criterion in classifying if-senten-ces. Dancygier calls the class of if-sentences that contain backshift ‘pre-dictive’ conditionals, since they are used for making predictions about future situations. For Dancygier, a common feature of predictions

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– conditional or not – is that they cannot be judged true or false at the moment of utterance. Nevertheless, predictions can be very acceptable to the listener because they are rooted in reality. Having knowledge of certain facts and laws, the speaker can arrive at a conclusion that has not yet manifested itself. For instance, a speaker who knows that it rains and that the match will start in five minutes, and furthermore has knowledge of the regulation that the match would be cancelled in case of rain, has solid reason to predict that the match will be cancel-led (1998: 46). It is when a speaker lacks some of the knowledge needed for a well-founded prediction that predictive conditionals are of use. If the match does not take place in five minutes but tomorrow, the speaker cannot know whether it will rain or not. However, he still can pre-dict the match will be cancelled, as long as he signals to the listener that his prediction is based on an assumption for which there is no sound basis. The ‘if-clause’ is used to signal exactly this: the speaker distances himself from the truth of the assumption. Moreover, since the assumption is not predicted itself, the marker of prediction ‘will’ is eliminated, resulting in 41: ‘If it rains, the match will be cancelled’ (1998: 47). Dancygier argues that in this respect, 42 and 43 are like 41:

42 If it rained , the match would be cancelled.

43 If it had rained, the match would have been cancelled.

Although 42 and 43 are marked as hypothetical, the predictive state-ment remains the same: the antecedent does not contain a marker of prediction whereas the consequent does. For that reason, Dancygier classifies 42 and 43 together with 41 as predictive conditionals (1998: 50). While 42 and 43 both belong to the class of predictive conditionals, there is of course a difference between the status of their antecedents and that of the antecedent of sentence 41. Both 42 and 43 contain what Dancygier calls ‘hypothetical backshift’: the tense of the verb is backshifted (even further) so as to indicate that the speaker distances himself from the assumption expressed in the antecedent. Not only is this assumption unknown / unknowable, but furthermore, the spea-ker has evidence that it is very unlikely (in 42) or even contrary-to-fact (in 43).38 Both 42 and 43 are therefore not only predictive, but hypotheti-cal as well (1986: 40).

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Dancygier not only classifies conditionals together that according to the standard division should be in different categories, but she also distinghuishes between conditionals that in the standard division are classified together. For instance, 44 would in the standard division be classified together with 41, based on the indicative mood:

44 If Rudolph is in the lobby, the plane arrived early.

Since in 44 the tense of the verb coincides with the time actually referred to, it is not marked with a backshifted verb form. That is why Dancygier classifies 44 as a non-predictive conditional and groups it with sentences like 45 and 46:

45 If I may ask, where were you last night?

46 When did you last see my husband, if I can still call him that.

In comparison with the class of predictive conditionals, the class of non-predictive conditionals is far more varied. Predictive conditionals are iconic with respect to the sequence of events referred to: the event in the antecedent precedes the one in the consequent. For non-pre-dictive conditionals this need not be the case, as can be seen from 44: there the consequent describes an event that ‘in reality’ precedes the event described in the antecedent. Secondly, in predictive conditionals the unassertability of the assumption is event-based: by means of ‘if’ the speaker distances himself from the assertion of the assumption because it is not ‘kno-wable’ at the time of utterance. In non-predictive conditionals the speaker can have many different reasons to distance himself from the assumption expressed in the antecedent. In 47 for instance, the teacher holds her knowledge in abeyance for the sake of argument:

47 If two and two makes four, four is an even number.

The teacher knows that two and two makes four but she is ‘putting aside’ this knowledge to show her pupils how she arrives at the con-

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38 It is difficult to see how an assumption can be unknown / unknowable and contrary-to-fact at the same time: an assumption that is contrary-to-fact is known – it is known to be false.

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clusion that four is an even number’ (1998: 114). Finally, predictive and non-predictive conditionals differ in the kind of relation between the antecedent and consequent. For predictive con-ditionals there is always a causal relation between the two: the rain in the antecedent of 41 is the cause of the match being cancelled. In non-predictive conditionals the antecedent and consequent can be related to each other in many different ways, and Dancygiers subdivides this category on the basis of the type of connection that is expressed.

3.3 Types of connection between the antecedent and the consequent

A second characteristic of conditional sentences that is considered to be basic by most authors who classify conditionals, is the conception that natural language conditionals only make sense if antecedent and consequent are somehow related. A conditional sentence such as 48 seems to be unacceptable, although both antecedent and consequent could be true:

48 If Pete drives a red Jaguar, John has curly brown hair.

The reason for this is that apparently there is no connection between the state of affairs described in the antecedent and the one described in the consequent. However, one can think of contexts where 48 is an acceptable senten-ce. Suppose you are trying to solve a puzzle where characteristics have to be paired with characters. It turns out that the characteristic ‘curly brown hair’ is left to either Pete or John. Furthermore, the character driving a red Jaguar is known to have blond hair. In a context like this, 48 is a meaningful conditional sentence.39 When conditionals like 48 are contextualized, the relation between antecedent and consequent becomes apparent and therewith the conditional becomes an accepta-ble one. As Johnson-Laird puts it:

‘(...) we can make sense of certain conditionals only by bearing

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39 48 is also an acceptable conditional in a context where both speaker and listener know that John is bald. It then expresses the speaker’s disbelief in the proposition that Pete is driving a red Jaguar.

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in mind that they are invariably taken to mean that some sort of relation is intended to hold between antecedent and consequent’ (1986:67).

Given the assumption that antecedent and consequent in natural language conditionals are related, several authors have classified conditionals on the basis of the kind of connection that holds. As was mentioned earlier, Nieuwint makes a distinction between conditional sentences where the relation between antecedent and consequent is unfree and sentences where that relation is free. Causal and logical re-lations are unfree, whereas what Nieuwint calls ‘stochastic’ reasoning is free. He uses this distinction (among other things) to explain the dif-ference between the following two well known contrasting sentences, first discussed in Adams (1970):

49 If Oswald didn’t kill Kennedy, then someone else did.

50 If Oswald hadn’t killed Kennedy, then someone else would have.

In 49 the relation between antecedent and consequent is logical: it must be rewritten as ‘If Oswald didn’t call Kennedy, then it follows necessarily that someone else did’ (given the fact that Kennedy was kil-led). 50 on the contrary should be rewritten as ‘If Oswald hadn’t killed Kennedy, then I predict someone else would have.’ For 50, the fulfil-ment of the consequent is ‘up to the speaker’ (he might decide not to predict the murder), 50 is therefore an example of stochastic reasoning and not a subjunctive version of 49 (Nieuwint 1992: 142). Johnson-Laird makes a rather different distinction. He distinguishes between three different degrees of relation: the antecedent can deter-mine the state of affairs in the consequent completely, as in 51, partially, as in 52 or not at all, as in 53.40

51 If someone is in a room, that room is not empty.

52 If the accused was on a train when the murder occurred, then he must be innocent.

53 If you’ve run out of petrol, there’s a garage down the road.

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40 All examples are from Johnson-Laird 1986:69-71.

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In 51 the antecedent determines the state of affairs completely, since there is no state of affairs thinkable where the antecedent is true and the consequent isn’t. In 52 this is not the case. In order to claim what is said in 52, one has to acknowledge implicit assumptions of all kinds: the murder hasn’t occurred in the train but somewhere else, someone cannot be in two places at the same time, etc. The condition expressed in the antecedent has to be taken in conjunction with other informa-tion in order to arrive at the conclusion expressed in the consequent. In 53 the information conveyed in the antecedent is superfluous for the occurrence of the situation described in the consequent: whether the listener has run out of petrol or not, the garage is down the road. 41 According to Johnson-Laird, these three categories should be distin-guished since the truth conditions of a conditional sentence depend on the category this sentence belongs to. If the antecedent determines the state of affairs in the consequent completely, the sentence ‘if p, then q’ is true if and only if ‘q’ is true in any mental model of ‘p’. If the antecedent is superfluous for the situation described in the conse-quent, the conditional sentence is true whenever the consequent is. If the antecedent determines the state of affairs in the consequent only partially, the conditional lacks truth conditions. Since the condition in the antecedent has to be taken in conjunction with ‘other information’ and it is impossible to establish which other information must be ad-ded, the ‘real’ antecedent of such conditionals is always undetermined. It is therefore impossible to examine models in which the antecedent is true. Yet another distinction is made by Noordman (1977). In his expe-riments on psychological processes in understanding sentences and inferring from sentences, he finds different results for sentences with

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41 When applied to Johnson Laird’s examples, Nieuwint’s distinctions are less clear than they might appear to be at first glance. Clearly in example 51 the link between antecedent and consequent is logical and therefore unfree. Presumably, he would call the relation in 53 unfree as well. Nieuwint considers this sentence to be elliptical since the ‘real q’ reads something like “(If you’ve run out of petrol), then the information that there is a garage down the road will be of interest to you (1992: 107).” This ‘real q’ doesn’t seem to be ‘up to the speaker’. With 52 however, matters are less clear. On the one hand it looks like an unfree relation: from the information in the antecedent the consequent follows. On the other hand, this conditional could be interpreted as ‘If the accused was on the train when the murder occurred, then I consider him to be innocent.’ In that case it is up to the speaker to consider the accused innocent, which makes the relation ‘stochastic’ and therefore free.

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what he calls a ‘condition consequence relation’ between antecedent and consequent and those with an ‘inference relation’. 54 is an example of the first and 55 of the latter:42

54 If John is ill, he is not going to his work.

55 If John is not going to his work, he is ill.

The distinction Noordman makes, rests entirely on the distribution of the cognitive cause and effect over the two clauses of the conditional. In 54 the antecedent contains the cause and the consequent the effect. In 55 this relationship is reversed: the effect is mentioned in the if-clause and the cause is mentioned in the then-clause. This difference in distribution amounts to a different interpretation of the two sentences. According to Noordman, 54 expresses the fact that John’s being ill is a condition or cause for his not going to his work, whereas 55 expresses something like ‘From John’s not going to his work one may infer John’s illness.’ The difference Noordman notices between 54 and 55 is also discussed by Comrie, although Comrie arrives at a different conclusion. In his view, the antecedent always represents a cause for the effect described in the consequent, not only in sentences like 54 but in 56 and 57 as well.43

56 If it will amuse you, I’ll tell you a joke.

57 If I saw John stealing, he is a thief.

For 56 the causal relation seems to go in the opposite reaction: telling the joke is the cause of the listener’s being amused and not vice versa. But Comrie contends there is a causal relation from antecedent to consequent as well: the listener’s future amusement is the cause for the speaker’s telling a joke. For 57 something similar is the case. Although seeing John steal is not the cause of him being a thief, one can say that seeing John steal caused the speaker’s belief in John being a thief (1986:81).44

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42 Examples given by Noordman (1977: 105).

43 Example 56 is taken from Comrie and example 57 is an adapted example from Comrie (1986: 81).

44 Sentence 55 could be analysed similarly.

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One could argue that the meaning of ‘causal’ is inadmissibly stretched if interpreted in the way Comrie does. But in fact one of the more influential semantic theories on conditionals reflects a similar view on causality.45 In her book From Etymology to Pragmatics. Metaphorical and Cultural Aspects of Semantic Structure (1992), Sweetser claims that in all conditionals the if-then-construction expresses the same thing: the an-tecedent describes a sufficient condition for the consequent. However, the interpretation of the condition-consequence relation is dependent on the domain the conditional belongs to. Sweetser makes a distinction between the content domain, the epis-temic domain and the speech act domain. She considers the content domain to be the most basic. In that domain the if-then connective ex-presses a causal or enablement relationship between the state of affairs described in the antecedent and the one described in the consequent. An if-then connective used in one of the other domains is metapho-rical: it doesn’t express a causal or enablement connection between states of affairs in ‘the real world’. In the epistemic domain the con-nective connects epistemic states: the knowledge of the hypothetical premise in the antecedent causes the knowledge of the conclusion. In the speech-act domain the state described in the antecedent enables or causes the speech act in the consequent. An example of a conditional belonging to the content domain is sentence 58:46

58 If he is already gone, (then) they will have to leave a message.

According to Sweetser, in the most natural reading of this sentence the ‘real world’ situation in which ‘he’ is already gone is a sufficient condi-tion for the real world situation in which ‘they’ leave a message. If the content of the antecedent and the consequent are reversed – as in 59 – the sentence is not a content but a epistemic conditional:

59 If they have to leave a message, then he is gone already.

Sweetser argues that this sentence should be interpreted as ‘If I know that they have to leave a message, then I conclude that he is gone

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45 Of course there are a lot of dissimilarities between Comrie’s and Sweetser’s views as well, see for instance Sweetser 1992:122.

46 Examples 58, 59 and 60 are Sweetser’s (1992: 123, 118).

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already’ (1992: 116). Finally, an example of a conditional in the speech-act domain would be 60:

60 If I haven’t already asked you to do so, please sign the guestbook before you go.

Speech act conditionals differ from content and epistemic conditionals in that the condition described in the antecedent seems not to deter-mine the consequent at all. In 60 the request to sign the guest book has been made, whether the speaker has already asked the listener to do so or not.47 Still, the request in the consequent is made conditional on the state of affairs described in the antecedent: it must only be considered to be made if it hasn’t been made before. The request in 60 can be called a conditional request. However, not all conditional sentences in which the consequent is not an assertion but rather some other speech act belong to the category of speech act conditionals. A sentence like 61 for instance, belongs to a different category, although it could be called a conditional threat:

61 If you don’t clean your room every week, we’ll throw you out!

In 61, the threat described in the consequent will only be effectuated if the condition described in the antecedent is fulfilled. The difference between 60 and 61 is that in 60 the request is made irrespective of the fulfilment of the antecedent: whether or not the speaker has asked the listener to sign the guest book before, this is now accomplished in this sentence. The consequent could very well be uttered just by itself. In 61 however the antecedent is an integral part of the threat: were the con-sequent uttered by itself, the message the speaker sends out changes considerably.48

To determine whether a specific conditional is a content, epistemic or speech act conditional, one has to evaluate the content of both clauses. Sweetser doesn’t give any linguistic clues for differentiating between the various types, although she indicates that sometimes verb forms

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47 This difference is more clearly visible in the traditional Austinian conditional ‘If you are hungry, there are biscuits on the side board’. Of course the biscuits are there, whether the listener is hungry or not.

48 Van der Auwera has discussed the difference between sentences like 60 and 61 in detail (1986:198-202 ).

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can give an indication of the ‘more natural’ interpretation. Moreover, conditional sentences can be ambiguous. According to Sweetser, for example, in sentence 62 an ambiguity arises between a content and an epistemic reading:

62 If he was already gone, (then) they had to leave a message.

The content reading can be paraphrased as ‘Whenever, in the past, he was gone before their arrival, they were (thereby?) obliged to leave a message.’ As an epistemic conditional, the sentence is taken to express something like ‘If I know that he was gone before they arrived (in this instance), then I conclude that they were obliged to leave a message’ (1992: 123-124). As was mentioned earlier, Sweetser’s tripartite division has become influential. In their tentative typology, Van Belle, Horsten and Schae-ken (2002) make a similar distinction between what they call conditio-nals with a non-inferential or content relation, an inferential relation, and a commentative relation between antecedent and consequent. The category of conditionals with a non-inferential relation includes several predictive subtypes. For instance, not only 63 but also a conditional promise like 64 belongs to this class:49

63 If there is oil on the surface, the road is dangerously slippery.

64 If you pass your exams, you will get a new bike.50

It is characteristic for conditionals with an inferential relation that the consequent contains a conclusion that is drawn on the basis of the antecedent, as in 65:

65 If Oscar is ill, the lobster must have been off.

The modal term ‘must’ in the consequent indicates the kind of infe-rence made. Conditionals with a commentative relation between ante-cedent and consequent are what Sweetser calls speech act conditionals.

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49 Examples given by Van Belle et al. (2002:110).

50 Van Belle et al note that conditional promises generally are interpreted biconditionally: the child will get a bike if she passes the exams and won’t get a bike if she doesn’t.

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Although Van Belle et al. claim that the difference between all three main categories of conditionals is based on several linguistic charac-teristics, they allude to the fact that many conditional sentences can be interpreted in either an inferential or a non-inferential way. For instance, sentence 66 can receive both readings:

66 If their car is in front of the house, they are in.

According to Van Belle et al., it is as easy to come up with a context where this sentence is taken to mean ‘Whenever their car is in front of the house, they are in’ (non-inferential) as it is to find one where it should be interpreted as ‘If it is true that their car is in front of the house, then I conclude that they are in.’ The classification in Dancygier (1998) also strongly draws on Sweet-ser’s division into content, epistemic and speech act conditionals. As mentioned above in section 3.1, Dancygier makes a distinction between predictive and non-predictive conditionals on linguistic grounds. These two main categories are subsequently subdivided on the basis of the type of connection between antecedent and consequent. According to Dancygier, predictive conditionals represent the central meaning of the if-then-conjunction and non-predictives are derivative. As a result, predictive conditionals are limited in the kind of relation that can hold between the antecedent and the consequent: they always belong to the content domain. Non-predictive conditionals are far more open to different kinds of relationships between antecedent and consequent. The two main ca-tegories of non-predictive conditionals are epistemic conditionals and what Dancygier calls conversational conditionals. The latter comprises not only speech act conditionals but also metatextual conditionals like 67:

67 Grandma is feeling lousy, if that is the appropriate expression.

Metatextual conditionals differ from speech act conditionals because the condition in the antecedent comments not on the performance of the speech act in the consequent, but on the utterance of this speech act. The conditionality is therefore not located at the illocutionary but at the locutionary level.

Finally, Eirian Davies proposed a classification of conditionals in her work On the Semantics of Syntax. Mood and Condition in English (1979).

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Although her classification is hardly quoted in the literature on condi-tionals, it nevertheless is worth mentioning here because Davies not only provides a detailed linguistic analysis of conditional constructions, but also links them to different systems of logic. Davies’ semantic ana-lysis is based on the idea that in verbal interaction four different roles can be discerned, that of the ‘teller’, the ‘decider’, the ‘performer’and the ‘knower’. An example of a sentence in which all of these roles are present is 68:51

68 He should have taken more care.

The teller is he who utters this sentence, or, to be more precise he who is ‘constructing a linguistic description and presenting it to another (or others) in a speech interaction’. The decider is the one that decides that ‘taking more care’ is the action that has to be performed, ‘deciding’ being “making a judgment about which occurrence value shall attach to an event.” The performer is ‘he’, namely the one “carrying out an activity or entering into / being in a relationship or state (including ‘existing’) in the ‘real world’ (1979: 65).” Finally, the knower is he who knows that ‘he did not take more care’. Davies describes the knower as the one “taking cognizance of the relation between a description and the ‘reality’ to which it refers so as to assign it a known occurrence value and relate it to the situation of utterance in terms of relative sequence in time”. The four roles do not necessarily correspond to four different partici-pants in the interaction (although this could be the case). In 68 it could well be that the speaker fulfils the roles of teller, knower and decider. In addition, all exchanges in verbal interaction need not involve all four roles. For instance, expressives like ‘blast!’ only involve the role of the teller (1979: 51). The analytical value of distinguishing between these roles is that it facilitates a systematic analysis of the surface distinctions of mood in English. Since types of conditional sentences often are connected to the mood of the verb, Davies framework of semantic analysis can be used to systematically categorize conditionals. In accordance with the four roles that can be fulfilled in interaction, Davies classifies condi-tionals into four different classes: ‘telling’-; ‘decision’-; ‘performance’- ; and ‘knowledge’-conditionals.52 This division is based on differences in

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51 Example given by Davies (1979: 51).

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the semantic status of the relation between antecedent and consequent. According to Davies, in these four classes different kinds of logical relation are involved. Telling conditionals roughly correspond to what Sweetser calls speech act conditionals. This class does not only contain classic speech act conditionals like ‘There are biscuits on the sideboard if you want them’ but also the conditional sentence in the following exchange:

69 Susan: I really like watching tennis.Jeff: If you like watching tennis, Wimbledon is being televised this afternoon.

In this context the speaker has just learned from his interlocutor that she likes tennis and introduces the if-clause only to connect his utte-rance to this preceding conversation. For decision-conditionals the then-clause always contains a decision feature: it always states that something should or should not happen. Examples of decision conditionals would be 70 and 71: 70 If John comes, phone Mary.

71 If it rains, you must take your umbrella.

The relation between antecedent and consequent is such that the com-mand or advice in the consequent only becomes effective when the condition described in the antecedent is fulfilled. When the condition in the antecedent remains unfulfilled, no decision is made, so the question as to whether Mary should be phoned or not or an umbrella should be taken or not remains unanswered. Davies specifically states that decision conditionals do not represent any form of argument (1979: 151). Their main application is for ‘contingency planning’ and

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52 It is rather difficult to see how the four different types of conditional

sentence relate to the four different roles Davies discerns. Perhaps the best way

to interpret Davies is to understand it as follows: in telling conditionals the act of

‘constructing a linguistic description’ of the consequent is performed only under

condition, in decision conditionals, the ‘decision’ in the consequent is made only

under condition, in performance conditionals, the activity / state in the consequent

is taken only under condition, and in knowledge conditionals, the knowledge of the

‘truth’ of the description expressed in the consequent is taken only conditionally.

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practical reasoning. The antecedent of a decision conditional doesn’t contain a premise and the consequent doesn’t realize a conclusion. It therefore does not follow the rule of contraposition, as can clearly be seen in 72 and 72’:

72 If genocide occurs, we must intervene.

72’ If we mustn’t intervene, genocide does not occur.

On the performance plane, Davies discerns three main types of condi-tional sentences: ‘open prediction’, ‘induction’ and ‘counterfactual’ con-structions. Open predictions express a ‘lack of speaker and addressee knowledge’ about the situation described in the antecedent: its status cannot be decided at the moment of speech. The relation between ante-cedent and consequent is one of cause and effect, as in 7353:

73 If the weather is wet, the roads will be treacherous.

Davies stretches the notion of cause and effect (just as Comrie does) to accommodate cases of ‘set inclusion’, as in 74:

74 If the painting is signed, it will be genuine.

According to Davies, prediction conditionals, like decision conditio-nals, are not constructions of argument. They are used to make limited predictions. The antecedent does not set forward a premise for a con-clusion in the consequent, but the consequent involves the ‘telling’ of a probability. Therefore these types of conditionals are not expressing truth functional logic but ‘a modal logic of occurrence’ (1979: 156).54

The second main type of performance conditionals are induction conditionals, like the conditional in 75:

75 If this plane has flown a thousand times without an accident, it won’t crash now.

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53 Examples 69 – 71 and 73 – 77 are given by Davies (1979).

54 This may explain why contraposition is not valid: “...it is not the case that we can argue on the basis ‘if x, then will y’, that ‘if not-will y, then not-x’ or that ‘if not-will y, then not-will x’. E.g. We cannot argue on the basis of ‘If the weather’s wet, the roads will be busy’ that ‘If the roads will not be busy, the weather isn’t wet’, and still less that ‘If the roads will not be busy, the weather won’t be wet’. Neither can we

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Just as in 73, in 75 a prediction is made about the occurrence of the event described in the consequent of the conditional sentence: the speaker considers it highly improbable that the plane will crash, given its immaculate track record. The difference between inductive conditionals and ‘open predictions’ like 73 is that the antecedent contains ‘accepted knowledge’: both speaker and addressee are taken to accept that the plane has flown a thousand times without anything happening to it. Davies calls this a ‘closed if’, related to ‘as’. Since the consequent of sentences like 75 makes a probability statement, induction conditionals realize – just like open prediction conditionals – implication relations described in a modal logic of probabilities and not a truth functional argument. The third and final type of performance conditional Davies describes is the counterfactual conditional. Davies gives the following example (1979: 157):

76 If the Germans had invaded England in 1940, they would have won the war.

Counterfactuals belong to the class of performance conditionals because they are, just like open predictions and inductive conditionals, concerned with a prediction of the occurrence of an event described in the consequent.55 In 76 for instance, the speaker predicts what would have happened if the Germans had invaded Engeland in 1940. The re-lation between antecedent and consequent is a performance relation, between the occurrence of one event as cause and the probability of another event as effect. Just like the other performance conditionals, counterfactual condi-

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argue that ‘if not-y, then not-will x’. (...) we do not allow that either a prediction con-cerning the state of the weather, or knowledge concerning the state of the weather may be based on a prediction / knowledge concerning the state of the roads. We do not allow that the state of the roads has any influence on what the weather does (Davies 1979: 154).”

55 Although the term ‘counterfactual’ seems to imply otherwise, Davies does not consider it to be necessary that the speaker and addressee consider the situation described in the antecedent to be contrary to fact. They might as well be neutral as to the occurrence of the event, as in the following example by Davies: ‘If John had been at the scene of the crime at the time when the murder was committed, Mary would have seen him leaving. So we must get hold of her to find out if she did see him.’ (1979: 158).

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tionals are not about information, and do not themselves represent an argument. Their antecedents do not contain a premise from which the conclusion in the consequent can be deduced. However, Davies argues they are closely related to deductive argument since they can be used as a premise in such an argument. Because the event described in the consequent is situated in the past, it may be known whether it occur-red or not. If we know that the effect described in the consequent did not occur, we can deduce that the cause described in the antecedent did not occur either. We know that Germany did not win the war, so we can conclude that the Germans have not invaded England in 1940. This conclusion is not realized in the conditional construction, but rather in the use of the construction as a premise in an argument. The counterfactual conditional construction only expresses a relation of a modal logic of probabilities, not a truth functional relation between propositions. The fourth and final category of conditionals Davies describes are the so-called ‘knowledge conditionals’. They differ from telling con-ditionals, decision conditionals and performance conditionals in that they are the only type of conditional that realizes a truth functional relation between propositions. In knowledge conditionals the antece-dent contains accepted knowledge and the consequent a conclusion deduced from this knowledge. An example of a knowledge conditional is 77:

77 If he is a local man, he must know about the old mine workings.

The conditional construction in 77 is explicitly marked as telling a de-ductive conclusion (by means of ‘must’). Knowledge conditionals can also be composed of two non-modal indicative clauses, as in ‘If whales are warmblooded then whales are mammals’ (1979: 162). There is a close connection between performance conditionals and knowledge conditionals, since the former can fulfil the role of an underlying premise for the latter. For instance, performance conditio-nal 74 ‘If the painting is signed, it will be genuine’ could serve as an underlying premise for the deductive construction ‘If the painting is signed, it must (will) be genuine’. Since knowledge conditionals per-mit reversal of the causal order of events, sentence 74 might as well be used as an underlying premise for a deductive construction leading to the conclusion that the painting is not signed. Whether the antecedent of a knowledge conditional describes a cause or an effect, it always contains knowledge of a proposition, which serves as a sufficient con-

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dition for knowledge of the proposition expressed in the consequent. Therefore, a knowledge conditional is the only type of conditional that realizes a truth functional relation (of material implication) between antecedent and consequent (1979: 166).

3.4 Conclusion

The different views on conditionals discussed in this chapter offer – each on their own grounds – ways to discriminate between parti-cular if-then sentences. Structure is sought and brought into the vast amount of conditionals, which facilitates the study of such sentences to a great extent. But can the distinctions made clarify the question asked in the last chapter? Do the proposed classifications offer a way to discriminate between conditionals that are unproblematic with regard to the definition of material implication and conditionals that are not? Let us put the classifications discussed in this chapter to the test. A classification can only be used to differentiate between unproblematic and problematic conditional sentences if the problematic sentence 11 and the unproblematic sentence 20 are classified in different catego-ries:

11 If the U.S. uphold subvention, then the European Union will notagree to negotiate.

20 If the bottle of olive oil is leaking, you have not closed it properly.

First of all, can the classifications based on the status of the antecedent – discussed in section 3.2 – be used for this purpose? Clearly, the the standard division based on the status of the antecedent fails to do so: both 11 and 20 are indicative, open conditional sentences and would therefore belong to one and the same category. The same is true for the interpretation Funk gives to the terms ‘open’ and ‘closed’, albeit for a different reason. Funk makes a distinction between conditionals in which the state of affairs described in the antecedent is still subject to manifestation and conditionals in which this state of affairs is already manifested. Conditionals belonging to the first category can be paraphrased as ‘If it happens that X,...’, condi-tionals belonging to the second category as ‘If it is true that X,...’. What would be the correct paraphrase for sentences 11 and 20? One could

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argue that 11 is an open conditional and must be interpreted as ‘If it happens that the U.S. uphold subvention, then the European Union will not agree to negotiate.’ However, the interpretation ‘If it is true that the U.S. uphold subvention, then the European Union will not agree to negotiate’ is equally possible. The same is true for sentence 20: perhaps the paraphrase for 20 that first comes to mind would be ‘If it is true that the bottle of olive oil is leaking, then you haven’t closed it properly’, but ‘If it happens that the bottle of olive oil is leaking, then you haven’t closed it properly’ seems equally acceptable. Funk’s classification therefore fails as well. Not because problematic and unproblematic sentences are necessarily put in the same category, but because it is the case that with some conditional sentences there exists an ambiguity between categories. The classification proposed by Dudman seems to be more promi-sing, especially since he points out that modus ponendo ponens, modus tollendo tollens, contraposition, hypothetical syllogism and strenghte-ning the antecedent are all unproblematic when the ‘if’- sentences are restricted to hypothetical interpretations. This observation is easily explained, he argues, when indeed hypotheticals are seen as conden-sed arguments (1986:17). Now if we look at 11 and 20, we find that in Dudman’s classification these sentences will be classified in two different categories. 11 repre-sents a what Dudman calls a conditional: it is not composed of two pri-or messages but should be seen as a subject-predicate sentence with an elaborate predicate, ‘the EU’ being the subject and ‘will not agree to negotiate if the US uphold subvention’ the predicate. It is therefore not surprising that 11 is problematic with regard to the definition of material implication. 20 belongs to the category of what Dudman calls hypotheticals: it is composed of two prior messages, ‘the bottle of olive oil is leaking’ and ‘you have not closed the bottle properly’ and can be interpreted as a condensed argument. The conditional that is unpro-blematic with regard to the definition of material implication is the-refore classified in the category of conditionals where modus ponendo ponens, modus tollendo tollens, contraposition hypothetical syllogism and strenghtening the antecedent are indeed unproblematic. Although Dudman’s classification can be used to differentiate bet-ween the problematic sentence 11 and the unproblematic sentence 20, it suffers from an ambiguity between categories as well. As Dudman says: “certain sentences can be used to send different messages.” From the sentence alone one cannot always tell which message is sent and therefore from the sentence alone one cannot always tell to which category it belongs. If we take for instance 78

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78 If it is sunny, the city is deserted.

The sentence in 78 can be interpreted in two different ways: it can be a habitual with a subject ‘the city’ and an elaborate predicate ‘is deserted if it is a sunny day’ or a hypothetical, consisting of the two prior mes-sages ‘It is sunny’ and ‘the city is deserted’. As long as there is no way to disambiguate between the two, Dudman’s classification suffers from the same problem as Funk’s classification. Finally, could the distinction Dancygier makes between predictive and non-predictive conditionals be of help? In Dancygier’s classifica-tion, sentences 11 and 20 would be classified in two different categories. 11 can be called a predictive conditional: the consequent contains a marker of prediction ‘will’, whereas the antecedent can be said to con-tain backshift. This sentence is best read as ‘If the US uphold subventi-on (in the future), then the EU will not agree to negotiate’. Sentence 20 is a non-predictive conditional, since the antecedent does not contain backshift. However, the class of non-predictive conditionals does not only contain unproblematic conditionals. What belongs to this category is a whole variety of conditional sentences that are problematic with regard to the definition of material implication: ‘if you are hungry, there are cookies on the sideboard’; ‘my best friend here – if I may call you that – says I am far too generous’; ‘If their car is not on the driveway, my friends are out’ – to name but a few. If Dancygier’s classification is at all helpful, the subclasses she defines on the basis of the way the ante-cedent and consequent are connected should be taken into account.

So let us turn to the classifications based on the connection between antecedent and consequent and see whether those offer a way to cate-gorize problematic and unproblematic conditionals in an univocal way. In both sentences 11 and 20 there is a causal link between the antece-dent and the consequent. In 11 the U.S. upholding subvention results in the European Union disagreeing to negotiate. In 20 not closing the bottle properly causes the bottle to leak. According to Nieuwint, both conditionals would therefore belong to the category of unfree relations between antecedent and consequent. In the classification of Johnson-Laird, both conditionals would finally be placed into the same category as well, since both can be characterized as conditionals in which the antecedent determines the state of affairs only partially. These two clas-sifications therefore provide no solution.

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At first sight, the classification proposed by Sweetser, Noordman and others, following a similar line of reasoning, seems to be of help in dividing conditionals into unproblematic and problematic ones. The problematic sentence 11 belongs to the class of content conditionals. There is a causal link between the antecedent and the consequent that can be characterized as a condition-consequence relation: the antece-dent contains the cause, the consequent the effect. The unproblematic conditional 20 is an epistemic conditional that is correctly paraphrased as ‘If I know that the bottle is leaking, I may conclude that you did not close it properly.’ There is an inference relation between the antecedent and the consequent. The effect (the bottle leaking) is described in the antecedent and the cause (not closing the bottle properly) is described in the consequent. Noordman would paraphrase this conditional as ‘From the fact that the bottle is leaking, one may infer that you did not close it properly.’ Conditionals 11 and 20 therefore end up in different classes. However, these classifications can only be said to divide conditionals in an univocal way if it can somehow be shown that all conditionals that contain an inference relation are unproblematic. Furthermore, there must not be a conditional sentence with a condition-consequence relation that is unproblematic as well. It is an impossible task to esta-blish whether the first prerequisite is met, therefore, let us focus on the second one: are there conditional sentences with a condition-conse-quence relation that are unproblematic when submitted to the logical operations of contrapostition, hypothetical syllogism and strengthening the antecedent? Such examples are not difficult to find. Sentence 63 seems to be a case in point:

63 If there is oil on the surface, the road is dangerously slippery.

Contraposition yields ‘If the road is not dangerously slippery, there is no oil on the surface’, which is unproblematic. Combined in a hypothe-tical syllogism with ‘If the road is dangerously slippery, the road is clo-sed for traffic’ 63 yields ‘If there is oil on the surface, the road is closed for traffic’, which is unproblematic as well. Finally, an unproblematic instance of strengthening the antecedent would be ‘If there is oil on the surface and the oil originates from a tank lorry turned on its side, the road is dangerously slippery.’56

In sum: the classifications proposed by Sweetser and Noordman and others cannot be used to discriminate between conditionals that are

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unproblematic with regard to the definition of material implication and conditionals that are not. It is true, sentences 11 and 20 belong to different categories, 11 being a content conditional and 20 being an epistemic conditional, but unfortunately one cannot say that all content conditionals are problematic and all epistemic conditionals are not, since examples of unproblematic content conditionals can easily be found.57

Let’s finally turn to Davies’ classification. She explicitly states that the definition of material implication is only relevant to one class of conditionals: knowledge conditionals. If it can somehow be shown that the class of knowledge conditionals indeed covers all conditionals that are unproblematic with regard to the definition of material implica-tion, whereas other conditionals indeed would be problematic, Davies’ account could be used to discriminate between conditionals that can be submitted to the evaluation criteria expressed in the definition of material implication and those conditionals that cannot. Davies characterises knowledge conditionals as follows: (1) they contain a causal relationship between the antecedent and the consequent (that can go from either cause to effect or from effect to cause); (2) the antecedent contains accepted knowledge; and (3) the consequent can be seen as a deductive conclusion based on the knowledge presented in the antecedent (as can be made explicit by adding ‘must’). Let us take a look whether the unproblematic conditio-nal 20 could be classified as a knowledge conditional.

20 If the bottle of olive oil is leaking, you have not closed it properly.

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56 One can also find examples where strenghtening the antecedent yields unde-sirable outcomes, as in ‘If there is oil on the surface and anti-slippery chemicals are applied, the road is dangerously slippery’. For now, it suffices to show that strengh-tening the antecedent is not problematic ‘by definition’.

57 Not only is 63 unproblematic with regard to the definition of material impli-cation, it can easily receive an epistemic reading as well. There is no impediment in rephrasing this sentence as ‘If I know that there is oil on the surface, then I con-clude that the road is dangerously slippery’. In fact, it is very hard, if not impossible to think of a content conditional that cannot be interpreted in an ‘epistemic way’ as well. ‘If I know that he is already gone, then I conclude that they will have to leave a message’ and ‘If I know that you pass your exams, then I conclude that you will get a new bike’ all seem to be unproblematic epistemic interpretations of content conditionals.

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The relationship between the antecedent and the consequent indeed is a causal one: that the bottle of olive oil is not closed, has caused it to leak. The third characteristic seems to be present as well: ‘you have not closed it properly’ could be seen as a deductive conclusion based on the fact that the bottle is leaking. The deductive character of the consequent could be emphasized by adding ‘must’. However, whether this conditional possesses the second characteristic is difficult to assess. Judged from the conditional sentence alone, one cannot determine whether the antecedent contains accepted knowledge or not. One would have to ask the participants in the conversation to find out whether this is the case. Since it generally cannot be established whether a conditional possesses this second characteristic, it is often impossible to classify conditionals as knowledge conditionals. Secondly, similar to the accounts of Funk, Dudman and others, some conditional sentences manifest ambiguity between the categories. In Davies’ discussion of the relation between performative conditionals and knowledge conditionals, the performative conditional ‘If the picture is genuine, it will be signed’ is word for word identical to the knowledge conditional that can be derived from it. Of course, the sen-tences differ in that the latter can contain ‘must’ whereas this remains unsuitable for performative conditionals. But how can one know whether it is legitimate to add ‘must’ or not? And if you cannot know this, how can you decide whether a particular conditional belongs to either the performance or the knowledge category?

None of the classifications discussed in this chapter are able as they stand now to unequivocally discriminate between a category of condi-tionals that is unproblematic with regard to the definition of material implication and a category of problematic conditionals. If one at-tempts to analyse and evaluate argumentatively used conditionals, one needs a division in categories based on the relevant evaluation criteria. First of all, conditionals that need different evaluation criteria, should be classified into different categories. Furthermore, all conditional sentences to which the same evaluation criteria apply, should end up in the same category. Finally, it should be impossible for one conditio-nal sentence to belong to more than one category. Only then can one be sure that the correct evaluation criteria are applied in evaluating a conditional sentence. Regarding the classifications discussed in this chapter, one can say that ultimately they all fail in making a precise distinction between dif-ferent conditionals. However, they do not fail for the same reasons and

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perhaps not all failure is equally grave. Although classifications that put conditionals with different evaluation criteria in the same category, or conditionals with the same evaluation criteria in different categories are not helpful for our purposes, classifications in which conditionals are ambiguous between categories can be used as a starting point. What these classifications – the ones by Funk, Dudman and Davies – have in common is that although the characteristics presented are clear in themselves, it is impossible to assess whether a specific condi-tional possesses these characteristics, i.e. the conditionals are ambi-guous between categories when the conditional is seen in isolation. As soon as a context is provided, the ambiguity of such conditional sentences disappears. Take for instance the ambiguous sentence 20.

20 If the bottle of olive oil is leaking, you have not closed it properly.

Seen in isolation, this sentence is ambiguous between an open condi-tional and a closed conditional (in Funk’s classification) or a perfor-mative and a knowledge conditional (in the classification proposed by Davies). However, when this sentence is embedded in the following context, only one interpretation remains:

20’ I don’t know whether the bottle of olive oil is leaking or not, but if it is leaking, you have not closed it properly. You were the last to use it.

At the moment of speaking, it is not known to either the speaker or the listener whether the bottle of olive oil is leaking or not. The conditional is therefore what Funk would call an open conditional and Davies a performative conditional. It is equally easy to find a context in which a knowledge reading of the conditional sentence is the natural interpretation. Take for instance the following dialogue:

20’’ Of course you haven’t closed the bottle properly! If it is leaking – and it is, as you can see – you haven’t closed it properly.

Here the antecedent indeed is common knowledge to the speaker and the listener, and the consequent can be seen as a deductive conclusion based on the knowledge presented in the antecedent; all characteristics of a knowledge conditional are present. How does this relate to the division between conditionals that do and

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conditionals that don’t comply with the definition of material implica-tion? If Davies is right in her assumption that knowledge conditionals are the only conditional sentences that realize a truth-functional rela-tion between the antecedent and the consequent, our attention needs to be shifted. Instead of looking at characteristics that such conditional sentences possess, we should be looking at characteristics of the con-text in which the conditional appears.

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4 Conditionals functioning as a connecting premise

4.1 Introduction

As can be seen from the last chapter, in making a distinction between conditionals that can and conditionals that cannot be subjected to the definition of material implication, a pivotal role is played by the con-text in which the conditional sentence appears. The context is neces-sary to determine whether a conditional possesses the characteristics that define knowledge conditionals: the antecedent containing accep-ted knowledge and the consequent containing a deductive conclusion. This context dependency does not mean that it will be impossible to say anything in general about conditional sentences to which the definition of material implication is applicable. By giving the context a closer look, one might get a better understanding of the role the conditional plays in this context. This might in turn lead to an insight into which characteristics the conditional has to possess in order to be able to fulfil this role. Let us start by taking a closer look at example 20” from the last chap-ter.

20’’ Of course you haven’t closed the bottle properly! If it is leaking – and it is, as you can see – you haven’t closed it properly.

In this context the conditional clearly is a knowledge conditional: there is a common understanding that the bottle is leaking, and from this a – what Davies calls ‘deductive’ – conclusion is drawn that the addressee has not closed the bottle properly. What is it in the context that brings about this interpretation of antecedent and consequent? Regarding the antecedent, the speaker alludes to a shared acknowled-gement of the truth of it, by stating explicitly that the bottle is leaking and by indicating that the addressee would agree with it since it is visible. Regarding the consequent, the interpretation that it contains a ‘deductive’ conclusion urges itself upon us since this conclusion is explicitly mentioned at the beginning. Also in contexts where less contextual clues are available, the inter-pretation of a conditional as a knowledge conditional seems justified, as in example 79:

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79 There is no reason to inform the Child Protection Office. If there is no evidence the father started the fire deliberately to hurt his children, there is no reason to do so.

Here again the deductive conclusion drawn in the consequent is ex-plicitly stated at the beginning. There are no clues however about the status of the antecedent. Nevertheless, I would claim it is just as reaso-nable in this context to assume that the speaker considers the antece-dent to contain accepted knowledge, because of the specific function the conditional fulfils. Both in 20” and 79 the conditional is used as a premise in support of a point of view: the speaker is not convinced from the outset that the listener will accept that ‘he did not close the bottle properly’ or ‘there was no need to inform the Child Protection Office’ and therefore uses argumentation to make these points of view acceptable. It is this context of argumentation that makes a conditional a knowledge conditional.

Argumentation characteristically comes about when there is a dif-ference of opinion concerning a certain point of view.58 It can for instance be the case that a speaker asserts something that is contested right away by the other party in a dialogue. Or the speaker says some-thing and anticipates such doubt. Even when there is no other party present, an internal difference of opinion can occur, for instance when someone is deliberating about what course of action to follow. Argu-mentation is subsequently put forward to remove the doubt and make a point of view acceptable. In the most simple case, a speaker who wants to convince a listener of a certain point of view puts forward one reason (argument, premise, ground) to support his standpoint, as in 80:

80 Night time is the best time to work, since at night time you won’t be distracted.

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58 I use the pragma-dialectic approach to argumentation, as presented by Van Eemeren and Grootendorst, not only because it is the only systematic approach for the analysis, evaluation and production of argumentation, but also because their approach is functional in nature, in the sense that according to them, ‘verbal expres-sions are not “by nature” standpoints, arguments or other kinds of units of langu-age use that are interesting to argumentation theorists. They only become so when they occur in a context where they fulfil a specific function in the communication process.’ (Van Eemeren&Grootendorst 2004: 3)

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In other situations the speaker might have to extend his argumenta-tion.59 A premise put forward in support of a standpoint can remove doubt in the mind of the listener only when the listener agrees that the premise is true. If the listener is not convinced that ‘at night time you will not be distracted’, this premise is in turn a point of view that has to be defended, as in 81:

81 Night time is the best time to work, since at night time you won’t be distracted. The neighbours only play their music loudly till 11 pm.

The speaker will have to continue to support his premises until he reaches a common starting point: a premise that the listener accepts as true. Extension of the argumentation can also come about in another way. Sometimes one reason does not suffice and more (coordinative) reasons are needed in order to remove doubt, as in 82:

82 It is dangerous to swim in that pool. It has been very hot these last days and the water is still.

It is only the combination of hot weather and still waters that makes it dangerous to swim, so both reasons are needed to support this point of view. Finally, bringing up more than one reason may serve the purpose of a back-up: if the listener is not convinced by the first reason, maybe he will be by the second. In 83 such multiple argumentation is used:

83 You don’t need to water the plants tonight. They have had more than enough water yesterday, and anyway the weather forecast says it will rain.

The plants having had more than enough water yesterday is a suffi-cient reason to adopt the standpoint. However, if the listener questions whether this is true, not all is lost, since he might be convinced by the second reason.

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59 For a complete survey of more complex argument structures see Snoeck Henkemans 1992.

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In this chapter I defend the claim that the definition of material im-plication is applicable only to conditionals that function as a premise in support of a point of view. However, it is not applicable to all such conditionals. In 11”, just as in 20” and 79, the conditional functions as a premise in support of a standpoint:

11’’ The U.S. should not halt the bombing. If the U.S. halts the bombing, then North Vietnam will not agree to negotiate.

The conditional in 11” is different from the ones in 20” and 79 since it cannot be submitted to contraposition. Contraposition would yield 11’, where the decision to uphold subvention seems to be dependent on the willingness to negotiate:

11’ If North Vietnam agrees to negotiate, then the U.S. will not have halted the bombing.

In order for the definition of material implication to be applicable, a conditional should not just function as a premise, but also as a specific kind of premise: one that forms the connection between another premise and the standpoint at issue. The conditionals in 20” and 79 do form this connection, whereas the one in 11” does not. In this chapter connecting premises are described in detail. First, in 4.2 the notion of connecting premise is elucidated and linked up with the definition of material implication and with the logical operations of contraposition, hypothetical syllogism and strenghtening the ante-cedent. Then, in 4.3 the characteristics a conditional must possess in order to be able to function as connecting premise are listed. Finally, in 4.4 evaluation criteria are proposed.

4.2 The role connecting premises play

In order to gain a better understanding of connecting premises, let us look at another example of argumentation:

84 Ikram doesn’t drink alcohol, since she is a Muslim.

In 84, the speaker apparently expects the other party in the discussion to question whether Ikram drinks alcohol or not. In order to convince

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him that Ikram doesn’t, the speaker puts forward a premise: ‘Ikram is a Muslim’. His argumentation can only be successful when the other party accepts this premise as being true. But acceptance of the premise is not enough. The other party can accept the premise and still not be convinced of the acceptability of the standpoint, as in 85:

85 True, Ikram is a Muslim, but there are enough Muslims that do drink alcohol. It just depends on how strictly religious they are.

This reaction is not directed at the premise put forward, but at the con-nection between the premise and the conclusion drawn from it. It is accepted as true that Ikram is a Muslim, but it is challenged that from this you can draw the conclusion that Ikram does not drink alcohol. This connection between premise and conclusion is what Van Eeme-ren and Grootendorst call an ‘unexpressed premise’. It can be made explicit and added to the argument so as to make the argument put forward logically valid.60 In this example it could amount to adding an if-then-sentence where the antecedent contains the premise and the consequent contains the standpoint.61 The argumentation then acqui-res the logically valid form of modus ponendo ponens. Schematically the standpoint and the argumentation put forward to support it can be represented as follows:

1.

Ikram does not drink alcohol

↑

1.1 1.1’

she is a Muslim – & – [if Ikram is a Muslim, she does not drink

alcohol]

It is not always the premise that expresses the connection that is left

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60 For a precise method of reconstructing unexpressed premises and the ratio-nale behind such reconstructions, see Chapter 6 of Van Eemeren and Grootendorst 1992.

61 Actually, according to Van Eemeren and Grootendorst, explicating this ‘logi-cal minimum’ is not enough. The analyst should formulate a pragmatic optimum: some statement that is more informative than the logical minimum but still can be seen as something the speaker is committed to. I will discuss this issue at the end of section 4.3.

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unexpressed.62 Sometimes a speaker leaves his standpoint implicit, as in 86:

86 If it rains, there is no reason to water the plants. And it is pouring.

Or he just puts forward the standpoint and the premise that expresses the connection and leaves out the ‘direct premise’63, as was the case in example 79:

79 There is no reason to inform the Child Protection Office. If

there is no evidence the father started the fire deliberately to hurt his children, there is no reason to do so.

In other situations all three elements – standpoint, direct premise and connecting premise – are present, as in 20”:

20’’ Of course you haven’t closed the bottle properly! If it is leaking – and it is, as you can see – you haven’t closed it properly.

Whether the connecting premise is expressed or unexpressed, it nevertheless fulfils a specific role. It is by means of the connecting premise that the truth or acceptability of the direct premise is transfer-red to the standpoint.64

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62 This is why I prefer ‘connecting premise’ over ‘unexpressed premise’. The first term denotes the function the premise fulfils and not a coincidental quality.

63 For easy reference I will call the not-connecting premise the ‘direct premise’. I have chosen the term ‘direct’ because of its contrast with indirect proof, in which a standpoint is explicitly supported by a connecting premise – a conditional of which the antecedent contains the negation of the standpoint under discussion.

64 The distinction between the direct premise and the connecting premise bears a strong resemblance to the distinction between ‘data’ and ‘warrant’ that Stephen Toulmin makes in his book The Uses of Argument (1958). The data are the facts ap-pealed to as a foundation for the claim (1958: 97) The warrant should be seen as an inference licence: a hypothetical statement that can act as a bridge and that autho-rises the step from the data to the claim (1958: 98). I decided not to use Toulmin’s terminology because what I call the connecting premise differs from a warrant in a significant respect: warrants are general hypothetical statements, whereas con-necting premises are by definition not general statements (see section 4.3).

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It is because of this role that the context in 20” presses for an inter-pretation of the conditional as a knowledge conditional. In a conditio-nal that functions as a connecting premise in a modus ponendo ponens, the two characteristics of knowledge conditionals Davies described are present: the antecedent contains accepted knowledge (or at least what the speaker expects to become accepted knowledge when this statement is in turn supported) – the premise the speaker expects the listener to accept as a common starting point – and the consequent contains a ‘deductive’ conclusion – the claim supported by this pre-mise.

My suspicion is that conditionals functioning as a connecting pre-mise may be unproblematic with regard to the definition of material implication. Not so much because they are knowledge conditionals, but because they fulfil a transferring function between the direct premise and the standpoint under discussion. Therefore, I want to include a second category of conditionals, since not only conditionals that Davies would call knowledge conditionals can function as a con-necting premise in argumentation. A conditional like the one in 87 can function as such as well:

87 Daniel is no athlete. If he were an athlete, he would have stamina. But he can’t climb the stairs without losing his breath.

In 87 the protagonist puts forward a standpoint ‘Daniel is no athlete’. In support of his standpoint, he puts forward a conditional sentence ‘If he were an athlete, he would have stamina.’ The argument used can be made valid by adding the (unexpressed) direct premise ‘he does not have stamina’. This premise is supported in turn by the statement that Daniel can’t climb the stairs without losing his breath. Schematically the argumentation can be respresented as follows:65

—————

65 The notation I use slightly differs from the pragma-dialectical notation in that I do not use use the apostrophe (like in 1.1’) to indicate that a statement is unex-pressed, but rather to indicate the connecting premise that forms the connection between the direct premise and the standpoint under discussion. To express that a statement is unexpressed, it is represented in square brackets.

90

1.

Daniel is no athlete

↑

1.1 1.1’

[he does not have stamina] – & – if he were an athlete,

↑ he would have stamina

1.1.1

he can’t climb the stairs

without losing his breath

In 87 the conditional is not used as a conditional in a modus ponendo ponens, but in a modus tollendo tollens: instead of deducing the truth of the proposition expressed in the consequent from the truth of the proposition expressed in the antecedent, the falsity of the proposition expressed in the antecedent is deduced from the falsity of the pro-position expressed in the consequent. For Davies, the conditional in 87 is not a knowledge conditional: the antecedent does not contain a proposition that is mutually accepted. Nevertheless, from my point of view the conditional can be judged to be a connective premise. The conditional transfers shared knowledge of the falsity of the proposition expressed in the consequent (hence the truth of the direct premise) to the falsity of the proposition expressed in the antecedent (hence the truth of the standpoint). So far I have argued there may be good reasons to assume that at least one category of conditionals that function as a connecting premise can be called knowledge conditionals. Furthermore, I have argued that a second category of conditionals can function as a con-necting premise. However, is it correct to assume that conditionals that function as a connecting premise are unproblematic with regard to the definition of material implication along with the logical opera-tions of contraposition, transitivity and strenghtening the antecedent? In order to answer this question let us take a closer look at one of the first modern representations of the definition of material implication: the one offered by Gotlob Frege. Frege writes:

Wenn A und B beurtheilbare Inhalte bedeuten, so giebt es folgen-de vier Möglichkeiten:A wird bejaht und B wird bejaht.A wird bejaht und B wird verneint.A wird verneint und B wird bejaht.A wird verneint und B wird verneint.

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bedeutet nun das Urtheil, dass die dritte dieser Möglichkeiten nicht stattfinde, sondern eine der drei andern (1964: 5).66

Frege describes four possibilities, which are the ones that are repre-sented in the truth table of material implication. I would say there is a close connection between the four possibilities Frege describes and the four situations that may occur in a discussion concerning a certain point of view. To illustrate what I mean, let us look once again at example 79:

79 There is no reason to inform the Child Protection Office. If there is no evidence the father started the fire deliberately to hurt his children, there is no reason to do so.

If we analyse this example, we arrive at the following structure: the standpoint put forward is (1) ‘there is no reason to inform the Child Protection Office’. The (unexpressed) direct argument is (1.1) ‘there is no evidence the father started the fire deliberately to hurt his children’. The connecting premise is (1.1’) ‘if there is no evidence the father started the fire deliberately to hurt his children, there is no reason to do so’.

1.

there is no reason to inform the child

protection service

↑

1.1 1.1’

[there is no evidence the – & – if there is no evidence the father

father started the fire started the fire deliberately to

deliberately to hurt his hurt his children,

children] there is no reason to do so

In this example, the ‘B’ in Frege’s definition stands for ‘there is no evidence the father started the fire deliberately’ and the ‘A’ stands for ‘there is no reason to inform the Child Protection Office’.

—————

66 The sign is Frege’s symbolic representation of the assertion of ‘if B then A’. See for an explanation of this sign, Frege 1964: 1.

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Suppose the antecedent of the connecting premise is true. In this specific context, this means that the direct argument is accepted; both parties agree there is no evidence the father started the fire deliberately to hurt his children. In that case, the conditional (if true) leaves us with just one possibility: the proposition expressed in the consequent is true as well. Or, in other words, there is indeed no reason to inform the Child Protection Office. This is the first of the four possibilities Frege depicts. If the direct argument is accepted but the other party can show that the Child Protection Office should be informed anyway, we have the third possibility. The antecedent is true, the consequent is false, so the conditional ‘If there is no evidence, there is no reason to inform the Child Protection Office’ has been shown to be false and must be retrac-ted. Now suppose the antecedent of the connecting premise is false, that is, the direct argument is rejected. It is shown that there is evidence the father started the fire deliberately to hurt his children. What does this mean for the standpoint put forward? It means the speaker needs to come up with new support for his standpoint if he wants to con-vince the listener. Or else he should retract his standpoint and concede that he was wrong. But nothing can be said about the truth of the pro-position expressed in the standpoint. This proposition can be false or true; we just don’t know. Or, to put it in other words, if the antecedent is false, either the second or the fourth possibility will be the case, we just do not know which one. The four possible situations Frege describes do not only coincide with the four possible outcomes of a discussion where a conditional functions as a connecting premise in a modus ponendo ponens. When a conditional functions as such in a modus tollendo tollens the same cor-relation can be found. Let’s take a closer look at 87:

1.

Daniel is no athlete

↑

1.1 1.1’

[he does not have stamina] – & – if he were an athlete,

he would have stamina

In this example the ‘B’ in Frege’s definition stands for ‘Daniel is an athlete’ and the ‘A’ stands for ‘Daniel has stamina’.67

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In this example, the situation where the direct premise is rejected is represented in the first and second situation Frege depicts. ‘Daniel does not have stamina’ (not-A) is false, hence A is true or ‘wird bejaht’. In that case nothing can be said of the standpoint put forward: Daniel may be an athlete or not, we don’t know. If the direct premise is ac-cepted – it is found that Daniel indeed does not have stamina (A wird verneint) – the conditional (if true) leaves us with just one possibility: the standpoint is true as well. Daniel is no athlete (B wird verneint). This outcome is reflected in the fourth situation Frege describes. And again the third possibility reflects the situation where the conditional sentence is found to be false: the direct premise is accepted (A wird verneint), whereas the standpoint is rejected (B wird bejaht). In sum: if we look at the four possibilities depicted by Frege, we see a complete overview of the four situations that could emerge after eva-luation of the argumention in support of a point of view. Either the di-rect argument is rejected, in which case the question remains unans-wered whether the proposition expressed in the standpoint is true or not, or the connecting premise is rejected by showing that the direct premise is true whereas the proposition expressed in the standpoint is false, or both the direct argument and the standpoint are accepted, and the antagonist retracts his doubt concerning the acceptability of the standpoint put forward.

The close correspondence between the situations described in the definition of material implication and those that can occur after the evaluation of the argumentation put forward in support of a point of view, makes it at least plausible that it is the category of conditionals functioning as a connecting premise that the definition should be restricted to. Let us see whether the context of argumentation can shed light on the logical operations of contraposition, hypothetical syllo-gism and strenghtening the antecedent as well. First of all, how does the logical operation of contraposition fit in with a context of argumentation? According to Frege, contraposition is important for indirect proofs. He writes:

—————

67 Although the conditional sentence is in the subjunctive mood, I represent B and A in the indicative mood. The subjuntive mood does not change a proposition, the speaker only indicates he distances himself from the truth of it (which in this case is not all that strange, since he is defending the contrary of ‘B’ by means of the contrary of ‘A’). Since for our present purpose it is the proposition that is of interest and not so much the speaker’s attitude towards it, I left this information out.

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Für die aus Bedingung und Folge bestehenden Gedanken gilt nun das Gesetz, daß unbeschadet der Wahrheit das Entgegengesetzte der Bedingung zur Folge und zugleich das Entgegengesetzte der Folge zur Bedingung gemacht werden darf. Die Engländer nen-nen diese Übergang contraposition. Nach diesem Gesetze kann man von dem Satze “Wenn (21/10)100 größer als 10 √1021 ist, so ist (21/20)1000 größer als 1021” übergehen zu dem Satze “Wenn (21/20)1000 nicht größer als 1021 ist, so ist (21/10)100 nicht größer als 10 √1021”. Und solche Übergänge sind wichtig für die indirekten Beweise, die sonst nicht möglich wären (1993b: 57).

Indirect proof would be impossible if contraposition did not hold. In an indirect proof, the contradictory of the conclusion is added to a set of premises and a contradiction is derived from it. Assuming that the initial premises are true, this means that the contradictory of the conclusion must be false and hence the conclusion must be true. The modus tollendo tollens in 87 is an example of a condensed indirect proof. In order to prove that Daniel is no athlete, the speaker supposes that he is and shows that this would lead to a contradiction. If he were an athlete, he would have stamina, whereas in reality he hasn’t. The con-clusion therefore must be that Daniel is not an athlete. Although this analysis of 87 might seem to be clear enough, it does not clarify why contraposition is of such importance to indirect proof – as Frege claims it to be. There seems to be no contraposition involved. The situation would be rather different had the speaker left the connecting premise implicit instead of the direct premise. Let’s suppose the speaker had supported his point of view in the following way:

87’ Daniel is no athlete, he doesn’t have stamina. He can’t climb the stairs without losing his breath.

The structure of this argumentation is straightforward and can be re-presented as follows (with the unexpressed connecting premise made explicit):

95

1.

Daniel is no athlete

↑

1.1 1.1’

he does not have stamina – & – [if Daniel doesn’t have

stamina,he is no athlete]

↑

1.1.1

he can’t climb the stairs without lossing breath

The importance of contraposition becomes apparent as soon as the protagonist is asked to support the (unexpressed) connecting premise in 87’. The basis for his claim that ‘If Daniel doesn’t have stamina, he is no athlete’ probably is that ‘Athletes have stamina’. However, this statement cannot be easily connected to the connecting premise, since cause and consequence are in the opposite order. The contrapositive of the unexpressed connecting premise in 87’ makes the connection possible. From the general statement ‘If one is an athlete, one has stamina’, it is deduced that ‘If Daniel were an athlete, he would have stamina’. Then, by means of contraposition we obtain ‘If Daniel does not have stamina, he is no athlete’, the connecting premise we need in order to pass the truth of the direct premise to the standpoint at issue. The result is the following (rather complex) structure:68

1.

Daniel is no athlete

↑

1.1 1.1’

he does not have stamina – & – [if Daniel doesn’t have

stamina,he is no athlete]

↑ ↑

1.1.1 1.1’1

he can’t climb the stairs If he were an athlete, he

without lossing breath would have stamina

↑

1.1’1.1

Athletes have stmina

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In comparison with the argumentative use of contraposition, the use of hypothetical syllogism in argumentation is straightforward. By means of an hypothetical syllogism, the speaker can create a shortcut in his argument. If we take the following dialogue:

88 Anthony: Theodore cannot have stolen the bracelet.Beth: Why not?Anthony: January 30 is a public holiday.Beth: That is true, but what’s your point?Anthony: Well, if January 30 is a public holiday, the shop was closed that day. And if the shop was closed, he cannot have stolen the bracelet.

The argumentation Anthony uses can schematically be represented in the following way:

1.

Theodore cannot have stolen the bracelet

↑

1.1 1.1’

January 30 is – & – [If January 30 is a public holiday,

a public holiday Theodore cannot have stolen

the bracelet ]

↑

______ 1.1’1a 1.1’1b

If January 30 is a If the shop was closed,

public holiday, he cannot have

the shop was closed that day stolen the bracelet

—————

68 The complexity of this structure might explain the results of the psychological experiments Johnson-Laird conducted : “Psychological experiments have shown that people with no training in logic cope reasonably well with arguments in the form of modus ponens (see Wason and Johnson-Laird 1972). (...) Ordinary reasoners have greater difficulty with arguments in the form of modus tollens (...)”(Johnson-Laird 1986: 56).

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Hypothetical syllogism can be used to support a connecting premise that is not immediately acceptable to the listener. The cause of the initial unacceptability is the shortcut the speaker took in the defence of his point of view: as a direct premise he puts forward something that is acceptable to the listener, but seems to be unconnected with the standpoint at issue. By means of hypothetical syllogism this link is clarified, since an intermediate step is added.69

Finally, how does the logical operation of strengthening the antece-dent relate to conditionals fulfilling the role of a connecting premise? At first sight, strengthening the antecedent does not fit in with the context of argumentation at all. In conditionals that fulfil the role of a connecting premise, the antecedent contains the premise(s) put forward in support of a point of view, and the consequent contains the conclusion drawn from it. For instance, ‘Max can fly, since he is a bat’ has as a connecting premise the conditional ‘If Max is a bat, then he can fly’. In turn ‘It is dangerous to swim in that pool. It has been very hot these last days and the water is still’ has as a connecting premise ‘If it has been very hot these last days and the water is still, it is dange-rous to swim in that pool’ If only one premise is sufficient to draw the conclusion desired, there is no reason to add an extra premise. There is no need to replace single argumentation by coordinatively compound argumentation: it would only enlarge the burden of proof of the speaker, since he does not have to only commit himself to the truth of one premise, but of two premises. Although the logical operation of strenghtening the an-tecedent allows for it, there is no need to say something like ‘If Max is a bat and is a baby, Max can fly’. So why would one want to strengthen the antecedent? The answer might be that one indeed does not want to, but at times one may have to strengthen the antecedent. Let us assume that the

—————

69 The conditionals used as premises in the hypothetical syllogism are the con-necting premises in the following piece of argumentation.

Anthony: He cannot have stolen the bracelet

Beth: Why not?

Anthony: The shop was closed that day.

Beth: How do you know?

Anthony: January 30 is a public holiday.

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conditional ‘If Max is a bat, he can fly’ is used as a connecting premise. In that case, the speaker supports his standpoint ‘Max can fly’ by the direct premise ‘Max is a bat’. An opponent disagreeing with this point of view, can do two things to counter argue. He can either attack the direct premise (Max is not a bat), or he can attack the connecting pre-mise. In order to do the latter, he has to show that situation 3 depicted by Frege is the case: Max is a bat (the antecedent is true) but cannot fly (the consequent is false). Since the consequent contains the standpoint under discussion, just stating that Max cannot fly will not suffice: the protagonist will not accept this statement; he is of the conviction that Max can fly. Therefore, the only way in which the opponent can conclusively attack the connecting premise is by supporting the state-ment that Max cannot fly (for instance by putting forward the counter-argument that Max was born this morning). If the speaker wants to maintain his original argumentation, he has to show that this counter-argument is irrelevant, meaning that, he has to be able to show that ‘If Max is a bat and was born this morning, he can fly’ is true as well. If he cannot do that, he will have to concede that the original connecting premise was false or at least unwarranted. The logical operation of strengthening the antecedent reflects therefore that in argumentation the speaker is committed to ‘If A..., then ‘no matter what’ B’. A strong claim, but necessarily so, since otherwise it would be impossible to argue against the connecting premise.

In this section I have argued that there is good reason to suppose that the definition of material implication should be restricted to conditio-nals that fulfil the role of a connecting premise. Not only because there is a close correspondence between the four situations the definition describes and the four possible outcomes in the evaluation of argu-mentation, but also because the context of argumentation can enhance our understanding of the logical operations of contraposition, hypo-thetical syllogism and strenghtening the antecedent. The next step is to determine what characteristics a conditional sentence must possess in order to be able to fulfil the role of a connecting premise. Then a distinction can be made between conditional sentences to which the definition of material implication is applicable and sentences to which it is not.

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4.3 Characteristics of conditionals that function as a connecting premise

In order to establish what characteristics a conditional sentence must possess so that it can function as a connecting premise, let us turn once again to Frege’s definition of conditionals. He writes: ‘Wenn A und B beurtheilbare Inhalte bedeuten, so giebt es die folgende vier Möglichkeiten’ (1964:5). Apparently A and B must be ‘judgeable contents’, but what does Frege mean by that? The distinction between judgeable and not-judgeable content is described as follows:

Nich jeder Inhalt kann durch das vor sein Zeichen gesetzte [fig 12] ein Urtheil werden, z.B. nicht die Vorstellung “Haus”. Wir unter-scheiden daher beurtheilbare und unbeurtheilbare Inhalte**).**)Dagegen wäre der Umstand, dass es Häuser (oder ein Haus) giebt (vgl. § 12), ein beurtheilbarer Inhalt (1964: 2).

I take this to mean that the antecedent and the consequent must con-tain something that can be judged. ‘House’ cannot represent a judge-ment in that way: it is not clear what this judgement would mean, that is, it is not clear under which circumstances this judgement would be correct. ‘There are houses’, on the other hand, is a content that is judgeable; that can be judged. The context of argumentation can clarify what ‘judgeable content’ means. If we look at the role the conditional sentence plays, it beco-mes clear why this prerequisite of judgeable content is so important. The conditional sentence that functions as a connecting premise pas-ses truth /falsity from the direct premise to the standpoint at issue. Of course it can only do so, when the truth / falsity of the direct premise is established. Only if both the speaker and the listener have commit-ted themselves to the truth of B, can this truth by means of ‘If B, then A’ be transferred to the standpoint of A, so that doubt regarding this statement can be removed after all. Similarly, in the case of a conditio-nal that functions as a connecting premise in modus tollendo tollens, fal-sity can only be transferred to the standpoint not-B if both the speaker

—————

70 The term ‘felicitously asserted’ refers to John Searle’s speech act theory. The felicity conditions for the speech act of assertion have been described by Searle in Speech Acts. An essay in the philosophy of language (1969: 66-67).

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and the listener have committed themselves to the falsity of A. Both the antecedent and the consequent must therefore contain propositi-ons that one can commit oneself to. They must contain propositions that can felicitously be asserted or denied.70 In other words, the antece-dent and consequent need to contain what Frege calls a ‘Gedanke’. Sometimes it is quite difficult to judge whether the antecedent and consequent of a conditional contain a Gedanke. First of all, general conditionals can cause difficulties. In ‘Gedankengefüge’ Frege says:

‘Was ich über den Ausdruck “Wenn B, so A” gesagt habe, darf nich so verstanden werden, daß jedes Satzgefüge dieser Form ein hy-pothetisches Gedankengefüge ausdrücke. Wenn “A” für sich allein kein vollständiger Ausdruck eines Gedankens, also kein eigentli-cher Satz ist, oder wenn “B” für sich allein kein eigentlicher Satz ist, haben wir einen andern Fall. In dem Satzgefüge

“Wenn jemand ein Mörder ist, so ist er ein Verbrecher”

drückt weder der Bedingungssatz noch der Folgesatz für sich genommen einen Gedanke aus. Ob das, was in dem aus dem Zusammenhange gelöste Satze “Er ist ein verbrecher” ohne hin-zukommenden Wink ausgedrückt wird, wahr oder falsch sei, läßt sich nicht entscheiden, weil das Wort “er” keine Eigenname ist, sondern in dem aus dem Zusammenhange gelösten Satze ohne hinzukommende Wink nichts bezeichnet. Folglich drückt unser Nachsatz keinen Gedanken aus, ist also kein eigentlicher Satz. Dasselbe gilt von unserem Bedingungssatze; denn er enthält ei-nen Bestandteil – “jemand” – , der ebenfalls nichts bezeichnet (1993c: 84-85).

At first sight, clauses like ‘He is a criminal’ or ‘Someone is a murderer’ seem to contain judgeable content. But in fact – in the context given

—————

71 Of course this conditional can function as a premise in what is called a ‘generalized’ modus ponendo ponens. To my judgment, a generalized modus ponendo ponens is a shortcut description of a ‘normal’ modus ponendo ponens, that is, the step from ‘∀x: Fx→Gx’ to Fa→Ga is left implicit. If someone puts forward the standpoint Ga, the complete lay out of the argument would be something like: Ga (standpoint), since Fa (direct premise) and Fa→Ga (if-then premise). The if-then premise is in turn supported by ∀x: Fx→Gx’. This analysis is discussed in depth in section 4.4.

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by the general conditional – there is no person to whom ‘he’ refers, and therefore it is not possible to decide whether ‘he is a criminal’ is true or false. The same goes for ‘someone is a murderer’, that – within this context – does not express ‘there is someone who is a murderer’. Therefore, neither the antecedent nor the consequent of the conditio-nal sentence ‘If someone is a murderer, then he is a criminal’ contains a Gedanke: the conditional sentence cannot be seen as a hypothetisches Gedankengefüge and as a result it cannot function as a connecting premise.71 It can be difficult to decide whether a conditional sentence should be seen as a general conditional or not. Consider sentence 89:

89 If it is over 25°C, there are about 5000 people at this beach.

This conditional sentence is ambiguous. It can be interpreted as a general statement, as in ‘Normally, if it is over 25°C, there are about 5000 people at this beach’, where the antecedent and consequent do not contain judgeable content. But 89 can be interpreted as a singular statement as well. Suppose someone wants to defend the point of view that there are currently about 5000 people at the beach, by means of the direct premise that it is currently over 25°C. In this context the antecedent and the consequent of the conditional in 89 do contain judgeable content: it can be checked whether ‘it is currently over 25°C’ as it can be checked whether ‘there are currently about 5000 people at the beach’.

Although Frege mentions only general conditionals, I think there is another category of conditionals that may at first seem but in fact do not (and cannot) represent a hypothetisches Gedankengefüge. The condi-tional sentence in 90 – where the consequences of a proposed course of action are sketched – represents a case in point:

90 We should pay off our debts, because if we pay off our debts, we don’t have to pay interest anymore.

‘We pay off our debts’ and ‘we don’t have to pay interest anymore’ seem to be propositions that can be judged to be either true or false. We even know what the judgement should be: both propositions are false. It is not true that ‘we pay off our debts’, since that is the situa-tion the protagonist wants to achieve. The same goes for the conse-quent: interest has to be paid since the beneficial situation where ‘we

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don’t have to pay interest anymore’ has not (yet) been realized. However, the propositions ‘we pay off our debts’ and ‘we don’t have to pay interest anymore’ do not express the same as the antecedent and the consequent of the conditional in 90. If we judge propositions to be true or false, we add what Frege calls a ‘Zeitbestimmung’: we consider whether we ‘pay off our debts’ / ‘don’t have to pay interest anymore’ is true at the moment of speaking.72 The antecedent and consequent in the conditional in (90) both lack such a Zeitbestimmung – the sentence does not tell us at which moment ‘we pay off our debts / don’t have to pay interest anymore’ is to be judged true or false. As a result, the antecedent and consequent cannot be considered to contain a Gedanke in Frege’s sense of the word. And since the antecedent and consequent do not contain a Gedanke, the conditional does not represent a hypothetisches Gedankengefüge and cannot function as a connecting premise. Conditionals like the one in 90 can be characterized as belonging to the class of conditionals that Dancygier calls ‘predictive’.73 It is characteristic of predictive conditionals that the antecedent contains backshift: although in 90 the antecedent refers to a future situation, the present tense is used. Another example of a predictive conditional is 41:

—————

72 Cf. Frege (1993a: 52): ‘Aber gibt es nicht auch Gedanken, die heute wahr sind, nach einem halben Jahre aber falsch? Der Gedanke z.B., daß der Baum dort grün belaubt ist, ist doch wohl nach einem halben Jahre falsch? Nein; denn es ist gar nicht derselbe Gedanke. Der Wortlaut “dieser Baum ist grün belaubt” allein genügt ja nicht zum Ausdrucke, denn die Zeit des Sprechens gehört dazu. Ohne die Zeit-bestimmung, die dadurch gegeben ist, haben wir keinen vollständigen Gedanken, d.h. überhaupt keinen Gedanken. Erst der durch die Zeitbestimmung ergänzte und in jeder Hinsicht vollständige Satz drückt einen Gedanken aus.’73 The distinction Dudman makes between conditionals, like sentence 41, and compounds, like sentence 33 ‘If Socrates is a man, Socrates is mortal’ seems to be of value here as well. According to Dudman, a compound like 33 is an if-sentence that is built from the two prior messages ‘Socrates is a man’ and ‘Socrates is mortal’. Compounds can therefore be seen as a hypothetisches Gedankengefüge. On the other hand, a conditional like sentence 41, is not built from two prior messages but is a subject-predicate sentence with a rather elaborate and complex predicate. In 41 the subject would be ‘the match’ and the predicate ‘will be cancelled if it rains’. Sen-tence 41 therefore does not contain two, but only one Gedanke. The difficulty with Dudman’s approach is however that he does not make clear why sentence 33 should not be seen as a subject-predicate sentence in which the subject is ‘Socrates’ and the elaborate predicate ‘is mortal if he is a man’.

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41 If it rains, the match will be cancelled.

Since the antecedent contains backshift, in 41 the antecedent seems – like the antecedent in 90 – to contain judgeable content: one can judge whether ‘it rains’ or not.74 But again, judging the proposition ‘it rains’ is not the same as judging the antecedent of the conditional sentence: participants in a dialogue using this conditional are not interested in whether it rains right now – which one evaluates in judging whether the proposition ‘it rains’ is true – but whether it rains at some indeter-minate time in the future. The antecedents of predictive conditionals like the one in 41 – lack a Zeitbestimmung as well.75 As a result, the antecedents of predicative conditionals do not contain a Gedanke, predi-cative conditionals do not represent a hypothetisches Gedankengefüge and cannot function as a connecting premise. One might say that by this strict interpretation of what a Gedanke is, I have extensively limited the use of reasoning and argumentation. Predictive conditionals typically reflect on the future (when in the indi-cative mood) or on what could have been different in the past (when in the subjunctive mood). By arguing that predictive conditionals cannot function as a connecting premise, it may look like I contend one can only discuss the here and now. But future happenings are not excluded from argumentation, as can be seen from the following example:

91 We can take it easy now, since we will miss the next train anyway.

In 91 the protagonist defends his claim ‘we can take it easy now’ by me-ans of the direct premise ‘we will miss the next train anyway’. Although this premise speaks of a situation that will take place in the future, it

—————

74 That the speaker is not referring to actual time is indicated by the tense used as well. A speaker who wants to refer to actual time would use the present continu-ous ‘It is raining’ and not the present simple ‘it rains’.

75 One could argue that the Zeitbestimmung in 41 is implied, and that the ante-cedent actually should read ‘If it rains at the time the match takes place, the match will be cancelled’. However, I doubt that it is correct to limit the interpretation of this sentence in this way. The conditional could just as well mean ‘If it rains 10 minutes before the match is scheduled, it will be cancelled’ or ‘If it rains during the first 20 minutes, the match will be cancelled’ (and – being indeterminate – perhaps it could even have all these interpretations at the same time...).

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can be accepted as true or rejected as false here and now. Suppose the train referred to leaves in ten minutes from the moment the discussion takes place. Moreover, suppose the participants engaged in the discussion know that it will take them at least twenty minutes to get to the railway station. In that context, the direct premise ‘We will miss the next train anyway’ would be judgeable. The antagonist may accept this premise and agree on taking it easy, or he may not accept the direct premise and say something like ‘You never know, the train may be delayed, let’s hurry anyway.’ He even can accept the direct premise and still reject the standpoint, i.e. when he says: “we still have to hurry, otherwise we might even miss the next one after this.” In that case, the antagonist rejects the connecting premise. Now what is the connecting premise in case of 91? The conditional sentence we have to add in order to make the reasoning deductively valid is expressed in 92:

92 If we will miss the train anyway, we can take it easy now.

The antecedent of 92 contains the same proposition as the direct premise and the consequent contains the same proposition as the standpoint. I would say both the antecedent and the consequent of this conditional do contain a Gedanke in Frege’s sense of the word. But then again, this conditional sentence differs from the one in 41. It is not a predictive conditional since the one decisive characteristic of predictive conditionals is absent – the antecedent does not contain backshift.76 The time referred to in the antecedent coincides with the time actually referred to: the future.77

Not only predictive conditionals concerning the future are excluded from usage as a connecting premise, it is also the case for predictive conditionals in which one reflects on what could have been different in the past. If we take another look at sentence 43:

43 If it had rained, the match would have been cancelled.In 43 the speaker considers what would have happened if the past had been different – if it had not been dry like it in fact was, but had rained. Like 41, 43 represents a predictive conditional. The antecedent

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76 I think this is what Dudman refers to when he writes: ‘...witness the diffe-rence between saying “If we miss the last bus, (we will have to walk)” and saying “If we will miss the last bus, (there’s no point in our running)”’ (1988: 7).

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is backshifted, since the past perfect is used although there is no refe-rence to a pre-past situation. Being a predictive conditional, 43 cannot function as a connecting premise. This is not to say that counterfactuals in general can not express a hypothetisches Gedankengefüge. In fact, we already saw one example of a counterfactual conditional that functioned as a connecting premise, the conditional in 87:

87 Daniel is no athlete. If he were an athlete, he would have stamina. But he can’t climb the stairs without losing his breath.

The conditional in 87, though ‘counterfactual’ does express two thou-ghts, the first being ‘Daniel is an athlete’ and the second ‘Daniel has stamina’. To be sure, in this conditional the subjunctive is used, but the subjunctive mood just serves to indicate that the speaker wants to distance himself from the possible truth of those two propositions. Which is far from unusual, since he explicitly indicates that ‘Daniel is an athlete’ is false and he supports the claim that ‘Daniel does not have stamina’ by pointing out that he can’t climb the stairs without losing his breath. The situation would have been different if the speaker had phrased the conditional as follows:

93 If Daniel had been an athlete, he would have had stamina.

The conditional in 93 is a predictive conditional: the speaker predicts what the situation would have been like if the present situation was different: Daniel is not the same old lazy person that we know, but an athlete. The predictive nature of the conditional causes the first back-shift in time: instead of the present tense the past tense is used. But since the speaker also distances himself from the truth / likelihood

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77 Contrary to what is often thought, ‘will’ is allowed in ‘if’-sentences. In the text book Advanced Grammar in Use one can read for instance: ‘We don’t use ‘if...will’ in conditionals. However, we can use ‘if...will’ when we talk about a result of so-mething in the main clause. ‘If it will help you to sleep, you can open the window’ (‘Helping you to sleep’, is the result of opening the window.)” (Hewings 1999: 200). In this example, the causal order is reversed: the antecedent contains the effect and the consequent the result. It might not be just a coincidence that conditionals where the causal order is reversed allow for ‘will’ in the antecedent, since such conditionals typically reflect reasoning.

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of the situation, time is backshifted once more, resulting in the past perfect tense. Therefore 93 does not represent a hypothetisches Gedan-kengefüge and hence it cannot be used as a connecting premise.

The prerequisite that both the antecedent and consequent represent a Gedanke excludes two types of conditional sentences from being used as a connecting premise. First of all, general conditionals like ‘If some-one is a murderer, he is a criminal’ are excluded. In the case of general conditionals neither the antecedent nor the consequent contains a Gedanke, since there is no entity to which ‘someone’ and ‘he’ refers to. As a consequence, it cannot be established whether ‘someone is a murderer’ and / or ‘he is a criminal’ is true or false. Secondly, predic-tive conditionals are excluded since the antecedent and consequent of those conditionals lack a Zeitbestimmung. Those two categories of conditionals that ‘may seem at first but do not in fact’ represent a hypothetisches Gedankengefüge can shed light on the counter-examples against hypothetical syllogism and contraposi-tion. Against hypothetical syllogism the following counter-examples were put forward:

12 If Brown wins the election, Smith will retire to private life. If Smith dies before the election, Brown will win it. So if Smith dies before the election, Smith will retire to private life.

13 If it had snowed, I would have gone skiing. If there had been a blizzard, it would have snowed. So if there had been a blizzard, I would have gone skiing.

It is clear why in 12 hypothetical syllogism yields undesirable results. Not one of the conditional sentences used is a conditional that can be employed as a connecting premise, since the conditionals are all predictive conditionals. In 13, the first conditional cannot be used as a connecting premise. Not because it is a counterfactual statement, but because it is a counterfactual statement of a specific kind. When the statement is rewritten in a non-counterfactual way, we get ‘if it snows, I will go skiing’, which is a predictive conditional again. Also when we look at 16, the example Stalnaker and D. Lewis use to show why transitivity fails, we see that in this logical operation as well, conditional sentences are used that do not represent a hypothetisches Gedankengefüge:

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16 If J. Edgar Hoover had been born a Russian, then he would have been a communist.If he had been a communist, he would have been a traitor.Therefore: If he had been born a Russian, he would have been a traitor.

The first conditional in 16 is a predictive conditional: the speaker reflects on how matters might have been different if the past had not been as we know it. It therefore does not make sense to engage it in the logical operation of transitivity. In the following counter-example against contraposition the pre-requisite of judgeable content is not met either.

11 If the U.S. uphold subvention, then the European Union will not agree to negotiate.

In sentence 11 the consequences of a proposed action are discussed: the consequent of this predictive conditional expresses (undesirable) consequences that will occur when the U.S. in the (near) future deci-des to uphold subvention.78

If a conditional does represent a hypothetisches Gedankengefüge, it can in principle function as a connecting premise in argumentation. However, for it to be applied succesfully as a connecting premise in a particular instance, something more is needed. If it is to be used as a connecting premise in a modus ponendo ponens, both the speaker and the listener must be able to commit themselves to the proposition expressed in the antecedent. To put it in Davies’ words, the antecedent has to contain accepted knowledge. If the speaker does not commit himself to this proposition, he cannot assert it and therefore cannot use it as a direct argument. If the listener does not commit himself to this proposition, it cannot function as a common starting point and therefore the doubt the listener has concerning the standpoint will not be removed. If the connecting premise is to be used in a modus tollendo tollens, both the speaker and the listener must be able to commit themselves to the contradictory of the proposition expressed in the consequent. In

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78 For a discussion of the evaluation criteria applicable to this kind of conditio-nal, see section 6.2.

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that case, it must be accepted knowledge that the proposition expres-sed in the consequent is false. If the speaker does not commit himself to the falsity of this proposition, he cannot put the contradictory of it forward as a direct premise in support of his point of view. If the liste-ner does not commit himself to the contradictory of this proposition, he will not accept the direct premise put forward and therefore he will not become convinced of the standpoint under discussion. Whether the speaker and listener will commit themselves to the proposition expressed in the antecedent or the contradictory of the proposition expressed in the consequent, is dependent upon their personal positions. Yet sometimes it is clear from the outset that such commitment is unlikely or even impossible. For example, this is the case for conditionals such as 10:

10 If it did rain, it did not rain heavily.

In this sentence the antecedent is of a concessive nature. Such a con-cessive conditional can be used in a conditional defence like 10’:

10’ It did not rain, the streets were dry. And if it did rain, it did not rain heavily.

In this context it becomes clear that the speaker does not want to commit himself to the statement that it did rain (as he would, if the conditional functioned as a connecting premise in a modus ponendo ponens). Not to speak of the fact that he would want to commit himself to the statement that it did rain heavily (as he would if the conditional functioned as a connecting premise in a modus tollendo tollens). Conditionals derived in the ‘paradoxes of material implication’ will not be used as connecting premises since the necessary commitment on either the truth or falsity of the component propositions is impos-sible for both the antagonist and the protagonist. According to the de-finition of material implication, one can infer ‘if p, then q’ from either the confirmation of the consequent or the denial of the antecedent. Both 94 and 95 are therefore true.

94 If Aristotle is born in 384 BC, then Frege is born in 1848.

95 If Frege is born in 1748, then Aristotle is born in 384 AD.

94 is true, since it is true that Frege is born in the year 1848; 95 is true

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since it is false that Frege is born in 1748. Although these two conditionals are true according to the definition of material implication, they are not acceptable when the role they are meant to fulfil in a discussion is taken into account. A speaker who wants to use these conditionals as a connecting premise will never be able to convince the other party of the truth of the standpoint he maintains. Let us assume that 94 is a connecting premise in a mo-dus ponendo ponens. In that case, the antecedent contains the direct premise and the consequent contains the standpoint defended. The argumentation has the following structure:

1.

Frege is born in 1848

↑

1.1 1.1’

[Aristotle is born in 384 BC] – & – if Aristotle is born in 384 BC,

Frege is born in 1848

At first sight nothing seems to be wrong here: when the premises are accepted, the conclusion (and hence the standpoint) can be accepted as well. Moreover, there is no reason to doubt the direct premise. But when the other party questions the connecting premise, the speaker will have difficulty in defending it. The reason he has for maintaining this premise is that Frege is born in 1848, which is the same as the standpoint he tries to defend (and is questioned by the other party). Therefore, a connecting premise deduced from the truth of the conse-quent cannot be used in modus ponendo ponens since that would lead to circular reasoning. A conditional derived from the truth of the consequent can also not be used as a connecting premise in modus tollendo tollens. A prota-gonist using a conditional like 94 is committed to the truth of the consequent, after all, it is the truth of the consequent that has made him consider the conditional to be true. However, in order to use this conditional in modus tollendo tollens, he has to commit himself to the falsity of this consequent – only then he can through modus tollendo tollens conclude that the antecedent is false as well. A protagonist using a conditional derived from the truth of the consequent as a con-necting premise in modus tollendo tollens would therefore contradict himself: he would commit himself both to the truth and the falsity of a proposition. A connecting premise deduced from the falsity of the antecedent

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also cannot be used to make a point of view acceptable. Using this connecting premise in a modus tollendo tollens would lead to circularity: it would be used to prove the falsity of the antecedent whereas the falsity of the antecedent is the ground for maintaining the connecting premise. Excercising it in modus ponendo ponens would lead to a con-tradiction. The speaker will be committed to the falsity of the antece-dent since that is the ground for maintaining the conditional whilst he commits himself to the truth of the antecedent in order to prove that the consequent of the conditional (the standpoint under discussion) is true. Although the definition of material implication allows for dedu-cing conditional sentences from the truth of the consequent or the falsity of the antecedent, these conditionals cannot be put to use as a connecting premise in the defence of a point of view. As Johnson has explained:

The solution of the paradox is therefore found in the consideration that though we may correctly infer an implicative from the denial of its implicans, or from the affirmation of its implicate, [...], yet the implicative,[...] so reached cannot be applied for purposes of further inference without committing the logical fallacy either of contradiction or circularity’ (1921: 42).

In this section I have defended the view that only conditional senten-ces that contain a Gedanke in both the antecedent and the consequent can function as a connecting premise. Furthermore, conditionals only will be used as a connecting premise if it is possible for both the speaker and the listener to commit themselves to either the truth of the proposition expressed in the antecedent or to the falsity of the proposition expressed in the consequent. The next step will be to formulate evaluation criteria for conditionals used in this way. Under what circumstances will such sentences be acceptable to the listener? But before I do so, let me respond to two objections that may be put forward against the way I have characterized connecting premises in this paragraph. First of all, one may disagree with the prerequisite of judgeable content. As a result of this prerequisite the characterisation of a connecting premise offered in this section is contrary to a common interpretation of unexpressed premises in the field of argumentation theory. The connecting premise as I described it can be equated with what Van Eemeren and Grootendorst call the logical minimum. They

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describe the logical minimum as follows:

The logical minimum is the premise that consists of the ‘if..., then...’ sentence that has as its antecedent the explicit premise and as its consequent the conclusion of the explicit argument (Van Eemeren & Grootendorst 1992: 64).

According to Van Eemeren and Grootendorst, the logical minimum cannot be adjudged as being the unexpressed premise.79 They replace it with what they call the pragmatic optimum: a statement that is more informative than the logical minimum but one that can still be deter-mined as something the speaker committed himself to in advancing a particular premise in support of his standpoint. As an example of the relationship between logical minimum and pragmatic optimum they use the following of argument (2a is the logical minimum and 2b is the pragmatic optimum)(1992: 64):

(1) Angie is a real woman

(2a) If Angie is a real woman, she is nosy. (2b) Real women are nosy.

(3) Therefore: Angie is nosy

In this example, the specific ‘if..., then...’-statement is replaced by a general statement, that could be rewritten as a general conditional ‘If someone is a real woman, she is nosy’.80

Van Eemeren and Grootendorst replace the logical minimum with the pragmatic optimum for the following reason:

Pragmatically, this [adding the logical minimum–jmg] is not enou-

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79 Van Eemeren and Grootendorst are not the only ones who maintain the view that the unexpressed premise should be something ‘more’ than just the premise that makes the reasoning logically valid. Hitchcock for instance claims that the unexpressed premise is a specific universal generalisation of the if-then sentence containing the premise in the antecedent and the conclusion in the consequent (1987: 83).

80 Generalisation is not the only way to make an unexpressed premise more informative, depending on the context, the pragmatic optimum can also be arrived at in other ways.

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gh. From the very fact that he advances this particular argumenta-tion for his standpoint it is already clear that the speaker assumes that this conclusion follows from this premise. The logical mi-nimum contributes nothing new, and is, therefore, superfluous. Identifying this logical minimum as the unexpressed premise me-ans that a violation of the third rule of communication [be efficient – jmg] is unnecessarily ascribed to the speaker (Van Eemeren & Grootendorst 1992: 64).

In my opinion, there is no reason not to equate the connecting pre-mise with the logical minimum. To be sure, the logical minimum is ‘implied’ by explicitly putting forward the direct premise and drawing the conclusion from it: in order to make the reasoning logically valid the logical minimum has to be added. That is why the speaker can leave the connecting premise (or the direct premise, or the stand-point) implicit (perhaps in order to avoid a violation of the third rule of communication). It is peculiar to claim that the analyst attributes such a violation to the speaker when making the unexpressed premise explicit.81 More importantly however, Van Eemeren and Grootendorst con-cede that ‘there are contexts where the analyst is forced to consider the logical minimum to be the pragmatic optimum’ (Van Eemeren en Grootendorst 1992: 66). This can for instance be the case when a point of view is supported by an elaborate coordinatively compound argumentation. If the pragma-dialectical analysis is correct, then the speaker in such contexts would necessarily be guilty of a violation of the Cooperative Principle, which would be odd, given that the argu-mentation in such cases can be perfectly acceptable. Finally, the analysis Van Eemeren and Grootendorst provide is problematic when the speaker does not leave the connecting premise implicit, but the standpoint, as in 86:

86 If it rains, there is no reason to water the plants. And it is pouring.

If we reason along the same lines, completing the reasoning by adding the standpoint ‘therefore, there is no reason to water the plants’ would lead to a violation of the third rule of communication. After all, the

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81 Cf. Krabbe (1985: 65-71).

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standpoint left unexpressed would be implied by putting forward the direct premise in combination with the connecting premise. It is hard to see how the logical minimum could be replaced by a pragmatic optimum in such a case.

A second objection that could be directed against the way connecting premises are characterised in this chapter would be that having a Gedanke in the antecedent and the consequent is not sufficient for a conditional to be able to fulfil the role of a connecting premise. Should there not be another prerequisite as well, such as a connection between the antecedent and the consequent? From my point of view, authors who claim there should be a connection, confuse the asser-tion of a conditional sentence with the grounds one has for asserting it, i.e. there is a difference between stating that where ‘either one of the situations 1, 2 or 4 does occur, situation 3 does not occur’ and the grounds or reasons one has for making that claim. A conditional like ‘If it is summertime, my father’s bookcase is full up’ can be used as a connecting premise: the proposition in the consequent could be a standpoint, the one in the antecedent could be a direct premise. Whether this connecting premise is acceptable to the listener is quite another matter. The question as to how it’s acceptability should be as-sessed, will be taken up in the next section.

4.4. The evaluation of connecting premises

Until this point, I have argued that the definition of material implicati-on is applicable to conditionals that function as a connecting premise. The conclusion that might be reached is that for one category of condi-tionals evaluation criteria are formulated: conditionals that function as a connecting premise are acceptable whenever they are true according to the definition of material implication, and unacceptable when they are false. However, the context of argumentation – though helpful as it has been – seems to be less rewarding confronting this issue. In the context of argumentation, it cannot be assessed whether a conditional is true according to the definition of material implication or not. To be able to perform this act, one should know whether the propositions expressed in the antecedent and the consequent are true or false. It only may be possible for one of these propositions – namely for the proposition put forward as the direct premise – but the other proposi-tion cannot be assessed in this manner. It was the controversy over the

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truth or falsity of the proposition that is expressed in the standpoint which created the need for argumentation in the first place. In order to establish the acceptability of a conditional sentence that functions as a connecting premise, one has to resort to something other than the definition of material implication. Fortunately, the field of argumentation theory provides an answer to what this something other may be. A part of the study of argumentation has been directed toward the notion of an argument scheme. An argument scheme is – like a logical form – an abstract entity that specifies the relationship between the direct premise and the standpoint. Van Eemeren and Grootendorst define this notion as follows:

Argument schemes pertain to the kind of relationship between the explicit premise and the standpoint that is established in the argumentation in order to promote a transfer of acceptability from the explicit premise to the standpoint. Argument schemes are more or less conventionalized ways of achieving this transfer (Van Eemeren & Grootendorst 2004: 4).

There are different ways in which the direct premise can be related to the standpoint. Sometimes a speaker bases his argumentation on a comparison, as in 96

96 €500.000,- is a reasonable price for this apartment. The apartment three doors down the street has sold for €500.000,- as well.

The price of €500.000 is considered to be reasonable because a simi-lar apartment has been sold for that price. A speaker can also use what Van Eemeren and Grootendorst call ‘symptomatic argumentation’, like in 97.

97 Emile does not eat macaroni and cheese, since he is a snob.

Here the direct premise and the standpoint are connected in a diffe-rent way. Not eating macaroni and cheese is seen as characteristic for snobs. Since Emile is a snob, the conclusion is drawn that he does not eat macaroni and cheese. From the point of view of argumentation theory, it is important to assess what kind of argument scheme is used. In relation to an argument scheme critical questions are formulated by means of which

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the argumentation put forward can be evaluated. In the case of 96, one of the critical questions that can be posed is ‘are there significant dif-ferences between the case sketched in the direct premise and the one sketched in the standpoint?’ If the apartment three doors down the street has a view of the park, then the comparison fails. Significant dif-ferences are not relevant in the case of 97. In that case one might look for an example of someone who is a snob but does eat macaroni and cheese.

Since argument schemes are concerned with the relation between the direct premise and the standpoint, and it is this relationship that is ex-pressed in the connecting premise, it seems reasonable enough to as-sume that the critical questions connected with the various argument schemes can be used to evaluate conditionals that function as a con-necting premise. However, at first glance it is not quite clear to what these critical questions are directed toward. Let us take a closer look at example 97. The argumentation used can be analysed as follows:

1.

Emile does not eat macaroni and cheese

↑

1.1 1.1’

he is a snob – & – [if Emile is a snob,

he does not eat macaroni and cheese]

Now how can an example of someone who is a snob and does eat macaroni and cheese affect the argumentation put forward? In the argumentation, the only person dealt with is Emile. In my opinion, the criticism contained in the counter-example is directed at something that is unexpressed. It is not aimed at the con-necting premise but at the ground the speaker has for maintaining the connecting premise. The speaker considers the connecting premise to be justified on the basis of the general statement that ‘snobs do not eat macaroni and cheese’ and it is this general statement that is attacked

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82 If I were to use Van Eemeren and Grootendorst’s words, I would say: ‘the pragmatic optimum supports the logical minimum.’ This analysis justifies the explication of the pragmatic optimum: the analysist is allowed to reconstruct it, not so much because the logical minimum is uninformative, but since the speaker can be expected to have acceptable grounds for the connecting premise. Contextual clues could give the analyst information on the kind of ground the speaker has for asserting the connecting premise.

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by the counter-example.82 The complete structure would be:

1.

Emile does not eat macaroni and cheese

↑

1.1 1.1’

he is a snob – & – [if Emile is a snob,

he does not eat macaroni and cheese]

↑

1.1’1

[snobs do not eat macaroni and cheese]

A speaker can have various grounds for maintaining a connecting premise. In 97 the general statement ‘snobs do not eat macaroni and cheese’ is the ground for ‘If Emile is a snob, he does not eat macaroni and cheese’. In 96 ‘the two apartments are comparable’ is the ground for maintaining that ‘if the apartment three doors down the street has been sold for €500.000,-, €500.000,- is a reasonable price for this apartment. I would claim that it is important to make a distinction between the connecting premise and the grounds one has for main-taining this premise. In this analysis, the connecting premise is a pre-mise like all others. This means that the evaluation of such premises can proceed along the line in which other premises are evaluated: if a connecting premise is challenged, the speaker will have to support it, or retract it. The ground put forward in support of the connecting premise can subsequently be criticised by showing that the ground is untrue, or by showing that the ground does not justify the conclusion that the connecting premise is true. This last way of criticizing is of special interest, since it gives the op-portunity to accept the ground and still reject the connecting premise. In such cases, one can accept the general rule, but deny that – or question whether – this general rule is applicable in a specific case. If we take the following dialogue:

98 Tony: Max can fly.Bob: How do you know?Tony: Bats can flyBob: Max can’t fly, his wings are torn.

Analysed in the traditional way, the argumentation structure which is reflected in this dialogue would be:

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1.

Max can fly

↑

1.1 1.1’

[he is a bat] – & – bats can fly

The criticism put forward by Bob can be seen as directed only at the pragmatic optimum ‘Bats can fly’. The direct premise is accepted, whereas the conclusion is rejected. Therefore, the second premise must be rejected and ‘Bats can fly’ must be retracted. When the pragmatic optimum is seen not as the connecting premise but as the ground for the truth of the connecting premise, the con-sequences of Bob’s criticism are less serious. In this analysis, the argumentation has the following structure:

1.

Max can fly

↑

1.1 1.1’

[he is a bat] – & – [if Max is a bat, he can fly]

↑

1.1’.1

bats can fly

Bob accepts that Max is a bat. He does not want to commit himself to the connecting premise ‘If Max is a bat, he can fly’. The torn wings confirm that the antecedent of this conditional is true whereas the consequent is false, and therefore the conditional is false. In this ana-lysis, it does not mean that he has to reject the general statement ‘bats can fly’. He can maintain this statement, whilst denying that from this general statement the particular statement ‘If Max is a bat, Max can fly’ can be deduced. The criticism is directed not at the general statement that forms the ground of the connecting premise, but at the connection between this general statement and the specific conditio-nal statement that functions as a connecting premise. If we look at ‘appeal to authority’ (one of the argument schemes that has been discussed elaborately in the literature) we find that the criti-cal questions can indeed be perceived as being directed either at the ground for the connecting premise or at the connection between this ground and the connecting premise. In 99 the protagonist supports his claim by means of an appeal to authority:

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99 As can be seen from Dr. Baumann’s book on the countries and people of Africa, the Nyimang know their own language.

The argument structure of 99 can be represented as follows:

1.

The Nyimang know their own language

↑

1.1 1.1’

Dr. Baumann says so – & – [if Dr. Baumann says in his book

in his book on the on the countries and people of Africa

countries and people of that the Nyimang know their own language,

Africa then the Nyimang know their own language]

↑

1.1’1

[Dr. Baumann is an authority]

For the evaluation of an appeal to authority, the following critical ques-tions have been proposed: 83

(a) Is the authority quoted correctly? (b) Is the quoted authority a specialist in the field? (c) Is the quoted authority unbiased? (d) Is his knowledge up-to-date? (e) Is there consensus in the field? (f) Is the field an acknowledged field of knowledge?

The first of these critical questions is not directed at the connecting premise but at the direct premise. By asking whether the authority is quoted correctly, one asks ‘is it true that Dr. Baumann says so in his book on the countries and people of Africa?’. Questions (b) and (d) are directed at the ground for the connecting premise, aimed at esta-blishing whether Dr. Baumann can indeed be called an authority.

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83 This list of critical questions is by no means meant to be exhaustive, I use it only to illustrate how different critical questions are related to different parts of the argument structure. For more information on critical questions that can be posed in the case of an appeal to authority, see Schellens (1984), Kienpointner (1992), Walton (1997), Groarke & Tindale (2004).

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Questions (c), (e) and (f) question the connection between the con-necting premise and the ground the protagonist has to maintain it. They are not aimed at challenging the authority of Dr. Baumann, but question whether his authority is sufficient to guarantee that what he says is true. If Dr. Baumann is biased, what he says might not be trust-worthy. If another authority claims the opposite and therefore there is no consensus in the field, it is not clear why one would prefer Dr. Baumann’s opinion over that of the other expert. If Dr. Baumann is an authority in a ‘self-proclaimed’ field, this again would not guarantee that what he says is true.84

Within the field of argumentation theory there is no consensus on how many argument schemes must be discerned and there is no consensus as to which critical questions are related to the various argument schemes. Therefore, I can not provide a complete set of evaluation criteria for conditionals that function as a connecting pre-mise. But I hope that this section may provide an indication of where to look: to evaluate a connecting premise, one should try to determine what ground the protagonist has for maintaining it. In some cases, one can use contextual information to identify the argument scheme used.85 In other cases, one may have to directly ask the protagonist. But once one knows what the ground for the connecting premise is, one can evaluate whether the connecting premise is acceptable. It will be acceptable when the antagonist can both accept the ground and the connection between the ground and the connecting premise.

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84 This criticism is not directed at the ground, since one does not question whether Dr. Baumann is in fact an authority in this self-proclaimed field. One just wonders whether being an authority in this self-proclaimed field justifies the con-clusion that what Dr. Baumannn says on the subject matter is in fact true.

85 For an overview of the contextual information that can be used, see Van Eemeren, Houtlosser & Snoeck Henkemans (2007).

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4.5 Conclusion

In this chapter, I have tried to show that although the definition of material implication and the logical operations contraposition, hypo-thetical syllogism and strenghtening the antecedent may yield akward results when applied to certain ‘if’-sentences, nevertheless, this does not mean they need to be discarded. On the contrary, the definition of material implication and the logical operations connected with it reflect accurately what may occur if one tries – by means of argumen-tation – to convince someone of the acceptability of a point of view . In this process, conditional sentences do play an important role, since they can function as a connecting premise. They either transfer the truth / acceptability of the Gedanke expressed in the direct premise to the Gedanke expressed in the standpoint (in the case of modus po-nendo ponens), or transfer the the falsity of the Gedanke expressed in the direct premise to the Gedanke expressed in the standpoint under discussion (in the case of modus tollendo tollens). Looking at the definition of material implication from the perspec-tive of argumentation also may clarify the confusion that has arisen concerning the paradoxes of material implication. In discussing those paradoxes the focus has been on either the truth of the consequent (when the conditional is true according to the definition of material implication just because the consequent is true) or the falsity of the antecedent (when the conditional is true according to the definition of material implication just because the antecedent is false). When one takes into account the function these conditionals are me-ant to fulfil in argumentation, one sees that this focus is mistaken. For the indicative conditionals that the definition of material implication is meant to represent (the ones functioning as a connecting premise in modus ponendo ponens), it is not important for the consequent to con-tain a ‘truth’. In fact, by definition, the consequent does not contain an accepted ‘truth’, since the proposition in the consequent is what needs to be proved: the consequent contains the claim that is defended.

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86 It is because of this agreement on the falsity of the consequent (and of the speaker’s commitment to the falsity of the antecedent), that a conditional func-tioning as a connecting premise in a modus tollendo tollens is always a subjunctive conditional: in the context of use the speaker is committed to the negation of the propositions expressed in the antecedent and consequent; cf section 4.2.

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What is important is that the antecedent contains a proposition both participants in the discussion can agree on. For the subjunctive condi-tionals that the definition of material implication is meant to repre-sent (the ones functioning as a connecting premise in modus tollendo tollens), the focus should not be on the falsity of the antecedent. The falsity of the antecedent is by definition not established – since in a modus tollendo tollens that is what needs to be proved. In a subjunctive conditional, the focus should therefore be on the common agreement concerning the falsity of the consequent.86

Finally, the context of argumentation can explain why ‘if’- sentences can only function as a connecting premise when certain prerequisites are met. The antecedent and consequent need to contain something that can be either asserted or denied, so that the same content (or its negation) can be put forward as a direct premise and standpoint. For that reason, both the antecedent and the consequent should contain a Gedanke – something that is judgeable, something of which one can determine whether it is either true or false (or accepted to be true or false).87 The conditional should represent (or: should have at least one interpretation in which it represents) a hypothetisches Gedanken-gefüge. With this prerequisite in mind, well-known counter-examples against contraposition and hypothetical syllogism can systematically be explained away: the conditionals used in these examples do not represent a hypothetisches Gedankengefüge but are predictive conditio-nals. As a result, these conditionals cannot function in those logical operations.88

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87 ‘It is true / false’ may refer too much to ‘brutal facts’ like ‘Frege was born in 1848’. I think ‘This book is well-written’ does express a Gedanke as well and a condi-tional like ‘If this book is well-written, you should buy it’ can be seen as a hypothetis-ches Gedankengefüge.

88 One well-known counter-example against contraposition has not been discus-sed: I did not explain why a sentence like 9 ‘If you would appreciate it, I could ask the manager for a special discount’ cannot be subjected to contraposition. Both clauses seem to contain assessable content: it can be decided whether the proposi-tions ‘You would appreciate it’ and ‘I could ask the manager for a special discount’ are true. It is clear however, that it does not make sense to interpret these sentences as a connecting premise; it is akward to say ‘I could ask the manager for a special discount, because you would appreciate it.’ In these instances the antecedent contains a condition that has to be met in order for the speech act expressed in the consequent to be carried out. Examples like 9 that are argumentatively used, are discussed in section 5.2.

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To limit the applicability of the definition of material implication to conditionals that function as a connecting premise means of course that ‘if-sentences’ that cannot function as a connecting premise now lack evaluation criteria. In the next chapters I will try to formulate evalution criteria for conditionals that fulfil a different function in argumentation. First, I will discuss conditionals that function as a standpoint, and in chapter 6, I will discuss conditionals that function as a constituent of an argument scheme, such as the one that is to be found in 90:

90 We should pay off our debts, because if we pay off our debts, we don’t have to pay interest anymore.

In formulating those evaluation criteria, the starting point will not be the definition of material implication, but rather the function that the conditional fulfils.

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5 Conditionals functioning as a standpoint

5.1 Introduction

Let me start this chapter by saying that the chapter heading might be misleading. As we have seen in the last chapter, any statement – if challenged – can become a standpoint that has to be defended when the antagonist calls for it. Therefore, any conditional sentence can ‘function’ as a standpoint, as soon as another party engaged in the dispute doubts whether this conditional sentence is true. In fact, in the last chapter examples were given of conditionals that function as a connecting premise but could just as easily be called a ‘conditional that functions as a standpoint’, since these conditionals were sup-ported by argumentation in order to convince the antagonist of their acceptability. Nevertheless, it is of importance to dedicate a separate chapter to conditionals that function as a standpoint because otherwise an interesting category of conditionals might escape our attention, na-mely those conditionals a speaker uses in the situation when he puts forward this standpoint only on a certain condition. The condition mentioned in the antecedent sets the stage for the discussion that will take place concerning the standpoint that is expressed in the conse-quent. In my opinion, there are three types of standpoint ‘on a condi-tion’: conditional standpoints, conditional defences and hypothetical standpoints. These different types vary in the stance both the speaker and the other party take with regard to the condition expressed in the antecedent of the conditional. Conditional standpoints are used when certain information needed for the discussion is not available at the time the discussion takes place. To allow the discussion to proceed, this information is posited explicitly at the beginning of it. An example of a conditional stand-point is given in 100:

100 I don’t know exactly when Tess will arrive, but if she is here on Wednesday, then we should all go to the theatre. Wednesday night is the final night King Lear will be performed and I have heard it is very good.

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It is characteristic of conditional standpoints that at the time the dis-cussion takes place, neither the protagonist nor the antagonist knows whether the antecedent is true or not. The antecedent is taken to be true and on that basis the discussion can be carried out. A speaker using a conditional defence takes a position ‘on condition’ as well. There are two ways in which a speaker can put forward a condi-tional defence. First of all, he can support his standpoint with multiple argumentation whilst introducing his second line of defence by means of a conditional. The antecedent of this conditional depicts the situation that the first line of defence fails to accomplish and the consequent res-tates the standpoint being defended. In 101 such a conditional defence is brought forward:

101 We shouldn’t remain home all day. It is far too sunny to stay inside. And even if it were cloudy, we should go out. We all need some fresh air.

The second way in which a conditional defence can be conducted is demonstrated in 102:

102 The prosecution has not been able to prove that my client dealt the blow that turned out to be fatal. Therefore, I request for his acquittal. However, if the jury considers the proof the prosecution delivered to be solid, my client should be discharged, given the circumstances under which this tragic event took place.

This example differs from 101 in that the original standpoint is not restated. It is retracted and replaced by another standpoint: the request for acquittal is replaced by a request for the client to be discharged. Ne-vertheless, 101 and 102 belong to the same category since the antecedent implies in both cases an explicit denial of the first line of defence. It is because of the status of the antecedent that 101 and 102 belong to the same category and differ from the conditional standpoint in 100. In 100, both parties in the discussion agree that it is uncertain whether Tess will arrive on Wednesday or not. In 101 and 102, the situation is quite different: there the speaker is convinced the antecedent is false. After all, it was the speaker who put forward a proposition contradicting the proposition expressed in the antecedent as his first line of defence. But although the speaker considers the antecedent to be false, he does not exclude the possibility that others are of a different opinion. For the other party engaged in the discussion, the antecedent may be true.89

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In case of a hypothetical standpoint, it is not only the protagonist who considers the antecedent to be false: the antagonist also shares this point of view. Both participants in the discussion agree that the antecedent is false and will not become true. The proposition is only maintained ‘for the sake of argument’. An example of a hypothetical standpoint is 103:

103 It is a pity Tess arrives not until Thursday. Had she been here on Wednesday, we should have gone to the theatre together. Wednesday night is the final night King Lear is performed and I have heard it is very good.

For the evaluation of argumentatively used conditionals it is important to differentiate between conditional standpoints, conditional defences and hypothetical standpoints. This is true, not only because the vari-ous ways in which a speaker can maintain a standpoint ‘on a condi-tion’ ask for different kinds of criticism, but also because the conse-quences of successful criticism vary. For instance, when the antagonist can show that the antecedent of a conditional standpoint is false, this will result in the discussion being abandoned, unless the protagonist rephrases his standpoint as a hypothetical one. On the other hand, when the antecedent of a conditional defence is criticized, there is no need to stop the discussion or rephrase the standpoint. In conditional defence, criticism of the antecedent only reinforces the argumentative strength of the first line of defence. In this chapter, conditional standpoints, conditional defences and hypothetical standpoints will subsequently be discussed. For each type, the relevant critical reactions are listed and the consequences of successful criticism are shown.

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89 That the speaker leaves this possibility open explains why using a conditional defence has two opposite effects. By putting forward more than one line of defence, the standpoint is supported more strongly. At the same time, the position of the speaker is weakened since the speaker explicitly points out to his interlocutor that his first line of defence might not be that strong. This latter effect would not have occurred if the speaker had only restricted himself to his first line of defence.

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5.2 Conditional standpoints

A conditional standpoint is typically put forward when there is uncertainty concerning a fact or uncertainty concerning the correct interpretation of a previous remark. Since the discussion can proceed only when this uncertainty is removed, the statement of fact or the interpretation must be taken as correct. Within the context created in that manner, the discussion can be carried on. In 100, it is not clear yet when Tess will arrive:

100 I don’t know exactly when Tess will arrive, but if she is here on Wednesday, then we should all go to the theatre. Wednesday night is the final night King Lear will be performed and I have heard it is very good.

This discussion can be schematically represented as follows:

1.

If Tess is here on Wednesday: we should all go to the theatre.

↑

_____ 1.1a 1.1b

Wednesday night is I have heard it is

the final night very good

King Lear will be performed

In 104, not uncertainty about a fact, but uncertainty about the correct interpretation of a previous remark, gives rise to a conditional stand-point.

104 I don’t know what our European friends mean by ‘a moment of meditation’, but if they mean the air strikes should be interrup-ted for novel peace negotiations, their suggestion is disastrous. Interruption of the air strikes allows for the reorganisation of the enemy troops. Furthermore, it would boost our enemy’s morale. They’ll find the strikes suspended although they have not met any of our demands, and that could be interpreted as proof of their power.

Once again, the situation depicted in the antecedent sets the stage

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for the discussion, the schematical representation of this discussion being:

if our European friends

mean by ‘a moment of

meditation’ that the air strikes

should be interrupted for 1.

novel peace negotiations: their suggestion is disastrous

↑ ↑

1.1 1.2

interruption of the interruption of

air strikes allows for the air strikes

for reorganisation would boost our

of the enemy troops enemy’s morale

↑

_____ 1.2.1a 1.2.1b

they’ll find the strikes that could be

suspended although interpreted as

they have not proof of their power

met any of our demands

By means of the conditionals in 100 and 104 the speaker proposes his point of view ‘on condition’: the standpoint expressed in the con-sequent can only be attributed to the speaker (or: the speaker only accepts the duty to defend this standpoint), when the condition expres-sed in the antecedent is met. The protagonist puts forward his opinion conditionally, because he only will be able to defend his standpoint successfully if the proposition in the antecedent is realized. If ‘Tess is not there on Wednesday’, a discussion on whether to go together with her to the theatre that night is senseless. And criticizing the proposal to interrupt the air strikes for peace negotiations only makes sense if that is indeed the proposal put forward by the European countries. Whether a standpoint can be put forward conditionally or not, is independent of the type of proposition the standpoint expresses. The standpoint can contain a prescriptive proposition, as in 100, where it is argued that a certain action should be taken. But it can also contain an evaluative proposition, as in 104 or a descriptive one, as in 105:

105 I don’t know when the women’s final is scheduled, but if it is scheduled today, it is cancelled.

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All that is needed for a conditional standpoint is that the antecedent contains information that is not (yet) available, but that indeed neces-sary for the discussion to proceed. As a result, it must be explicitly assumed. The defence of a conditional standpoint resembles the logical form of a conditional proof in many ways. Schematically, a conditional proof can be represented as follows:

XYZA......BA → B

In a conditional proof, an assumption [A] is added to the set of premi-ses that forms the basis of the proof [X, Y, Z]. Subsequently, the proof continues within the context of that assumption, until the desired conclusion [B] is reached. Finally, the context of the assumption is left, whilst adding the assumption as an antecedent to the conclusion [A → B]. Conditional proof resembles the defence of a conditional standpoint in that an assumption is used as background for the reasoning that takes place. It differs however regarding the aim of the reasoning: whereas a conditional proof is used in order to prove a conditional sentence, in a defence of a conditional standpoint, proof of a con-ditional sentence is not the main concern. One is not (primarily) concerned with proving a conditional sentence that could be used as a connecting premise in, for instance, a modus ponens. One does not want to show that it is true that from ‘A’ one can deduce that ‘B’. The discussion is focused on the standpoint expressed in the consequent and the condition expressed in the antecedent is only there because it is a necessary precondition for that standpoint.90

How can a conditional standpoint be criticized? Criticism of the condi-tional sentence as a whole is not possible. Conditional standpoints are comparable to other conditional speech acts such as 9:

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9 If you would appreciate it, I could ask the manager for a special discount.

Sentence 9 can be seen as an (indirect) offer. The offer expressed in the consequent is presented as only being made if one of the felicity conditions for making an offer is met: the recipient must like that which is offered. 91 But although the offer is made through a conditio-nal sentence, through the act of putting forward sentence 9, the offer is made. Although the comparison may not hold in it’s entirety, I think that conditional standpoints have much in common with conditional offers like 9 and other conditional speech acts. One of the preparatory condi-tions for putting forward a standpoint is that the speaker believes he can support his standpoint with argumentation (Houtlosser 1995: 79). This then makes it clear that in 100 the speaker has to put forward his standpoint conditionally:

100 I don’t know exactly when Tess will arrive, but if she is here on Wednesday, then we should all go to the theatre. Wednesday night is the final night King Lear will be performed and I have heard it is very good.

If the speaker were to put forward his standpoint unconditionally – knowing that it is not clear whether Tess will be there or not – the prepatory condition would not be met. In that case, the speaker cannot

—————

90 This is not to say that a conditional sentence that functions as a conditional standpoint never can function as a connecting premise in a modus ponens. Sup-pose both parties engaged in the discussion about the conditional standpoint ‘If Tess is here on Wednesday, we should all go to the theatre together’ agree that it is a good idea to go to the theatre with Tess. Any doubt regarding the conditional stand-point has been removed. Now suppose a few days later it turns out Tess will arrive on Tuesday. In that case, the antecedent of the conditional standpoint is acceptable to both parties. Furthermore, it has been agreed upon that in the situation when Tess is there on Wednesday, it is a good idea to go to the theatre together. Therefore, the conditional ‘If Tess is here on Wednesday, then we should all go to the theatre together’ can function as a connecting premise and a statement like ‘Tess is here on Wednesday, so we should all go to the theatre’ makes perfect sense.

91 Consult Sweetser, who describes conditional speech acts as follows: ‘the performance of the in-process speech act (the apodosis) is presented as being condi-tional on some factor expressed in the protasis’ (1990: 120).

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believe he can succesfully support his standpoint with argumentation, since he knows there may be a fatal counter-argument: Tess may not be there. This counter-argument would make his standpoint untena-ble and therefore he presents his standpoint as only being put forward if the condition in the antecedent is met, i.e. the fatal counter-argu-ment is excluded. This means a speaker putting forward a conditional standpoint says something like ‘In case the antecedent is true, my standpoint is that X’. As a result, criticism of the conditional as a whole is not possible. Doubting whether X is really his standpoint, or denying that it is his standpoint, is pointless. Just as with any other conditional speech act, by putting forward the conditional standpoint, the speech act is carried out and the standpoint is taken.92

Nevertheless, the following two reactions seem to be directed at the conditional sentence as a whole:

106 Is it true that we should all go to the theatre if Tess is here on Wednesday?

107 It isn’t true that we should all go to the theatre if Tess is here on Wednesday.

Although 106 and 107 seem to question and criticize the conditio-nal sentence as a whole, the doubt / criticism is directed only at the

—————

92 I realize that it may be difficult to see the distinction between a conditio-nal standpoint and a standpoint about a conditional proposition functioning as a connecting premise like ‘If Emile is a snob, he doesn’t eat macaroni and cheese’, especially since criticizing the standpoint would in both cases involve showing the consequent to be false given the antecedent. Still, I think this distiction is impor-tant. First of all, an attack on a standpoint about a conditional functioning as a connecting premise would rather be aimed at either the ground of the connecting premise or at the connection between the ground and the connecting premise. In the case of a conditional standpoint, the opponent does not seem to have that op-tion. Secondly, conditional standpoints differ from standpoints about conditionals functioning as a connecting premise in that contraposition is not valid for conditio-nal standpoints, e.g. someone putting forward 100 ‘if Tess is here on Wednesday, then we should all go to the theatre’ would not be committed to ‘If we should not all go to the theatre, Tess is not here on Wednesday’ – as it is not so for conditional speech acts in general. Thirdly, in the case of conditional standpoints ‘not (if A, then B) seems to express the same as ‘if A, then not-B’, where in the case of a standpoint about a conditional this is not the case (see section 5.5).

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consequent: the standpoint put forward conditionally is attacked. In 106 it is questioned whether it is a good idea to go to the theatre toge-ther, in 107 this is denied. That the criticism is indeed directed at the consequent can be seen from the kind of response 106 and 107 would receive. A relevant reaction to 106 and 107 would be ‘but it is the final night King Lear will be performed and I have heard many good things about it’ – a reaction by which the proposition expressed in the conse-quent is supported and not the conditional sentence as a whole. An attack on the consequent of a conditional standpoint amounts to an attack on the standpoint put forward under a condition. If the antagonist accepts the antecedent and goes along with the hypothe-tical context sketched, he can either question the consequent or put forward the opposite standpoint. In both cases, within the hypothetical context, a discussion takes place about the acceptability of the stand-point conditionally put forward. This happens for instance in 108:

108 We should not all go to the theatre that night, I think Tess would hate that play. The last time I saw her she explicitly told me she hates ‘Shakespeare updated’.

The antagonist accepts the antecedent of the conditional standpoint and goes along with the hypothetical context in which Tess is there on Wednesday. However, he disagrees with the standpoint conditionally put forward and argues that the consequent of the conditional is incor-rect. Subsequently, within the hypothetical context, he puts forward argumentation in support of his point of view. Up until now, the other party in the discussion has always been willing to go along with the hypothetical context proposed by the protagonist. It is just as well possible that he is unwilling to do so. In such cases, the other party criticizes the antecedent of the conditional standpoint. He might for instance say that the antecedent is untrue.93 Since the protagonist only has taken an obligation to defend his point of view under that condition, a successful attack on the truth of the

—————

93 Again, this illustrates it is the function that the conditional fulfils that deter-mines what kind of criticism is relevant / acceptable and what is not. A conditional that functions as a connecting premise could never be criticized in such a way, in fact it would be seen as a grave logical mistake if the conditional ‘If Daniel is an atlete, he has stamina’ were criticized by pointing out that Daniel is not an athlete, exactly because the conditional does not imply the truth / falsity of the Gedanke expressed in its antecedent and consequent.

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antecedent results in the cancellation of the standpoint and all the arguments put forward to support it, or it results in the necessity to reformulate the standpoint as a hypothetical one. However, not every attack on the antecedent leads to this result. In some cases, the antecedent of the conditional standpoint can be untrue, without making a discussion about the conditional standpoint pointless. This could happen in the case of 109:

109 I don’t know exactly how tall Ann is, but if she is 1,35 meter, we must take a ride on that rollercoaster. I have heard it is abso-lutely terrific.

Ann’s length is relevant to the discussion, since the rollercoaster is only accessible for people over 1,35 meter. Therefore, the protagonist only accepts the burden of proof for his standpoint if this precondition is met. Now suppose Ann is not 1,35 but 1, 40 meter. In that case the antecedent of the conditional standpoint is strictly speaking untrue. However, the discussion concerning the hypothetical standpoint can proceed, since the untruth of the antecedent does not affect the tena-bility of this standpoint: the precondition that Ann is allowed to take a ride on the rollercoaster is still met. The antecedent of a conditional standpoint can also be challenged by pointing out that the proposition expressed in the antecedent is not untrue, but very unlikely. An antagonist is in such cases not willing to go along with the hypothetical context sketched since he finds it highly unrealistic. A discussion on a standpoint put forward in an unrealistic setting might be seen as pointless. When a speaker puts forward his standpoint conditionally because there is uncertainty concerning the correct interpretation of a previous remark, criticism directed at the antecedent is comparable to a reaction to the fallacy of the straw man. In the straw man fallacy, the standpoint of the opposing party is deliberately distorted so as to make it easier to attack. If the interpretation given in the antecedent is too far away from what might be meant by an individual who partakes in the dis-cussion, this could be a reason to reject the context proposed (whether this distortion was deliberate or not).

In sum: in addressing a conditional standpoint, the antagonist can do two things: he can either reject the hypothetical context proposed (by criticising the antecedent), or he can go along with the hypotheti-cal context and question or reject the standpoint put forward in that

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context (by criticizing the consequent). If he takes the first course and succeeds, the discussion will be abandoned since the standpoint and the argumentation put forward in support of it have become pointless. If he takes the second course, then a discussion will be conducted on the tenability – in the context sketched in the antecedent – of the standpoint put forward.

5.3 Conditional defence

A speaker using a conditional defence puts forward a point of view ‘on condition’ as well. In 110 a conditional defence is used:

110a The plan to close all service offices must be abandoned. First of all, it is not true that it is too expensive to keep the service of-fices open. The annual report shows that only a small percentage of the turnover is dedicated to the cost of these offices. And even if it were too expensive, the plan to close the offices should be dropped. Closing the offices would not provide a solution, since ‘Mobile service employees’ in combination with permanent camera observation will cost just as much.

An analysis of 110 yields the following schematic representation:1.

the plan to close all service offices must be abandoned

↑

1.1

it is not too expensive to keep the service offices open

↑

1.1.1

the annual report shows that only a small percentage of the turnover is dedicated to

the cost of these offices

1

even if it were too expensive: the plan to close the offices should be dropped

↑

1.2

closing the service offices would not provide a solution

↑

1.2.1

‘mobile service employees’ in combination with

permanent camera observation will cost just as much

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In a conditional defence, the main standpoint is defended with a minimum of two lines of defence whilst the second line of defence is introduced by means of a conditional sentence. At first sight, condi-tionals that function as a conditional defence do not seem to belong to the category of conditionals functioning as a standpoint. After all, it is the second line of defence that is preceded by a conditional sentence. Should a conditional defence therefore not rather be seen as a conditional that functions as an argument? A closer look at such conditionals reveals however, that the conditional sentence does not contain any argumentation. In the antecedent the situation is sketched in which the first line of defence does not hold; in the consequent the standpoint is restated. The conditional sentence can therefore not be seen as support for the standpoint under discussion. A conditional defence is used when the protagonist wants to put forward two lines of defence to which he cannot be committed simul-taneously. If he wants to bring forward his second line of defence, he has to first sketch a context in which the first argument is said to be untrue, otherwise he would contradict himself. In 110, the argument that ‘the plan to close the service offices does not provide a solution’ is in contradiction with the argument that ‘keeping the service offices open is not too expensive’. The claim that a course of action is no so-lution to the problem, presupposes that there is a problem. Therefore, this second line of defence can only be brought forward in a context where the first line of defence does not hold. In 110, it is clear why the speaker feels the need to add a condition to the second line of defence. However, a conditional defence can also be put forward in contexts where there is no apparent risk of contradic-tion, as in 101:

101 We shouldn’t remain home all day. It is far too sunny to stay inside. And even if it were cloudy, we should go out. We all need some fresh air.

The first line of defence in support of the standpoint that ‘we should not remain home all day’ is not in contradiction with the second one: one can commit oneself simultaneously to ‘it is far too sunny to stay inside’ and ‘we all need some fresh air’. Why then is the second line of defence preceded by a conditional in which the first line of defence is negated and the standpoint restated? A clue is given by Eggs in his article on the use of ‘even if’. Eggs writes:

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Wird ein irrealer Konditionalsatz durch selbst wenn eingeleitet, so muß er als Zurückweisung eine möglichen Folgerung seitens des Gesprächpartners verstanden werden (1979:429).

According to Eggs, a speaker using an ‘even if’ sentence like the one in 101 suspects that the other party engaged in the conversation will draw a certain conclusion. By means of the conditional sentence intro-duced by ‘even if’, which contains the irrealis in the antecedent, this conclusion is then rejected. Now what conclusion does the speaker expect from his opponent? If we take another look at the conditional sentence in 101, just one con-clusion seems to be possible. The conditional ‘Even if it were cloudy, we should go out’ can only be seen as a rejection of ‘If it is not far too sunny to stay inside, then we may remain home all day.’ That means, apparently the speaker expects the other party to conclude that if the first reason happens to be false, the standpoint is false as well. From a logical point of view, this is rather odd, since the speaker seems to expect that in that case the other party will be committing the fallacy of denying the antecedent. This oddity can be explained when we shift our attention from the propositions expressed in the sentences in 101 to the function these propositions fulfil in the context of argumentation. The standpoint put forward in 101 is ‘we should not remain home all day’. This standpoint is supported by the argument that ‘it is far too sunny to stay inside’. Now, suppose the other party engaged in the discussion shows that it is not sunny at all. In that case, the defence fails. If the defence fails, the protagonist has to retract his standpoint: he has not been able to remove the doubt concerning the acceptability of the standpoint and one cannot commit oneself to something which is not considered to be acceptable.94 Therefore, if the other party manages to show that the defence fails, he can conclude from this failure that the speaker will retract his standpoint. The conditional used in a conditional defence is meant to reject this conclusion: even if the first line of defence fails, the standpoint is maintained.

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94 In pragma-dialectics, one of the rules of critical discussion pertains to the closing stage of the discussion. In what Van Eemeren and Grootendorst call rule 14a, it is stipulated that ‘the protagonist is obliged to retract the initial standpoint if the antagonist has conclusively attacked it (...)’ (2004:154).

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It is not the case that in all types of conditional defence the speaker can maintain the standpoint he initially put forward. Sometimes a speaker uses a conditional defence to put forward an alternative stand-point, as in 102:

102 The prosecution has not been able to prove my client dealt the blow that turned out to be fatal. Therefore, I request for his ac-quittal. However, if the jury considers the proof the prosecution delivered to be solid, my client should be discharged, given the circumstances under which this tragic event took place.

The argumentation in 102 can schematically be represented as follows:

1.

my client must be aquitted

↑

1.1

the prosecution has not been able to prove my client dealt the blow that

turned out to be fatal

1.

if the proof is considered to be solid: my client should be discharged

↑

1.1

the circumstances under which this

tragic event took place are such that

his act is not punishable

In 102, the speaker thinks he has been able to show conclusively that there is not enough evidence to consider his client to be guilty as charged. Therefore, he argues his client must be acquitted: he must be declared not guilty. However, as is the case with other conditional defences, the speaker does not exclude the possibility his interlocutor may be of a different opinion. He leaves room for the jury to accept the evidence submitted by the prosecution as being conclusive. Only if that is the case, is the alternative position taken: the speaker puts forward the standpoint that his client should be discharged. His client will be considered guilty as charged, but will not be punished, possibly because he acted out of self-defence. As in other forms of conditional defence, in 102 the speaker antici-pates his first line of defence may fail. In order to not to be left empty

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handed, he advances an alternative standpoint as well. Both stand-points are not of the same order: the standpoint initially put forward is preferred over the alternative standpoint. Only if the former standpoint cannot be defended conclusively, will the speaker resort to the latter one. This is illustrated more clearly by the following legal example:

111 My client is not legally liable for the damages the claimant suffered. Therefore I ask Your Honour to find against the claimant. However, if Your Honour considers my client to be legally liable, I ask to reduce the damages to €5.000,-, since the claimant is partially responsible for the occurrence.

In 111 it is clear that the first standpoint is the one preferred: if the judge agrees, the client does not have to pay anything. Only if the judge is not convinced by the defence of this standpoint, does the defendant take the alternative position. In that case, the client is legally liable – albeit not for the full amount.

Whether the speaker restates his standpoint or retracts it and replaces it with an alternative one, ultimately the evaluation of conditionals that are used in a conditional defence proceeds along the same lines. In conditional defence, the speaker puts forward a standpoint under a certain condition. For that matter, conditionals used in conditional defence have a lot in common with conditionals used as a conditional standpoint. As is the case with conditional standpoints, attacking the conditional sentence as a whole is not possible. A speaker putting forward a conditional defence says something like ‘if my first line of defence fails, my standpoint is X’. Questioning whether this is his standpoint, or saying that it is not, does not make sense. By using this conditional sentence, the speaker actually puts forward the standpoint. That conditionals used in conditional defence differ from condi-tionals used as a conditional standpoint becomes clear when the antecedent of the conditional is attacked. With regard to conditional standpoints, after a successful attack on the truth or possibility of the antecedent the protagonist has to withdraw his standpoint and all the argumentation put forward in support of it. In a conditional defence, such an attack has a rather different effect. If the conditional is such that the standpoint is restated in the consequent, attacking the ante-cedent leads to a reinforcement of the standpoint put forward. Since the antecedent depicts the situation in which the first line of defence fails, challenging the antecedent amounts to confirming the first line

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of defence. If the conditional is such that the consequent contains an alternative standpoint, the antecedent depicts the situation in which the primary standpoint is rejected. Therefore, an attack on such an antecedent amounts to acknowledging the primary standpoint. This leaves an attack on the consequent of the conditional as the only reasonable follow up to a conditional defence. In 101 it could for instance be argued that going out is not a good idea because it will be too enervating. In 102 one could doubt whether the circumstances of the incident indeed are such that the suspect should be discharged and in 111 the claimant could argue that the damages should not be reduced to €5,000,-. As a result, a discussion will be conducted on the tenability of the different standpoints at issue – within the assumed context that the first line of defence fails.

5.4 Hypothetical standpoints

If a speaker puts forward a hypothetical standpoint, he advances a standpoint on a condition, just as he does when enunciating a condi-tional standpoint or conditional defence. What makes the category of hypothetical standpoints different from the two categories discussed earlier is the status of the antecedent. The antecedent of a conditional used as a hypothetical standpoint contains something the speaker considers to be untrue / impossible. Moreover, the speaker deems it to be out of the question that others could think differently. Although the proposition expressed in the antecedent is false, it is taken to be true ‘for the sake of argument’ and on the basis of this assumption, the discussion is carried on further. In 103 an example of a hypothetical standpoint is given:

103 It is a pity Tess arrives not until Thursday. Had she been here on Wednesday, we should have gone to the theatre together. Wednesday night is the final night King Lear is performed and I have heard it is very good.

In 103 both participants in the discussion know that Tess will not be there on Wednesday Nevertheless, they continue discussing whether in the event that Tess could be there on Wednesday, it would be a good idea to go to the theatre together. Hypothetical standpoints can not only contain a prescriptive pro-

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position, as in 103, but also can contain an evaluative or a descriptive proposition. An example of a hypothetical standpoint containing an evaluative proposition is 112:

112 It is a pity this book is written by a winner of the Nobel Prize. Had it been written by a debutant, it would have been outstan-ding. The characters are well-developed and the subject mat-ter is original. Moreover, the constant changes in perspective makes one curious about what will happen next.

Both the protagonist and the antagonist agree that the book under discussion is not written by a debutant. Still, within the hypothetical context that a debutant did write it, the book is evaluated as outstan-ding. Furthermore, the speaker expects that the other party will not immediately agree with this evaluation. In order to convince him, the speaker supports his hypothetical standpoint with argumentation. In 113 the hypothetical standpoint contains a descriptive proposition:

113 What a lucky thing the match is scheduled for next week! If it had been scheduled for today, it would have been cancelled. Not only out of respect for the Duchess who lost her husband, but also because it is pouring.

Again, in 113 both the protagonist and the antagonist know that the situation sketched in the antecedent is contrary-to-fact: the match has not been scheduled for today but for next week. Despite their know-ledge to the contrary, they discuss within the hypothetical context whether the descriptive standpoint is acceptable.

Since both the antagonist and the protagonist agree that the antece-dent of a conditional that functions as a hypothetical standpoint is false, an attack on the antecedent is fruitless. Still, 114, that is men-tioned below, seems to be a relevant reaction to the conditional in 112:

114 Yes, but the book is not written by a debutant.

In such cases, the antagonist explicitly denies that the situation sket-ched in the antecedent obtains. He thereby does not reject the hypo-thetical standpoint as such (as can be seen from the ‘yes’), but rather indicates that he does not want to conduct a discussion within such an unreal and impossible situation.

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As is the case with the other conditionals that function as a stand-point, it doesn’t make sense to question or criticize the conditional sentence as a whole. It is useless to question whether the speaker adopts the proposition expressed in the consequent in the hypothetical situation sketched in the antecedent: by putting forward the condi-tional he actually does. Even responses like 115 should not be seen as critcism of the conditional sentence as whole, but rather as criticism of the standpoint expressed in the consequent.

115 Is it true that the novel would be outstanding if it had been written by a debutant?

115 demonstrates that the other party indicates he does not (immedi-ately) agree with the statement that the novel would be outstanding in the hypothetical context sketched. That the hypothetical standpoint is criticized, indeed can be seen from the kind of follow up 115 could receive: the speaker has to either retract his standpoint that the novel would be outstanding, or he has to come up with arguments in sup-port of it.

5.5 Conclusion

Conditional standpoints, conditional defences and hypothetical stand-points differ in the stance both the speaker and the other party take with regard to the proposition expressed in the antecedent. In the case of a conditional standpoint, the question whether this proposition is true is clearly open: both the speaker and the other party do not know whether it is true or false. In the case of a conditional defence, the two parties engaged in the discussion might have a difference of opinion on the truth of the proposition expressed in the antecedent. The spea-ker thinks this proposition is false: otherwise he would undermine his first line of defence. However, he does not exlude the possibility that the other party is of a different opinion. In the case of a hypothetical standpoint, both parties agree; to be sure, not on the uncertainty of the proposition expressed in the antecedent – as in the case of a conditio-nal standpoint – but on the falsity of it. As a result, successful criticism of the antecedent yields different outcomes in all three cases. If the other party rejects the hypothetical context sketched by the antecedent of a conditional standpoint– by

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showing the antecedent to be untrue or impossible – the standpoint and all the support put forward in defence of it, will be retracted (or changed into a hypothetical standpoint). Discussing it would be superfluous. In the case of a conditional defence, such criticism only reinforces the first line of defence. The antecedent of a hypothetical standpoint cannot be criticized in this manner: both parties agree that the proposition expressed in the antecedent is false. But the antagonist might be altogether unwilling to conduct a discussion just ‘for the sake of argument’. Despite these differences, there are similarities between these three types of conditionals that function as a standpoint. First of all, criti-cizing the conditional sentence as a whole is pointless. Conditionals that function as a standpoint indicate the fact that the speaker com-mits himself to the standpoint expressed in the consequent under the condition mentioned in the antecedent. It does not make sense to question or deny that the speaker adopts this standpoint: by using the conditional, he does. Secondly, in all three uses a reasonable follow up is a discussion on the acceptability of the standpoint expressed in the consequent – within the context sketched in the antecedent In that respect, conditionals that function as a standpoint display a characteristic of conditionals that Stalnaker already has drawn our attention to (1975: 173). In colloquial speech, the negation of a condi-tional often is equivalent to a conditional with the same antecedent together with a negated consequent. Suppose a discussion takes place on the following conditional standpoint:

116 I am not sure whether grandmother will come to your birthday or not, but if she comes, we cannot go out for a picnic

The other party can attack this standpoint by negating the conditional, as in 117:

117 It is not true that if grandmother comes, we cannot go out for a picnic.

But indeed he can say (and probably more frequently will say) the same using a conditional with the identical antecedent and a negated consequent:

117’ If grandmother comes we can go out for a picnic.

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After all, sentence 117’ indicates more clearly that the discussion centers around the acceptability of the standpoint expressed in the consequent. That this equivalence is characteristic of conditionals that function as a standpoint and is not characteristic of conditional sentences in general, can be illustrated by the following example:

118 Of course Marc is a Catholic. If his parents are Catholics, then Marc is a Catholic.

In response to 118 the other party cannot choose freely between 119 and 119’ because those sentences clearly do not have the same mea-ning:

119 It is not true that if Marc’s parents are Catholics, Marc is a Catholic.

119’ If Marc’s parents are Catholics, Marc is not a Catholic.

In 119, the question whether Marc is a Catholic or not remains unset-tled. 119 only expresses that from Marc’s parents being Catholics, one cannot conclude that Marc is a Catholic as well, because the denomi-nation of Marc’s parents is not a sufficient reason to do so. The other party thereby does not exclude that Marc is a Catholic: he just does not want to draw this conclusion on the basis of the truth of the direct premise. Sentence 119’ expresses (in this context) something different. The other party argues that the premise put forward by the protagonist leads to the opposite conclusion: from Marc’s parents being Catholics, one can conclude that Marc is not a Catholic.

The conditionals discussed in this chapter fulfil a different function than the ones discussed in the previous chapter. As a result, the cha-racteristics the conditional must possess in order to be able to fulfil this function, differ as well. This becomes clear when we compare conditionals that function as a hypothetical standpoint and conditio-nals that function as a connecting premise in a modus tollendo tollens. Although in both cases the conditional is in the subjunctive mood, the status of the antecedent differs. In a conditional functioning as a hypo-thetical standpoint, both parties agree the proposition expressed in the antecedent is false. It is merely considered to be true ‘for the sake of argument’. In a conditional functioning as a connecting premise in a

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modus tollendo tollens, the question whether the proposition expressed in the antecedent is false is not yet settled. On the contrary: the discus-sion is aimed at proving this, because the standpoint is the negation of this very proposition. Along the same lines one can explain how a conditional functioning as a connecting premise in a modus ponendo ponens differs from a conditional functioning as a conditional standpoint. A conditional can only function as a connecting premise in a modus ponendo ponens if both parties can agree on the truth of the antecedent. After all, the an-tecedent contains the same proposition as the direct premise and the conditional is used to ‘transfer’ acceptability from this direct premise to the standpoint under discussion. In a conditional standpoint, the acceptability of the antecedent is not established. It is because both parties do not know whether the proposition expressed in the antece-dent is true that the standpoint in the consequent is only put forward ‘under condition’.

Since the use of a conditional as a conditional standpoint requires that the conditional possesses certain characteristics, some categories of conditionals are more apt to function as a conditional standpoint than others. The non-hypothetical conditionals belonging to Dancygier’s category of ‘predictive conditionals’ seem to be tailor-made to fulfil this role. Predictive conditionals are characterized by the feature that the situation sketched in the antecedent is not yet known. There is in Funk’s words ‘objective uncertainty’ about the truth of the antecedent since the state of affairs depicted in the antecedent did not yet mani-fest itself and is therefore unverifiable. To continue with the discus-sion in spite of this uncertainty, a speaker may put forward his point of view only on the condition that this state of affairs is taken to be ‘realized’. This is not to say that predictive conditionals by definition function as conditional standpoints. And the opposite does not hold true either: lack of objective uncertainty does not mean a conditional cannot func-tion as a conditional standpoint, as can be derived from 109:

109 I don’t know exactly how tall Ann is, but if she is 1.35 meter, we must take a ride on that rollercoaster. I have heard it is abso-lutely terrific.

Of course Ann’s height can be established and the uncertainty is therefore only momentarily subjective. But for the participants in the

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discourse this is irrelevant: this information is not known to them, but since it is needed for the discussion to proceed it has been posited explicitly in the antecedent as a condition for the standpoint. It is not only irrelevant whether the proposition is objectively uncer-tain or not, it is also irrelevant what the analyst thinks of the propo-sition expressed in the antecedent. What matters only is the stance participants in the discussion have on the issue. Sentence 120 provides us with such an example:

120 If Hitler had invaded the UK, the UK would have had a German head of state for a while.

An analyst might be tempted to think this conditional ‘is’ a hypo-thetical standpoint (and might question whether this hypothetical standpoint is correct). Hitler never invaded the UK and therefore the antecedent is ‘objectively known to be false’. But it might very well be the case that the parties involved in the discussion are not so know-legeable about this subject matter. Hence, the following context is imaginable:

120’ Hitler did not invade the UK. If he had invaded the UK, the UK would have had a German head of state for a while, and I have never heard of such a thing, have you?

In 120’ the conditional does not function as a hypothetical standpoint but as a connecting premise in a modus tollens, aimed at convincing the other party that Hitler did not invade the UK. One has to know the stance the participants take, and therefore one cannot say of a conditional sentence that it ‘is’ a conditional stand-point or alternatively a connecting premise just from looking at it in isolation. One has to take the context into account. Many conditional sentences can fulfil different functions (although not simultaneously). Let’s take another look at 20:

20 If the bottle of olive oil is leaking, you have not closed it properly.

This conditional cannot only ‘be’ a conditional standpoint as in 20’, it can ‘be’ a connecting premise just as well, as in 20”:

20’ I don’t know whether the bottle of olive oil is leaking or not, but if it is leaking, you have not closed it properly. You were the last to use it.

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20’’ Of course you haven’t closed the bottle properly! If it is leaking – and it is, as you can see – you haven’t closed it properly.

Conditionals ‘are’ not conditional standpoints or connecting premises, rather, these are the argumentative functions a conditional may fulfil. And since it is the function that determines the characteristics a con-ditional needs to have in order be able to fulfil this function, in the last instance, the capability of interpreting and evaluating a conditional requires that one takes the context into account.

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6. Conditionals functioning as a constituent of an argument scheme

6.1 Introduction

Conditionals can not only fulfil the argumentative function of a con-necting premise or standpoint, they also can function as a constituent of an argument scheme. In such cases, one of the direct premises in support of the standpoint put forward is a conditional sentence. A speaker could use a conditional for an argument from example, as in 121:

121 Forcing someone to do what you want leads you nowehere. If I had forced you to come along to that festival, then the whole day would have been ruined because you would not have en-joyed it.

In 121 the conditional describes a hypothetical situation, that serving as an example, supports the standpoint under discussion. For some argument schemes it is obvious that a conditional can be of value. A speaker using pragmatic argumentation – for instance pro-moting a policy by pointing out the desirable consequences connected to it – might very well bring up a conditional. The antecedent of this conditional depicts the situation where the policy is implemented, and the consequent shows what the outcome will be in that situation. Together with the (implicit) positive evaluation of this outcome, the conditional supports the standpoint that the course of action should be followed. In 90 such a conditional is used:

90 We should pay off our debts. If we pay off our debts, we don’t have to pay interest anymore.

In support of his standpoint ‘we should pay off our debts’ the spea-

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95 The conditional can also be put forward in a condensed form by leaving the

antecedent implicit, as in ‘We should pay off our debts because then we don’t have

to pay interest anymore’.

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ker advances the conditional ‘if we pay off our debts, we don’t have to pay interest anymore’. He defends his proposal by pointing out the favourable consequences that will result as soon as the policy is introduced.95

The argument scheme that Perelman and Olbrechts-Tyteca call ‘dilemma’ (1969:236) also calls for conditional direct premises. The type of standpoint ‘whatever you do, Y will occur’ is easily supported with argumentation that depicts consequences resulting in different hypothetical situations, as in 122:

122 Whether you exert yourself or not, they will never accept you. If you do the most you can, they will perceive you as a pusher trying to get to the top. If you do not throw yourself into it, they will exclude you because of lack of commitment.

For other argument schemes the use of conditional direct premises is less compelling: the speaker can choose whether he puts forward his argument as an assertion or as a conditional. In 123 the speaker chooses a conditional to support his standpoint with an argument from authority:

123 The performance of King Lear in the municipal theatre is anutter disaster. Had Shakespeare been in the audience, he would have hated it and would have made it impossible for the actors to perform.

The speaker argues that the play is a disaster by pointing out that an expert in the field (the author of the play) would immensely disap-prove of it. An appeal to authority can just as easily be brought forward without using a conditional , as in 124:

124 The performance of King Lear in the municipal theatre is anutter disaster. The theatre critic in News of the Day called it ‘the worst thing happening in the way of theatre’.

In his classification of argument schemes, Kienpointner (1992) explicitly says that the speaker has a choice in bringing forward his argument by means of a conditional. He distinguishes – following Quintilianus – between real en fictitious argument schemes:

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Bei realen Argumentationsschemata handelt es sich um solche, bei denen der Sprecher von Wahrheit / Warscheinlichkeit der Prämissen in bezug auf die reale Welt ausgeht; sie sind typischerwei-se in Indikativ formuliert. Bei fiktieven Argumentationsschemata argumentiert er dagegen auf der Grundlage der Möglichkeit bes-timmter kontrafaktischer Annahmen in den Prämissen in bezug auf der realen Welt mehr oder weniger nahestehende bzw. ähnli-che mögliche Welten; sie sind typisch in Konjunktiv II formuliert (Kienpointner1992:242).

Although this fragment might suggest that Kienpointner has the view that some argument schemes are fictitious whilst others are not, ultimately, this is not the point he is making. Whether a scheme is fictitious or not depends on the way it is used: whenever the speaker presents the direct premise as true or probable, the argument scheme is real, and whenever he explicitly indicates that the proposition expressed in the direct argument is not in accordance with the facts (kontrafaktisch), the scheme is fictitious. Neither Perelman and Olbrechts-Tyteca (1969), nor Schellens (1985) distinguishes between real and fictitious argument schemes. However, without reference to the specific nature of the premises used, they discuss various examples where the speaker employs a conditional in support of his point of view. In this chapter I discuss argument schemes that ‘by nature’ call for a conditional as a premise and argument schemes where use of a condi-tional is optional. Unfortunately, it is impossible to give an exhaustive overview of conditionals functioning as a constituent of an argument scheme. Primarily, because in the field of argumentation theory there is no consensus about the number of schemes that can be discerned. Furthermore, an exhaustive overview is limited by the fact that there is no consensus on the characteristics the various schemes possess, which makes it difficult to assess what type of conditional can be used. Therefore, I restrict myself to the discussion of four argument sche-mes: pragmatic argumentation, dilemma, argument from authority and argument from example. These schemes can serve as an illustra-tion of how different argument schemes call for the different characte-ristics that a conditional must possess in order to function succesfully as a a constituent of them.

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6.2 Conditionals as a constituent of pragmatic argumentation

A speaker using pragmatic argumentation defends a policy by poin-ting at positive (or negative) consequences. It is based on the principle that one should go after that what is desirable and avoid the undesira-ble. The standpoint is typically a prescriptive proposition: the speaker argues that a certain policy or course of action must or must not be followed (Van Eemeren & Grootendorst 1992: 159).96 90, 125 and 126 can be seen as examples of pragmatic argumentation.

90 We should pay off our debts. If we pay off our debts, we don’t have to pay interest anymore.

125 We should not pay off our debts. If we pay off our debts, we lose the possibility of tax deduction on our interest.

126 We should have paid off our debts. Had we paid off our debts, we would not have to pay interest anymore.

In 90, the standpoint ‘We should pay off our debts’ is supported by pointing out the positive effect of taking this course of action. In 125 the speaker advises against paying off the debts on the basis of a negative effect. 126 is much like 90 in that a positive effect is used as an argument. The difference between the two is that the course of action sketched in 126 cannot be realised. The speaker argues that it would have been better if in the past a different decision had been made, sin-ce a different course of action would have led to a positive outcome.97

It is characteristic for pragmatic argumentation that the policy expressed in the standpoint is the means to a certain end, being the

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96 Houtlosser (1995: 180) argues that the term ‘prescriptive proposition’ must be restricted to propositions where the speaker obliges the listener to do (or not do) something. Propositions whereby a third party is addressed Houtlosser calls ‘evalua-tive propositions’, since in a strict sense, the speaker does not summon anyone. (1995: 178). I suggest categorizing all propositions that contain a course of action / policy together (and perhaps avoid using the term ‘prescriptive’) in order to set them off from ‘real’ evaluative propositions like ‘I like this book’. Such evaluative propositions cannot be supported by referring to negative consequences. A state-ment like ‘I don’t dislike this book, because if I would nobody would buy it’ is not acceptable

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realization or prevention of the consequences sketched. The argu-mentation structure of pragmatic argumentation consists of at least three elements: the standpoint and two coordinative premises. The first premise depicts the consequences that will result if the policy is implemented. It is this premise that typically takes the shape of a conditional sentence. In the antecedent of this conditional the speaker sketches the situation in which the policy is implemented and in the consequent he indicates what the consequences of this policy will be. The second premise consists of an evaluation of these conse-quences: are they desirable or not? This second premise sometimes remains implicit, as in 90, where it is assumed that ‘not paying interest anymore’ is a desirable consequence.98 Schematically the argument scheme of pragmatic argumentation can be represented as follows:

1.

We should [not] do X

↑

_____ 1.1a 1.1b

If X, then Y _ Y is [not] desirable

A speaker who wants to criticize a conditional used as a direct pre-mise in pragmatic argumentation can aim his criticism both at the antecedent and at the connection between the antecedent and the consequent. In the antecedent, the situation is sketched in which the proposed policy is implemented. One reason to be unwilling to go

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97 All these examples Kienpointer classifies as fictitious pragmatic argumen-tation because the speaker makes a prognosis (in 90 and 125 or because the course of action proposed cannot be realized any longer (in 126) (1992: 353). Real (non-fictitious) pragmatic argumentation, according to Kienpointner, has the following structure:

Wenn die Folgen einer Handlung eine Bewertung X rechtfertigen, ist auch

die Handlung selbst mit X zu bewerten/ (nicht) zu vollziehen.

Die Folgen der Handlung sind mit X zu bewerten

Also: Die Handlung ist mit X zu bewerten/ (nicht) zu vollziehen (1992: 341).

98 This description of pragmatic argumentation is in keeping with the descrip-tion Feteris has provided (1997: 122): ‘In its most simple form, (...), the argumen-tation consists of one normative statement that states that effect Y is desirable and one empirical statement that states that action X leads to effect Y.’

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along with the hypothetical situation sketched in the antecedent could be that this situation has already been realized. Another reason not to go along with this hypothetical situation might be that the situation described in the antecedent cannot be realized.99 In reponse to 90, one could say there is no money to pay off the debts. In that case, the pos-sibility of the proposition expressed in the antecedent is questioned, which amounts to saying that the proposed policy is not feasible.100

Doubting whether the situation sketched in the antecedent is the case, or denying it is, is pointless. The protagonist cannot be committed to the truth of the situation sketched in the antecedent: his argumenta-tion is aimed at making this situation happen (or preventing it from happening). If someone criticizes the connection between the antecedent and the consequent, the criticism can be directed at the causal relationship bet-ween the policy proposed and the alleged positive or negative results. This causal relationship can be criticized by showing that the action proposed does not lead to the result depicted in the consequent.101 In the examples given, such an attack does not seem to be possible: pay-ing off debts does indeed lead to not having to pay interest anymore. Similarly, it leads to losing the possibility of tax deduction. In other ca-ses it is exactly the causal relation between antecedent and consequent that is questionable, as in 127:

127 We should not create a fund to subsidize research on wind energy, since then all research done on solar energy will be abandoned.

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99 At first glance, this type of attack seems to be irrelevant in the case of coun-terfactuals such as the one in 126. The policy proposed in those cases is impossible since another course of action has already been executed. Still, in cases like these an attack on the feasibility of the proposed policy is appropriate. There is nothing wrong with a reaction like ‘we could not have paid off our debts, where would we have gotten the money from?’

100 Feasability is one of the stock issues in the academic debate. There are many parallels between criticism of the conditional that forms part of pragmatic argumen-tation and the stock issues. If one challenges the claim that ‘paying off the debts leads to not having to pay interest anymore’ – a criticism of the causal connection between antecedent and consequent – then one questions the effectiveness of the policy. If one points out that the desired outcomes will come about anyway – also when the policy is not implemented – then the necessity of the policy is questioned.

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Here indeed one could question whether subsidies on research in the field of wind energy will result in the abandonment of research done in the field of solar energy. It might just as well be that people doing research on solar energy will continue doing so. It is even conceivable that such subsidies would boost research into all kinds of sustainable energy. In extreme cases, questioning the causal connection between the antecedent and the consequent can even amount to accusing the other party of the fallacy of the slippery slope. This accusation seems justi-fied in the case of 128:

128 The pill should not be sold at the chemist’s. If we allow that, in ten years time we will find DIY-packs for IVF in the freezer compartment of the supermarket.

Of course, it is very doubtful whether taking one step ‘down the hill’ by selling the birth control pill at the chemist’s would result in sliding down to the bottom of the hill altogether. The connection between the antecedent and the consequent can not only be attacked by questioning the causal relationship between the two. There is also a kind of criticism possible that is related to the re-lationship of means and ends that pragmatic argumentation typically expresses. The consequences depicted in the consequent represent the reason why the policy proposed should be implemented: by means of this policy, the consequences depicted in the consequent can be reali-zed or avoided. This means the conditional should have at least two more charac-teristics. First of all, the consequences described in the consequent should not represent the actual situation. If they were already realized, then there would be no incentive for the policy proposed. The condi-tional in 129 suffers from this shortcoming:

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101 The causal relation between the antecedent and consequent is not necessarily linked to some ‘law of nature’. Sometimes it is in the hands of the speaker whether the effect depicted in the consequent will take place or not, for example when a father says to his son ‘You should tidy your room, because if you don’t , you can’t go out with your friends tonight.’ In those cases, the consequent contains either a reward or threat. For an evaluation of conditionals used in pragmatic argumenta-tion, it does not matter whether the consequences are in the hands of the speaker or not. If the son has reason to believe (on the basis of experience) that his father’s threats are usually empty, this will cast doubt on the ‘causal’ connection between antecedent and consequent.

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129 We should marry, because then we can combine our tax returns.

Apart from being a rather prosaic reason to get married, unmarried couples can combine their tax returns just as well. The policy proposed is therefore unnecessary. Secondly, the consequences described in the consequent should not be bound to materialize anyway. If they could even occur in the case that the policy is not realized, the reason for this policy would evapo-rate. A policy supported by pointing out positive consequences would not be necessary because the end would just as easily be reached without the means. An interlocutor expressing this type of criticism might use what Perelman and Olbrechts-Tyteca call an argument from redundancy: ‘the argument of redundancy prompts one to abstain from action, since any additional action would be of no avail (1969: 281)’. Even when the speaker is of the opinion that something should not be done, the consequent must meet the last two requirements mentioned above. In those cases it is less clear that pragmatic argu-mentation expresses a means / ends relationship of, since the speaker argues that one should refrain from action. As an example, in 130, the speaker states that the US should not proceed with military action:

130 The US should not take their recourse to military action. If their army intervenes, it will destabilise the region.

The aim strived for here is to keep the region from becoming desta-bilised. According to the speaker, this aim can be reached if the US refrain from military action. The ‘means’ to this end is therefore ‘the US do not take their recourse to military action’.

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102 They are not biconditionals in the truth-functional sense of the word, because contraposition would not hold. Conditionals functioning as a constituent of pragma-tic argumentation typically are predictive conditionals, which do not lend themsel-ves to contraposition (see section 4.3).

103 This is what Comrie refers to when he writes: ‘In terms of the context in which ‘If you do that, I’ll hit you’ is normally uttered, the conversational implicature that ‘if’ is to be interpreted as ‘if and only if’ falls out naturally: the utterance is intended as a prohibition, giving motivation to comply with the prohibition (namely, not getting hit). If the speaker hits the addressee anyway, or rather, if the addressee assumes that the speaker may hit the addressee anyway, then the motivation behind the prohibition is lost, i.e. the utterance becomes incoherent.’(1986: 78)

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Examples like 130, illustrate that conditionals functioning as a consti-tuent of the argument scheme of pragmatic argumentation are in fact kinds of biconditionals.102 The speaker in 130 could very well believe that the region might become destabilised for other reasons, but he only supports his summons for the US to refrain from military action if he can be committed to the proposition that the region will not be destabilized if military action is withheld. The conditional can only support the standpoint adequately if the antecedent is presented as a sufficient condition for the consequent with the implication that its contradictory would also be a sufficient condition for the contradictory of the consequent.103 The speaker is therefore committed to ‘if p, then q’ and ‘if not-p, then not-q’. It is for this reason that Renate Rubinstein finds fault with people who argue that Israel should change it’s policy because this policy would lead to anti-Semitism.

A selfish but understandable motive, since it takes a very long time – especially when you are born in the Netherlands after World War II – to see that anti-Semitism is not based on any reasonable ground, so that it does not help you to behave properly, not to kill the president, not to let the lion escape from the zoo, because the anti-Semite will hate you no matter what (...). Which does not mean of course that you could not have major objections against the so-lutions Israel chooses to solve its problems. (Renate Rubinstein (1984) Naar de bliksem? Ik niet. Amsterdam: Meulenhoff, p. 122, my translation – jmg)

The anti-Semite will hate the Israelis, whether they change their policy or not. Therefore pointing out that Israels behaviour leads to anti-Semitism is not an adequate ground for the view that Israel should change it’s policy (although Rubinstein does not exclude the possibility that this standpoint is acceptable – be it on different grounds). One might be of the opinion that if conditionals that function as a constituent of pragmatic argumentation are interpreted as a kind of biconditional, then one ignores that a discussion on a proposed action often can end up in discussing several alternative ways to reach the same objective, as in the following discussion:

Nick: We should subsidize wind energy, because that would re-duce the use of fossil fuels by 15%. Ann: I agree that we should reduce the use of fossil fuels, but I

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don’t think subsidizing wind energy is the way to go about it. If we just encouraged energy saving, we would also reduce the use of fossil fuels by 15 % and don’t have the disadvantages of subsidies.

The two conditionals functioning as a premise in pragmatic argumen-tation are (a) ‘If we subsidized wind energy, we would reduce the use of fossil fuels by 15%’ and (b) ‘If we encouraged energy saving means, we would reduce the use of fossil fuels by 15%’. Since both conditio-nals have the same consequent, one might argue those conditionals cannot be biconditionals. If wind energy is not subsidized, this doesn’t mean necessarily that the use of fossil fuels will not be reduced by 15%, because this goal could have been reached by the encouragement of energy saving. However plausible this may sound, I think this view is mistaken. Conditionals like (a) and (b) discuss a scenario in which something is changed with respect to the actual situation: one considers what would happen if ‘wind energy is subsidized’ or ‘energy saving is encouraged’. In evaluating such conditionals, one should judge whether in the sce-nario sketched in the antecedent, the consequent would be the case. But it is only possible to say something intelligible about that, if it is assumed that ‘other things are equal’, i.e. if the actual situation is only amended by the situation sketched in the antecedent (including per-haps some other changes so that the presuppositions of ‘wind energy is subsidized’ are met, like ‘enough funds’ et cetera).104 Otherwise one could always think of something that hinders the consequent from being realized, such as ‘we are subsidizing wind energy and all of the sudden a strong cool down of the earth occurs that results in unex-pected energy needs and therefore leads to an increase in use of fossil fuels by 50%’. The antecedent of conditional (a) describes the situation in which wind energy is subsidized and ‘other things are equal’ – i.e. there is no encouragement of an energy saving means. In this inter-pretation, the conditional sentence is indeed a kind of biconditional: if wind energy is subsidized (and other things are equal), the use of fossil fuels will be reduced by 15% percent, and if wind energy is not

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104 This procedure is also known as the Ramsey test.

105 In that respect, conditionals that function as a premise in pragmatic argu-mentation clearly differ from the ones used as a connecting premise. Whereas strenghtening the antecedent is valid for conditionals that function as a connecting premise (as I have argued in section 4.2), it is not valid for conditionals functioning as a premise in pragmatic argumentation.

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subsidized (and other things are equal), the use of fossil fuels will not be reduced by 15%.105

In sum: a conditional can only function successfully as a constituent of the argument scheme of pragmatic argumentation when the an-tecedent depicts a situation that is not yet realised and that is in fact re-alizable. Furthermore, there should exist a causal relation between the antecedent and the consequent: if the situation depicted in the antece-dent is realized, the consequences depicted in the consequent should occur as well. Finally, the relation between antecedent and consequent has a sort of biconditional nature: the speaker is not just committed to ‘if p, then q’, he is committed to ‘if not-p, then not-q’ as well. If the consequences described in the consequent already are realized, or if they will take place anyway, the conditional cannot function as a direct premise in support of the standpoint under discussion.

6.3 Conditionals as a constituent of a dilemma

In the argument scheme ‘dilemma’ conditionals are used (just as in pragmatic argumentation) for the purpose of sketching the conse-quences a particular course of action will have.106 A dilemma in the colloquial sense of the word is usually seen as a necessary choice between two evils. A speaker facing a dilemma has to choose between two courses of action, but can’t decide because both actions lead to equally grave consequences.107 In 131 for instance, the speaker faces the dilemma whether he should accept the apartment or not.

131 I don’t know whether we should accept this apartment or

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106 Schellens sees a dilemma as a kind of subtype of pragmatic argumentation. However, the evaluation criteria for the conditionals used in these schemes differ. Therefore, I discuss conditionals used as a constituent in the argument scheme ‘dilemma’ in a separate section.

107 Although Perelman and Olbrechts-Tyteca use the term ‘dilemma’ as well for arguments like example 122 ‘Whether you exert yourself or not, they will never ac-cept you. If you do the most you can, they will perceive you as a pusher trying to get to the top. If you do not throw yourself into it, they will exclude you because of lack of commitment’, these arguments are not a dilemma in the colloquial sense of the word. Examples like 122 I will discuss hereafter.

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not. If we accept it, we will loose our accumulated rights and will have to wait at least seven years before being eligible for another one. If we don’t accept it, we will have to wait God knows how long before being offered some acceptable place to live.

Although the term ‘dilemma’ is most often used as a choice between two evils, the alternatives that the speaker has to choose from need not necessarily to be negative. A speaker may also be faced with a dilem-ma when he has to choose between two possibilities that are equally desirable. In 132, the speaker cannot decide how to spend the evening:

132 I would really like to have dinner at your place tonight. I am just stuck in a dilemma: Christopher invited me over to his cottage and since Jacky will be there as well I think it will be great. On the other hand, I would really enjoy catching up with you after all this time.

When one confronts the problem of ‘dilemma’, it is not the con-sequences of the alternative courses of action that are undesirable (although that could be the case), rather, it is undesirable that a choice in general has to be made.108 The speaker cannot make a rational choice, because the consequences of the alternative courses of action are equally (un)desirable. A dilemma therefore has two characteristics. First of all, the speaker is faced with a necessary choice between possible courses of action, for example, he has to either accept or reject the apartment. Secondly, it is impossible to make a rational choice between the alternatives because both have equally major advantages / disadvantages, for example, either he looses the accumulated rights or there is little chance another apartment will be offered shortly. As a result, in a strict sense, the speaker does not take up a position. These two characteristics are represented on different levels of the argument structure:

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108 In the description of the term ‘dilemma’ in Merriam Webster, this is pointed out as well: ‘Although some commentators insist that dilemma be restricted to instances in which the alternatives to be chosen are equally unsatisfactory, their concern is misplaced; the unsatisfactoriness of the options is usually a matter of how the author presents them. What is distressing or painful about a dilemma is having to make a choice one does not want to make.’

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1

whether we should do ‘X’ or not

cannot be decided

↑

_______ 1.1a 1.1b

either we do ‘X’ and ‘Y’ will happen, or ‘Y’ and ‘Z’ are equally

we don’t do ‘X’ and ‘Z’ will happen. undesirable

↑

_______1.1a.1a 1.1a.1b 1.1a.1c

if we do ‘X’, if we don’t do ‘X’, either we do ‘X’ or

then ‘Y’ then ‘Z’ we don’t do ‘X’

The argumentation consisting of the substandpoint 1.1a and the sup-port thereof, is what logicians call a ‘complex constructive dilemma’. It is called ‘complex’ because the conditionals do not have the same consequent, and it is called‘constructive’ since in the disjunction in 1.1a. the antecedents of the conditionals are confirmed and not denied (Encyclopedia Brittanica 23: 228). 1.1a.1c expresses the necessity of a choice and 1.1b expresses that the consequences of the alternatives are equally undesirable.

Since the argument scheme of dilemma bears a clear resemblance to the argument scheme of pragmatic argumentation, the criticism of the conditionals used in a dilemma coincides in general with the critical remarks that can be directed at conditionals used in pragmatic argumentation. However, because the conditionals used in a dilemma are interrelated in such a specific way, the consequences of successful criticism will differ. One could criticize the antecedent of the conditional by pointing out that the situation depicted in the antecedent is already realized, or may never be realized. In the case of 131, the antagonist could say it is impossible to accept the apartment, because the term for reply has already expired. As a result of this criticism, the first alternative – ac-cepting the apartment – is eliminated and the second alternative – not accepting the apartment – is realized. The dilemma is thereby solved: the speaker is no longer faced with a difficult choice. Not only the antecedent can be criticized, but the antagonist can also criticize the connection between the antecedent and the consequent First of all, he could argue that the consequences sketched in the

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consequent do not necessarily follow. In the case of 131, he could point out that rejecting the apartment does not necesarily lead to a disaster, because an invitation has arrived to view another apartment. Since in that case the negative consequence of rejecting the apartment is removed, the scale can be tipped in favour of this alternative. Secondly, the antagonist could show that the antecedent of the conditional is not a necessary condition for the consequent. If he manages to convince his interlocutor that the consequences in one conditional will oc-cur anyway, i.e. whether one of the alternatives is chosen or not, this (dis)advantage will then drop out of the equation. The outcomes of the alternative courses of action will no longer be equally (un)desirable, so that a rational choice between the two alternatives can be made.

The dilemma’s discussed in 131 en 132 correspond to the meaning of ‘dilemma’ in colloquial speech. In logic, the term ‘dilemma’ is used for other kinds of argument as well – even if a difficult choice does not have to be made. The argumentation in 133 represents what is called a simple constructive dilemma (Encyclopedia Brittanica 23: 228):

133 Whatever the result of the vote will be, our action committee can be disbanded. If the law on referendum is voted through, our committee can happily adjourn – we will have reached our goals. But also if it is voted down we can discontinue. If we don’t reach our goals now, there is no chance we ever will.

The conditionals in 133 do not depict courses of action and the pos-sible consequences that could result from it. The speaker sketches two possible future scenario’s: one in which the law on referendum is voted through and one in which it is voted down. According to the speaker in both cases the action committee can be disbanded.

As can be seen from the argument structure, this second type of dilemma does have something in common with a dilemma in the col-loquial sense of the word discussed earlier.

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1.

whatever the result of the vote will be, our action committee can be disbanded

———— 1.1a 1.1b 1.1c

if it is our committee if it is we the referendum

voted can happily voted can is either voted

through adjourn down discontinue through or

↑ ↑ voted down

1.1a.1 1.1b.1

we will have if we don’t reach

reached our our goals now,

goals there is no chance

we ever will

It contains two conditionals in which different scenarios are discus-sed and a premise which states that either of these scenarios will take place. The only difference is that the speaker does not have to make a choice. Therefore, there is no need to consider the pros and cons.

As a result, the conditionals used in this second type of dilemma must be criticized in a different way. For instance, criticism of the ante-cedent of these conditionals is not relevant. Suppose the antagonist knows on good authority that there will be a majority who vote against the law. This information will not help him in criticizing the protago-nist’s argumentation: the protagonist will hold on to his point of view that the action committee can be disbanded. From his perspective, it is irrelevant what the outcome of the vote will be: he states that the com-mittee can be disbanded no matter what. Moreover, the connection between the antecedent and the conse-quent of the conditional differs from that of conditionals used in a dilemma in the colloquial sense of the word, because it is not necessa-rily a causal one. In fact, the consequent must be seen as a kind of con-ditional standpoint. The speaker is actuallly stating something to the effect that ‘If the law is voted through, my standpoint is that our action committee can be disbanded.’ To doubt whether this is his standpoint, or to argue that it is not, is pointless. By using the conditional, he has brought forward his standpoint under a condition. The only relevant criticism is a critique that could be directed to the consequent of the conditional. If the consequent is criticized, within the hypothetical context sketched in the antecedent, a discussion will take place on the acceptability of the proposition expressed in the

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consequent. In fact, in 133 the speaker already did foresee that his conditional standpoints would be challenged, since he immediately advances argumentation in support of them.

The conditionals used in the two types of dilemma discussed in this paragraph differ considerably. Conditionals that are a constituent of a dilemma in the usual sense of the word can be seen as expressing a causal relation between the antecedent and the consequent. Condi-tionals that are a constituent of the second type of dilemma do not so much express a causal relationship, but should be interpreted as a kind of conditional standpoint, the result being that to fulfil their role suc-cessfully, conditionals which function as a premise in a dilemma of the first category need to fulfil different requirements than conditionals functioning in a dilemma of the second category .

6.4 Conditionals as a constituent of an argument from authority

A speaker uses an argument from authority when he tries to make a reasonable case for his standpoint by quoting a ‘specialist in the field’. In 124, the speaker supports his opinion on a theatrical performance by citing a theatre critic.

124 The performance of King Lear in the municipal theatre is anutter disaster. The theatre critic in News of the Day called it ‘the worst thing happening in the way of theatre’.

The speaker claims that his standpoint ‘The performance of King Lear in the municipal theatre is an utter disaster’ is true because an expert in the field has claimed that it is so. In a hypothetical appeal to autority, the speaker does not refer to a statement actually made, but alludes to a statement a particular authority would have made had he been in the position to express his opinion on the matter. The direct premise takes the shape of a condi-tional, as in 123:

123 The performance of King Lear in the municipal theatre is an utter disaster. Had Shakespeare been in the audience, he would have hated it and would have made it impossible for the actors to perform.

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In 123, the speaker supports his standpoint by a hypothetical judge-ment of Shakespeare’s in absentia. The antecedent of the conditional depicts the situation in which Shakespeare would have attended the play and the consequent contains the opinion Shakespeare would have had in that situation (according to the speaker). In 123, the speaker uses a hypothetical appeal to authority because the authority being referred to is dead and therefore is no longer capa-ble of making a judgement. Another reason to put forward an appeal to authority hypothetically is when a statement could not be expected from the authority referred to, as in 134:

134 If it were up to the cat, she would buy Whiskas.

In the hypothetical situation that the cat could speak out on this issue, Whiskas would be the cat food preferred. When the authority put forward does not exist in real life, an ap-peal to this authority is not necessarily hypothetical. One could, for instance, refer to a ‘real statement’ by a fictitious person like Sherlock Holmes without using a conditional, as in 135:

135 We did not need any more information to decide. As Sherlock Holmes says: ‘all good thinking depends on deduction’.

Alternatively, one could refer to a comment made in the past by some-one who is no longer alive. The argument scheme is only hypothetical when the direct argument takes the shape of a conditional where the antecedent depicts the hypothetical situation in which it is possible for an authority to make a comment while the consequent contains the judgment made.

How can a conditional used as a direct premise in an appeal to autho-rity be criticized? An attack on the truth or possibility of the antece-dent is pointless: the speaker knows that Shakespeare did not and could not see the play, he also knows that it is not possible for the cat to decide. At first glance, a response like ‘Yes, but Shakespeare is dead, isn’t he’ might seem to be directed toward the truth of the antecedent. However, an antagonist reacting in this way does not consider the conditional to be untrue. As can be seen from the ‘yes’, he acknowled-ges that in the hypothetical context where Shakespeare would attend, he could judge unfavourably. Nevertheless, he rejects the use of this conditional as a premise in support of the standpoint put forward. He

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disapproves of the use of fictitious authorities and therefore does not want to enter the hypothetical context sketched. An antagonist not necessarily unwilling to be persuaded by fictitious authorities could challenge the conditional used in that scheme by arguing that within the context sketched in the antecedent the conse-quent does not hold. In reaction to 123 an antagonist could say:

136 What nonsense, I think he would have loved it! Don’t forget that Shakespeare’s plays were written for the common people. It is only in recent times that his plays are seen as works of art.

As a result, within the hypothetical context in which Shakespeare is able to comment, a discussion could emerge on the question as to whether he would have loved or hated the performance. In a similar fashion, a discussion on the cat’s opinion could start after a contributi-on like ‘She would not buy Whiskas, she would go to the best butcher to get some fresh heart’. The antagonist would even have the possibility to conclusively show that the authority quoted does have quite a different opinion on the matter under discussion, as in 137:

137 Mother: ‘Of course you are not going on holiday to France by yourself. If your father heard of this plan, he would think you would be absolutely crazy!’

Daughter: ‘Actually, I have already presented it to dad and he was not unsympathetic towards it.

In short: an argument from authority is put forward hypothetically when the authority quoted is presumed to not have been in a situation to comment on the subject under discussion (since he is dead, unable to speak, did not hear about it, etc.). By means of the conditional, a context is sketched in which the authority is able to comment. The consequent of this conditional contains the speaker’s opinion on the matter. In reaction to a hypothetical argument from authority, the antagonist can do two things: either he refuses to go along with the hypothetical context sketched in the antecedent or he accepts it. After a rejection, the speaker has to retract his hypothetical appeal to autho-rity. In case of acceptance, a discussion could start on the (conditonal / hypothetical) standpoint that the consequent correctly reflects the authority’s opinion.

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6.5 Conditionals as a constituent of an argument from example

In an argument from example the speaker advances one or more examples in order to support the standpoint under discussion. A well-known form of argument from example is induction, where a speaker presents a large amount of representative examples to infer a general statement. In 138, the speaker infers from a variety of examples that after the cooking of fish, a nasty deposit remains in the pan:

138 Always when fish is cooked, a nasty deposit remains in the pan. Last time, when we had salmon, it took me an hour to scrape it off. And when you cooked pasta with fish sauce, even the cover was completely covered. And look at the pan now: I can hardly remove it.

An indicative argument from example can be seen as demonstration of a general rule. In a discussion, it is not always necessary to demon-strate such a rule; sometimes one can render a general rule acceptable in another way. A speaker could put forward an argument from aut-hority: the fact that an authority in a certain field endorses the general statement, could make this statement acceptable to the interlocutor. Yet another way to support a general statement is to use an illustra-tive argument from example.109 In such cases, the speaker does not have to come up with several representative examples but can limit himself to a prototypical one. By means of this example, a general rule that was not acceptable to the antagonist prima facie, is made accepta-ble.110 In 139, such an illustration is used :

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109 The distinction between illustration and example is discussed extensively by Perelman and Olbrechts-Tyteca. According to them this distinction is important because illustrations do not fulfil the same function as examples: ‘Whereas an example is designed to establish a rule, the role of illustrations is to strengthen adherence to a known and accepted rule, by providing particular instances which clarify the general statement, show the import of this statement by calling attention to its various possible applications, and increase its presence to the consciousness.’ As a result, illustrations and examples cannot be evaluated in the same way: ‘While an example must be beyond question, an illustration need not be, as adherence to the rule does not depend upon it’ (1969: 357). The terms ‘inductive’ and ‘illustra-tive’ argument from example are introduced by Kienpointner. He designates an argument from example ‘inductive’ when the generalized statement is the main standpoint in the discussion and ‘illustrative’ when the statement functions as a Schlußregel in a larger context (1992: 366).

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139 You never should force a child to do something, it leads you nowhere. For years your mother forced you to eat vegetables and now you dislike them even more.

The single example indicated here is not enough to prove the general statement that a child never should be forced to do something. Ho-wever, the general rule might now be acceptable for the interlocutor because the abstract principle is developed by means of a concrete interpretation. That illustrative and inductive arguments from example indeed do differ is also exemplified by a difference in the use of hypotheticals. A speaker using an inductive argument from example cannot replace real observations with hypothetical examples. This would amount to circular reasoning, because the general rule prescribes how the hypo-thetical examples must be constructed in order to be able to function in support of it.111 On the other hand, hypothetical examples are extre-mely useful in an illustrative argument from example. By constructing hypothetical examples one can stress certain characteristics in order to make the most reasonable case, as in 121:

121 Forcing someone to do what you want leads you nowehere. If I had forced you to come along to that festival, then the whole day would have been ruined because you would not have en-joyed it.

—————

110 Not all authors consider such ‘illustrations’ to be arguments. Schellens for instance – inspired by the distinction Perelman and Olbrechts-Tyteca make – states: ‘In some cases, it is questionable whether it is correct to see examples as argu-ments. Does the speaker put forward an example in defence of the general rule, or does he just want to use it to illustrate this rule? (1985: 192).’ The idea that illustrati-ons are no arguments, could originate from the way Perelman and Olbrechts-Tyteca describe the function illustrations fulfil – ‘to strengthen adherence to a known and accepted rule.’ With regard to a known and accepted rule, no arguments are needed. However, I think Perelman and Olbrechts-Tyteca want to draw attention to the dif-ference between inferring (or demonstrating) a general rule not yet formulated (not yet known and accepted) and the suppport of a general rule already demonstrated.

111 Kienpointner does discuss fictitious inductive arguments from example: ‘Pro-blematisch sind auch induktieve Beispielargumentationen, denen fiktive Beispiele zugrundegelegt werden. Hier steht nämlich zusätzlich zu Fragen der Generalisier-barkeit die Wirklichkeitsnähe der fiktiven Beispielfälle zur Debatte’ (1992: 372). Ho-wever, the example he uses contains an illustrative and not an inductive argument from example.

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To illustrate a general rule, the speaker constructs an hypothetical example that is tailored to his interlocutor, thereby increasing his chan-ces of success.

Conditionals that are used as a constituent of an (illustrative) argument from example can be criticized in more or less the same way as condi-tionals in a hypothetical appeal to authority. First of all, the question is whether the interlocutor is willing to ‘enter’ the hypothetical situation depicted in the antecedent. A relevant reaction to 121 would be ‘You would never force me to go along, you always efface yourself far too much’. For some reason, the interlocutor finds the example too unrea-listic, and therefore rejects it. If the antagonist is willing to accept the hypothetical context sketched in the antecedent, a second way of criticizing the conditional emerges by starting a dicussion within this context regarding the acceptability of the proposition expressed in the consequent. In the case of 121, he could for instance argue that the whole day would not necessarily be ruined, since he might have enjoyed it – although he would not have expected that at all.

6.6 Conclusion

If any chapter in this dissertation illustrates the fact that the interpre-tation and evaluation of conditionals is dependent on the function they fulfil, it was the current chapter, which was concerned with conditionals functioning as a constituent of an argument scheme. The importance of determining the function a conditional fulfils has been demonstrated, first of all, since it was found that not all argument schemes lend themselves to the use of a direct premise in the form of a conditional. In an ‘inductive argument from example’, one cannot use ‘hypothetical examples’, since that would amount to circularity: the hy-pothetical examples are in that case constructed in line with the general statement they are meant to prove. If a conditional can be used as a direct premise, it may depend on the specific subtype of the argument scheme as to how this conditional must be evaluated. Conditionals used in a dilemma in the colloquial sense of the word, depict the consequences that will occur if alternative courses of action are taken. The antecedent represents the situation in which a course of action is implemented and the consequent sketches

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what will happen in that situation. These conditionals can be criticized by either attacking the antecedent – indicating that the policy cannot be implemented – or by questioning whether the consequences will in-deed result. Conditionals used in a simple constructive dilemma have quite different antecedents and consequents. Here the antecedents depict alternative situations, whereas the consequent expresses what according to the speaker would be the case / should be done in those situations. Here criticism of the antecedent is pointless: such criticism would never lead to the protagonist changing his point of view. More-over, criticism of the connection between the antecedent and the conse-quent does not make sense. Conditionals that fufill this function can be seen as conditional standpoints, and as we saw in section 5.2 in case of a conditional standpoint, criticism of this relationship is pointless. Whereas the argument scheme of a dilemma has shown that the con-ditionals used need to be evaluated differently depending on the very subtype of the scheme, in other cases, conditionals can be evaluated in more or less the same way although they function as direct premises in rather different argument schemes. There is for instance only a slight distinction in the interpretation and evaluation of conditionals that function as a direct premise in an appeal to authority and conditio-nals that function as a direct premise in an illustrative argument from example. In both cases the conditionals can be seen as hypothetical standpoints and the antagonist can respond to them by either rejecting the hypothetical context sketched or by questioning whether in that particular context the consequent (the standpoint) holds true. The two uses of conditionals only differ in the way this criticism is executed. It is the use of a conditional as a direct premise in pragmatic argu-mentation that illustrates perhaps most clearly that the argumentative function a conditional fulfils is of influence on its evaluation. It is because of the policy standpoint defended – together with the means / ends relationship that pragmatic argumentation expresses – that condi-tionals only can function successfully as a direct premise in pragmatic argumentation if certain precise criteria are met. Not only should the antecedent contain a possibility (otherwise the policy defended is not feasible), there must also be a causal relationship between the antece-dent and the consequent. Apart from that, this relation must display a kind of biconditional nature (otherwise the policy is unneccesary). Looking at conditionals from the perspective of argumentation, there-fore, not only explains why conditionals can have certain characteris-tics, but also is useful in explaining why those characteristics must be present.

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7. Summary and conclusions

The course we have pursued in the search for a way to analyze and evaluate argumentatively used conditionals, has been a winding one. Our starting points were the ‘evaluation criteria’ first formulated by Philo of Megara and then later Frege. Both Philo of Megara and Frege described the circumstances in which a conditional is true, namely, a conditional is false when the antecedent is true and the consequent is false. In all other circumstances, the conditional is true. This description – now commonly known as the definition of ma-terial implication – has met with much criticism, as have the logical operations of contraposition, hypothetical syllogism and strengthening the antecedent that are closely related to it. The criticism is more often than not quite compelling. Take for instance the paradoxes of material implication: it seems incorrect to call a conditional sentence true just because its antecedent is false or because its consequent is true. Also the counter-examples against contraposition, hypothetical syllogism and strengthening the antecedent are difficult to ignore, as is illustra-ted by 11 and 11’, 12 and 14.

11 If the U.S. uphold subvention, then the European Union will not agree to negotiate.

11’ If the European Union will agree to negotiate, then the U.S. do not uphold subvention.

12 If Brown wins the election, Smith will retire to private life. If Smith dies before the election, Brown will win it. So if Smith dies before the election, Smith will retire to private life.

14 If Max is a bat, Max can fly. So: If Max is a bat and has been born this morning, Max can fly.

To abandon this definition and the logical operations that are associa-ted with it, and then to try to find alternative ways to describe condi-tionals, seems to be a natural course to take. Section 2.3 describes a series of alternative logics that have resulted from taking that course. On the other hand, in Section 2.4 it is argued that abandoning the definition of material implication and the reasoning based on contra-position, hypothetical syllogism and strengthening the antecedent,

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may lead to the loss of something valuable. Not only does the defini-tion of material implication form a connection between the truth of a conditional and the validity of some argument forms, there is also something intuitively plausible to contraposition, hypothetical syl-logism and (although perhaps less so) strengthening the antecedent. Besides, many examples can be given where those operations seem to be entirely justifiable. The question was therefore raised whether it would be possible to distinguish between two categories of conditio-nals: conditionals that are unproblematic with regard to the definition of material implication together with the logical operations mentioned above and ‘problematic’ conditionals. The definition of material impli-cation could then at least provide evaluation criteria for one category of conditionals.

In Chapter 3, I discussed whether the linguistic tradition in the study of conditional sentences could be of help in finding a way to distin-guish between those two categories of conditionals. The linguistic tradition has shown that it is not unusual to categorize conditionals, since the differences between conditional constructions and between various uses of the same construction are of special interest to the lin-guist. Several classifications were discussed for the purpose of judging whether a unequivocal distinction between problematic and unproble-matic conditionals could be made. Unfortunately, it was found that the classifications discussed could not be used to distinguish between problematic and unproblematic conditionals, although they failed to make such an unequivocal dis-tinction for quite different reasons. Notably, the classifications of Da-vies, Funk and Dudman seemed promising, since these classifications do not group problematic conditionals together with unproblematic ones. Their main shortcoming is that some conditionals are ambigu-ous: they could be classified in different categories. Davies, for instance, describes a category of conditionals that could considered to be the category of unproblematic conditionals, since she explicitly states that what she calls ‘knowledge conditionals’ are the only conditionals that realize a truth-functional relation between the antecedent and the consequent. It is characteristic for this category of conditionals that the proposition that is expressed in the antecedent is accepted by both parties engaged in the conversation. Yet, from a con-ditional seen in isolation, one cannot tell what position the parties take towards the antecedent. This means that one cannot decide whether a given conditional belongs to the category of knowledge conditionals

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and as a result, this conditional remains ambiguous between catego-ries. The classifications offered by Funk and Dudman suffer from the same ambiguity. Fortunately, the ambiguity disappears when the conditionals are placed in context. The conclusion reached in chapter 3, is that atten-tion must be shifted from the characteristics of the conditional to the characteristics of the context in which the conditional appears.

In Chapter 4, a context was provided that makes it possible to specify the conditionals that are unproblematic with regard to the definition of material implication. As was mentioned above, Davies contends that a conditional can only count as a knowledge conditional if both parties accept the antecedent. Argumentation offers a context in which this criterion is naturally met. Argumentation comes into play when one party engaged in a discus-sion tries to convince the other party that his point of view is correct. In order to do so, he puts forward a statement that his opponent agrees with and tries to show that if he agrees with this statement, she should agree with the initial point of view as well. The following example was used to illustrate this:

84 Ikram doesn’t drink alcohol, since she is a Muslim.

In this case there is a difference of opinion on the question whether Ikram drinks alcohol or not. Now that both parties agree that Ikram is a Muslim, the protagonist uses this statement as a premise in support of his claim. Of course, the protagonist will only be able to remove the antagonist’s doubt about this claim when he can show that agreement with the statement ‘Ikram is a Muslim’ means that the statement ‘Ikram doesn’t drink alcohol’ should be met with agreement as well. That is, apart from the premise ‘Ikram is a Muslim’ there is a second premise the protagonist is committed to: the premise ‘if Ikram is a Muslim, she doesn’t drink alcohol’. This premise I call the ‘connecting premise’, since it provides the connection between the ‘direct premise’ (Ikram is a Muslim) and the claim (Ikram doesn’t drink alcohol).Not only an application of modus ponendo ponens – like the one just mentioned – contains a connecting premise, such a connecting pre-mise is present in applications of modus tollendo tollens as well, as in 87:

87 Daniel is no athlete. If he were an athlete, he would have stamina. But he can’t climb the stairs without losing his breath.

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Although Davies would disagree with me here, I claim that in condi-tionals that function as a connecting premise in a modus tollendo tollens there is shared agreement between the speaker and the listener too, be it that in this case both parties do not agree on the acceptability of the antecedent, but on the falsity of the consequent. As a result, a conditional that functions as the connecting premise in an applica-tion of modus tollendo tollens fulfils a ‘transferring’ function as well: it transfers agreement on the falsity of the proposition expressed in the consequent to the proposition expressed in the antecedent. Chapter 4 is aimed at showing that the definition of material im-plication is unproblematic if its use is restricted to conditionals that function as a connecting premise in an application of either modus ponendo ponens or modus tollendo tollens. First of all, it is shown that the four situations described in the definition of material implication coincide with the possible outcomes of a discussion where a condi-tional functions as a connecting premise. Moreover, the context of argumentation makes it possible to explain the intuitive validity of the logical operations connected to the definition of material implication. It is shown how contraposition is needed in the case of indirect proof, how by means of hypothetical syllogism a connecting premise can be supported that is not immediately acceptable to the other party and how strengthening the antecedent is indispensable for a constructive attack on the connecting premise. The context of argumentation makes it possible to specify the requirements that need to be met so that a conditional can and will function as a connecting premise. First of all, the antecedent and the consequent need to contain what Frege calls a Gedanke: something that can be judged to be either true or false, after all, the content of the antecedent and consequent will be asserted (or, in case of modus tol-lendo tollens, denied) in the direct premise and the claim. This does not only exclude general conditionals like ‘If someone is a murderer, he is a criminal’ from functioning as a connecting premise, but also condi-tionals such as ‘If we pay off our debts, we will not have to pay interest anymore’. In such so-called ‘predictive conditionals’ the time indicated by the tense of the verb in the antecedent precedes the time referred to (the present tense is used whereas the antecedent refers to the future). The antecedents of such conditionals do not contain a Zeitbestim-mung and hence cannot be judged true or false. This first requirement explains the well-known counter-examples against contraposition and hypothetical syllogism: those counter-examples all contain conditio-nals that cannot function as a connecting premise.

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That a conditional can function as a connecting premise does not mean that it will be used as such. The conditionals arrived at in the paradoxes of material implication and the conditionals that express a concessive will not be put to use as a connecting premise because using them as such would either lead to conflicting commitments for the protagonist, or to circularity. Just to give an example, suppose a conditional is deduced from the falsity of the antecedent. Using it as a connecting premise in modus ponendo ponens is not possible. It would lead to a contradiction because the speaker would then have to commit himself to the truth of the antecedent. After all, it is this proposition that needs to be put forward as the direct premise. This commitment is in conflict with his commitment to the falsity of the antecedent that the speaker has taken upon himself by deducing the conditional from it. Using this conditional in modus tollendo tollens would lead to circula-rity, since the conclusion drawn in that case would be that the proposi-tion expressed in the antecedent is false, which was the starting point of our proof.

Up until this point, the reunification of logic and argumentation the-ory, where argumentation theory is used to clarify logical principles, seems to be a happy undertaking. By looking at the definition of mate-rial implication together with the logical operations of contraposition, hypothetical syllogism and strengthening the antecedent from the per-spective of argumentation theory, the role of this definition and those operations in the process of reasoning can be clarified. Moreover, when the definition of material implication is restricted to conditionals that function as a connecting premise, compelling counter-examples to those logical operations can be explained away in a systematic man-ner. Finally, focussing on the commitments of the participants results in disarming the paradoxes of material implication. However, with regard to one of the central aims of this thesis – fin-ding a way to evaluate argumentatively used conditionals – our inten-ded destination has not come within reach. To be sure, at first glance it may seem that one category of argumentatively used conditionals has been provided with the evaluation criteria laid out in the definition of material implication. But if the perspective of argumentation is consistently maintained, it will soon be realized that the definition of material implication does not suffice. Suppose one wants to evaluate a conditional that functions as a connecting premise in a modus ponendo ponens. In that case, the antecedent contains a proposition that is true (or at least commonly accepted by the interlocutors), since it is this

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proposition that is put forward as the direct argument. If we only use the truth table of material implication to evaluate the conditional, this means that in order to decide whether the conditional is true, we should focus our attention on the consequent. If the consequent is true, the conditional as a whole is true and if the consequent is false, the conditional as a whole is false. But unfortunately, the truth value of the consequent is not yet known / accepted: it is exactly this proposi-tion that is expressed in the standpoint under discussion and therefore created the need for argumentation in the first place. A similar complication is to be found in the case of conditionals that function as a connecting premise in a modus tollendo tollens. In such instances, the consequent contains a proposition that is commonly considered to be false, since the negation of this proposition is put forward as the direct argument. In an evaluation of the conditional that uses only the truth table of material implication, the attention is therefore shifted to the antecedent: if the antecedent is true, the condi-tional as a whole is false, if the antecedent is false, the conditional as a whole is true. But in this case, the truth value of the antecedent is not yet known / accepted, it being the negation of the proposition expres-sed in the standpoint under discussion. The above remarks indicate that in the search for a way to evaluate argumentatively used conditionals, we should strike out on a new course. Fortunately, within argumentation theory, the route to be followed has already been suggested. In argumentation theory, the re-lation between the direct premise and the conclusion drawn from it is expressed in an argument scheme. In the last section of Chapter 4, it was contended that an argument scheme should be interpreted as the ground a speaker has for maintaining his connecting premise. Althou-gh in argumentation theory the distinction between the connecting premise and the ground one has for maintaining it is not made, I claimed that this distinction has important advantages. For example, it makes the consequences of criticizing a connecting premise in many instances less severe. Suppose one claims that ‘Max can fly, since he is a bat’. In argumentation theory, this example is currently analyzed as follows: the standpoint ‘Max can fly’ is supported by the direct premise ‘Max is a bat’ and by the unexpressed premise ‘Bats can fly’. Conse-quently, a counter-argument like ‘Max has been born this morning’ – aimed at the unexpressed premise – results in the protagonist ha-ving to retract the general statement ‘Bats can fly’. When a distinction is made between the connecting premise and the ground one has for entertaining it, ‘Bats can fly’ is interpreted as the ground one has for

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maintaining the connecting premise ‘If Max is a bat, he can fly’. The above criticism can then be interpreted as rather being directed to the connection between the ground and the connecting premise, making it possible to maintain the former statement whilst retracting the latter one. A great advantage to the notion of an argument scheme is that in ar-gumentation theory it typically is combined with critical questions for the evaluation of those schemes. Because of the close relation between argument schemes and connecting premises, these critical questions indicate how connecting premises based on different grounds can be critized. Although there is much discussion in the field regarding the number of argument schemes that can be discerned, along with uncertainties regarding the kind of critical questions that are associ-ated with the different argument schemes, the theory of argument schemes at least provides for a starting point for the evaluation of conditionals that function as a connecting premise. For this category of conditionals, the above mentioned aim of this thesis – finding a way to evaluate argumentatively used conditionals – is therefore more or less within reach.

Given that conditionals functioning as a connecting premise are provided with evaluation criteria, the question now remains how conditionals that fulfil other argumentative functions can be analyzed and evaluated. Chapter 5 and Chapter 6 were aimed at doing just that. In Chapter 5 conditionals that function as a standpoint were discus-sed and in Chapter 6 conditionals that function as a consituent of an argument scheme were dealt with. The term ‘conditional functioning as a standpoint’ is used for those instances where the protagonist indicates he only wants to take upon himself the burden of proof for his standpoint ‘if a specific condition is met’. It has been argued that this category consists of three types of standpoints, depending on the position both participants take on the proposition expressed in the antecedent. Regarding the first type – a conditional standpoint – it is assumed both parties do not know whether the proposition expressed in the antecedent is true, as in 100:

100 I don’t know exactly when Tess will arrive, but if she is here on Wednesday, then we should all go to the theatre. Wednesday night is the final night King Lear will be performed and I have heard it is very good.

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The antecedent is merely supposed to be true, and on that basis the discussion is carried on. In response to a conditional standpoint, the other party can attack the antecedent by showing that it is false. The protagonist will than retract his standpoint and all the support he has put forward in defence of it, since the condition in the antecedent is not met. The other party could also show that it is very unlikely that the proposition expressed in the antecedent will be realized. In such instances he is unwilling to go along with the hypothetical context sketched and the discussion cannot proceed. If the other party provi-sionally accepts the antecedent, a discussion can start on the question whether within this hypothetical context the standpoint expressed in the consequent is correct or not. An attack on the connection between the antecedent and consequent is pointless. A conditional standpoint should be interpreted as a conditional speech act, and in conditional speech acts the act expressed in the consequent is performed as soon as the conditional is uttered. Therefore, by saying ‘if X, my standpoint is Y’ the standpoint ‘Y’ has been put forward. Regarding the second type – a conditional defence – the main stand-point is supported by means of at least two lines of defence. The se-cond line of defence is introduced by a conditional with an antecedent that depicts the situation that the first line of defence is untenable. The consequent of this conditional contains either a repetition of the main standpoint, or an alternative standpoint that is less preferred by the protagonist. An example of a conditional defence is 101:

101 We shouldn’t remain home all day. It is nice and sunny. Andeven if it were cloudy, we should go out. We all need some fresh air.

Conditional defences differ from conditional standpoints in that in the case of a conditional defence the protagonist is of the opinion that the proposition expressed in the antecedent is untrue. After all, the prota-gonist has just put forward a line of defence that is inconsistent with the antecedent of the conditional used as a conditional defence. The other party may be undecided on the question whether the antecedent is true or not. As with conditional standpoints, in the case of a conditional defence, an attack on the connection between the antecedent and consequent is pointless. Furthermore, an attack on the antecedent of the conditional does not make much sense either: criticizing the antecedent only rein-forces the first line of defence. This leaves an attack on the consequent

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(or on the arguments supporting the consequent) as the only reasona-ble follow up to a conditional defence. Finally, the third type – hypothetical standpoints – are characterized by both participants agreeing that the proposition expressed in the antecedent is false and cannot become true, as in 103:

103 It is a pity Tess arrives not until Thursday. Had she been here on Wednesday, we should have gone to the theatre together. Wednesday night is the final night King Lear is performed and I have heard it is very good.

The proposition is only maintained ‘for the sake of argument’. This agreement on the falsity of the antecedent makes an attack on the antecedent of the conditional pointless. However, the other party may respond by explicitly stating that the proposition in the antecedent is not true, in order to indicate that he is unwilling to conduct an hypo-thetical discussion. But of course this party can also go along with the hypothetical context sketched in the antecedent, resulting in a discus-sion on the question whether the standpoint expressed in the conse-quent is acceptable within this hypothetical context.

Chapter 6 was dedicated to conditionals that function as constituents of an argument scheme. Since there is no consensus on the number of argument schemes that can be discerned, and since many argu-ment schemes lack a precise description, there has been no attempt to provide a complete overview of conditionals that fulfil such a function; the attention is rather focused on conditionals used as constituents of pragmatic argumentation, of dilemmas, of arguments from authority and of arguments from example. The use of a conditional as a premise in pragmatic argumentation illustrates most clearly how the function that a conditional fulfils, influences the way this conditional must be evaluated. In pragmatic argumentation, a certain policy statement is defended by pointing at either desirable or undesirable consequences. An example of pragma-tic argumentation is 90:

90 We should pay off our debts. If we pay off our debts, we don’t have to pay interest anymore.

Pragmatic argumentation expresses a means / ends relation, whereby the policy is the means and the achievement of positive outcomes

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or the avoidance of negative outcomes is the end. Conditionals can only successfully function as premises in pragmatic argumentation if several quite precise criteria are met. First of all, the antecedent should describe a possibility (otherwise the policy is not feasible). Secondly, there should be a causal relationship between the antecedent and the consequent (otherwise the policy is not effective). Finally, the connec-tion between the antecedent and the consequent should be of a kind of biconditional nature (otherwise, the policy is not necessary). The conditional can be successfully attacked by showing that either one of those criteria is not met. When a conditional is used as a constituent of a dilemma, the re-quirements it must meet depend on the type of dilemma put forward. Chapter 6 discussed two types of dilemmas: dilemmas in the col-loquial sense of the word and simple constructive dilemmas. In the case of a dilemma in the usual sense of the word, it is argued that a decision cannot be made because the alternative options lead to equally unfavorable (or favorable) consequences, as in 131:

131 I don’t know whether we should accept this apartment or not. If we accept it, we will loose our accumulated rights and will have to wait at least seven years before being eligible for another one. If we don’t accept it, we will have to wait God knows how long before being offered some acceptable place to live.

The conditionals functioning as part of such a dilemma can be at-tacked by showing that the antecedent is impossible – which amounts to showing that one of the proposed course of actions cannot be implemented. Furthermore, it could be questioned as to whether the consequences depicted would actually occur. Finally, it could be argued that the consequences depicted in the consequent will occur anyway. In that case, those (favorable or unfavorable) consequences drop out of the equation, since the proposed action is not necessary to bring those consequences about. In a simple constructive dilemma, it is argued that whatever pos-sibility happens to be realized, the result is the same. Example 133 represents a case in point:

133 Whatever the result of the vote will be, our action committee can be disbanded. If the law on referendum is voted through, our committee can happily adjourn – we will have reached our goals. But also if it is voted down we can discontinue. If we don’t

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reach our goals now, there is no chance we ever will.

If a conditional functions as a premise in a simple constructive dilemma, criticism of the antecedent is pointless: the speaker argues that his claim is true whatever possibility happens to be realized, and has for each conditional functioning as a premise already taken into account that the situation sketched in its antecedent might not occur. Such a conditional can be seen as a specific type of conditional standpoint and should be evaluated accordingly: a reasonable follow up would therefore be a discussion on the question as to whether the standpoint expressed in the consequent can indeed be maintained in the context sketched in the antecedent. When taking a closer look at conditionals that function as the con-stituent of an argument from authority, we see that those conditionals can be determined to be a specific kind of conditional standpoint as well. A speaker may put forward an argument from authority by me-ans of a conditional if the authority quoted is presumed not actually to have been in a position that would allow him to comment on the subject under discussion. By means of the conditional, a hypothetical context is sketched in which the authority would be in a situation that allows him to comment on this subject and the consequent would describe what the speaker thinks the comment might be. An example of a hypothetical appeal to authority is 123:

123 The performance of King Lear in the municipal theatre is anutteer disaster. Had Shakespeare been in the audience, he would have hated it and would have made it impossible for the actors to perform.

Conditionals fulfilling this function can be criticized by either re-jecting the hypothetical context that is sketched or by questioning whether in this context the authority would indeed have commented in this manner. With regard to conditionals functioning as a constituent of an argument from example, it was found that it is crucial to know what subtype of this argument scheme one is dealing with. A distinction was made between an inductive argument from example – where the examples are put forward in order to derive a general rule – and an illustrative argument from example – where a general rule is not so much ‘proven’ but made plausible by means of a well-chosen, prototy-pical example. In 138 one finds an inductive argument from example

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and in 139 an illustrative argument from example:

138 Always when fish is cooked, a nasty deposit remains in the pan. Last time, when we had salmon, it took me an hour to scrape it off. And when you cooked pasta with fish sauce, even the cover was completely covered. And look at the pan now: I can hardly remove it.

139 You never should force a child to do something, it leads you nowhere. For years your mother forced you to eat vegetables and now you dislike them even more.

In an inductive argument from example, there is no room for ‘hypo-thetical’ examples. To be sure, in that case one could construct the example in such a way that the general rule is supported, but this sup-port is not convincing since it presupposes the rule it is meant to sup-port. Illustrative arguments from example lend themselves quite well to ‘hypothetical’ examples. Such examples allow the speaker to tailor his argument to the audience he is trying to convince. In criticizing conditionals that function as an illustrative argument from example, the other party could either criticize the antecedent, or criticize the consequent within the hypothetical context the antecedent sketches. In the first case, this party is unwilling to go along with the example because it is found to be too unrealistic. In the second case, he goes along with the hypothetical context sketched, but does not agree that in this context the standpoint expressed in the consequent holds.

Although the route towards it has not been a straightforward one, I believe that in this thesis the intended destination of finding a way to analyze and evaluate argumentatively used conditionals has been reached. The pragma-dialectical approach to argumentation, with its emphasis on the functionalization of the subject matter in particular, made it possible to formulate valuable distinctions between different types of conditional sentences. However, with regard to this final destination, there are still many uncharted areas. Due to the unclarity regarding the number of argument schemes that can be discerned and the precise description of the various argument schemes themselves, this thesis contains only a tentative sketch of the way in which con-ditionals that function as a connecting premise can be evaluated. In order to refine this sketch, it would be necessary to have an overview of the different grounds one can have in maintaining a connecting

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premise. It may be difficult to know how many argument schemes have to be discerned, but in formulating the critical questions belon-ging to each particular argument scheme, the distinction made in this thesis between the connecting premise and the ground a speaker has for maintaining it, can be of value. If one realizes that the support for a connecting premise can be challenged in two ways – one can criticize the ground as well as the connection between this ground and the connecting premise – it becomes possible to map out the critical questions in a more systematic way. The lack of consensus in the field of argument schemes has also led to many uncharted areas with regard to the analysis and evaluation of conditionals that function as a constituent of an argument scheme. Chapter 6 gives by no means a complete overview of the ways condi-tionals can function as such. But although the present treatment of conditionals functioning as a constituent of an argument scheme is rather tentative, it has become clear that when studying conditionals, it is important to take the different argument schemes into account. Pragmatic argumentation forms a case in point: the role the condi-tional fulfils specifies the criteria that a conditional sentence must meet in order to function succesfully as a constituent of this argument scheme.

Apart from the uncharted areas due to the lack of consensus on argument schemes, there are still other parts of this thesis that call for elaboration. As it stands now, it may be difficult to perceive the distinction between conditionals that function as a connecting pre-mise in modus tollendo tollens (If Daniel were an athlete, he would have stamina) and conditionals functioning as hypothetical standpoints (If Daniel had been an athlete, he would have had stamina). The same holds for the distinction between conditional standpoints that contain a descriptive proposition and connecting premises where the connec-tion is based on a causal relationship. It also may be equally difficult to differentiate between other categories of conditionals. I think that the focus on the commitments of the participants might form a lead as to how one might clarify these distinctions. As was argued in Chapter 4, the antecedent of a conditional that functions as a connecting premise in an application of modus ponendo ponens needs to contain a Gedanke; something that can be judged to be either true or false at the moment the discussion takes place. A protagonist attemp-ting to support his claim by means of a direct premise, presupposes that the antagonist accepts this premise as true and also accepts that

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through the connecting premise the truth of the antecedent is transfer-red to the consequent. In the case of a conditional standpoint, such mu-tual agreement on the truth of the antecedent is not presupposed. On the contrary, the only agreement that is presupposed is that at the time the discussion takes place it is unknown whether the antecedent is true or not. In a similar manner, the (expected) commitments of the partici-pants are different in the case of a connecting premise in an application of modus tollendo tollens and in the case of a hypothetical standpoint. In the first case, there exists a difference of opinion about the falsity of the antecedent, whereas in the case of a hypothetical standpoint, the protagonist presupposes that the antagonist agrees with him that the proposition expressed in the antecedent is false. It would be interesting to see whether and – if so – how those com-mitments can be externalized by the linguistic construction through which the conditionality is expressed. Drawing on the vast amount of research done within the field of linguistics concerning the different ways to express conditionality, it may be possible that some conditio-nality markers are more adequate in the case of a connecting premise in an application of modus tollendo tollens and yet others in the case of a hypothetical standpoint, because such markers often give some in-formation about the speaker’s attitude with respect to the propositions expressed. Such linguistic clues could in turn be used (in combination with contextual information) to correctly analyze and eventually evalu-ate argumentatively used conditionals.

A final uncharted area that may prove worthwhile investigating, is the way in which several parts of the conditional can be criticized. To give an example: in chapter 6 it was argued that a conditional that functi-ons as a constituent of pragmatic argumentation can be criticized by questioning the causal link between the antecedent and the conse-quent. Relevant criticism might demonstrate that it is untrue or very unlikely that the cause depicted in the antecedent leads indeed to the effect sketched in the consequent. How the antagonist should go about criticizing this causal link, and what reasons he might put forward in order to substantiate his criticism has not been discussed. A second example, would be criticism of the connection between the ground one has for maintaining a connecting premise and the connecting premise itself. Although it was indicated that such criticism could be quite fruit-ful and that some of the critical questions that are related to a specific argument scheme are precisely aimed at this connection, nevertheless, it remained unclear along which lines such criticism would proceed.

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In order to provide answers to these questions, it may be beneficial to reunify logic and argumentation theory again. Where propositio-nal logic was valuable in elucidating conditionals that function as a connecting premise and vice versa, additional logical approaches may be helpful in clarifying other argumentative functions that conditio-nals can fulfil. Probability logic, for instance, which has been devised to deal with questions of causality, may be of help in specifying the criticism that can be brought forward against the causal relation bet-ween the antecedent and consequent of a conditional that is employed in pragmatic argumentation. By calculating the probabilities of the various consequences, it may be possible to weigh the advantages and disadvantages of a specific policy in a more precise manner. Regarding the case of pragmatic argumentation in which past actions are evalu-ated, possible world semantics might elucidate how the connection between the antecedent and consequent of the conditional must be evaluated. The concept of the closest world – the world in which most ‘other things are equal’ – may offer insights for evaluating whether the conditional is indeed of the requested biconditional nature. Finally, the connection between the ground one has for maintaining a connecting premise and the connecting premise itself, seems to be a topic that has extensively been discussed in several non-monotonic logics. It would be interesting to see whether argumentation theory could benefit from the insights in this field.

Although I realize that this proposal for analyzing and evaluating argumentatively used conditionals is still very rudimentary, the frame-work offered seems to clarify at least some of the argumentative uses of conditionals. Moreover, it may be just because of this attempt that the uncharted areas can be located with more precision. Therefore, I hope that this thesis at least partly answers Fischer’s plea to pay more attention to propositions that are not presented as true, but are merely supposed ‘for the sake of argument’. My appeal in turn would be to increase this focus on conditionals in argumentation, because this the-sis has indicated that the role played by conditionals in argumentation and reasoning cannot be denied.

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Samenvatting

Conditionele uitspraken vervullen in argumentatie een nuttige functie. Een spreker die een bepaalde maatregel bepleit, kan zijn standpunt bijvoorbeeld onderbouwen met een conditionele uitspraak waarin wordt geschetst welke positieve uitwerking deze maatregel zal hebben, zoals in 1:

1 Laten we dat huis kopen. Als we daar wonen, is er genoeg ruimte voor iedereen. Jij zult dan ook de tuin hebben die je altijd al wilde. Bovendien hoeven we de kinderen dan niet meer iedere morgen weg te brengen: ze kunnen gewoon zelf naar school lopen.

Een spreker kan ook een conditionele zin gebruiken om aan te geven dat hij de verdedigingslast voor een standpunt alleen op zich wil ne-men wanneer aan een bepaalde voorwaarde is voldaan, zoals in 2:

2 Ik weet niet of ik met je mee kan, maar als we samen gaan, dan zouden we de auto kunnen nemen. Ik weet zeker dat mijn ou-ders het geen probleem vinden als we mijn moeders auto lenen.

Daarnaast kan een spreker een conditionele uitspraak gebruiken om een scenario te schetsen dat ooit verwezenlijkt had kunnen worden, maar nu onmogelijk is, zoals in 3:

3 Had ik die baan als masseuse bij Google maar aangenomen, dan zou ik me nu nergens meer zorgen over hoeven maken. Ze boden me aandelen aan en die zouden nu een fortuin waard zijn.

Hoewel conditionele zinnen in argumentatie veelvuldig worden gebruikt, bestaat er binnen de argumentatietheorie geen systemati-sche methode voor de analyse en evaluatie van dergelijke uitspraken. Dit betekent echter niet dat conditionele zinnen in de wetenschap onbesproken zijn gebleven. Binnen het vakgebied van de logica houdt men zich al sinds het einde van de 4e eeuw voor Christus bezig met de vraag wat een als-dan-zin betekent en onder welke omstandigheden een dergelijke zin als waar moet worden beschouwd. Rond die tijd for-muleerde Philo van Megara zijn beroemde stelling dat een als-dan-zin alleen onwaar is wanneer het antecedent waar is en het consequent

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onwaar, een stelling die direct aanleiding gaf tot veel kritiek. Opvallend genoeg formuleerde Frege in 1848 – zonder op de hoogte te zijn van de stelling van Philo van Megara – een beschrijving van conditionele uitspraken die hiermee grote overeenkomsten vertoonde en die nage-noeg dezelfde kritische reacties opriep. In reactie op deze kritiek zijn diverse alternatieve logische benaderingen van conditionele zinnen ontwikkeld. Conditionele zinnen hebben niet alleen de aandacht van logici gewekt, ook linguïsten hebben zich uitgebreid met als-dan-zinnen beziggehouden. Zij hebben zich daarbij primair gericht op de wijze waarop conditionaliteit in de taal kan worden uitgedrukt. Daarbij pro-beren linguïsten tevens te verklaren waarom sprekers soms uitdruk-kingen gebruiken die wijzen op conditionaliteit, terwijl daarvan geen sprake lijkt te zijn. Een beroemd voorbeeld hiervan is de zogeheten ‘Austin-conditional’: ‘Als je honger hebt, staan er koekjes op de kast’. Het opmerkelijke in deze zin is dat de aanwezigheid van de koekjes op de kast afhankelijk gemaakt wordt van de behoefte van de luisteraar (terwijl de koekjes er uiteraard altijd staan, of de luisteraar nu honger heeft of niet). Gesteund door deze lange traditie in de studie van conditionele uitspraken, doe ik in dit proefschrift een voorstel voor een model voor de analyse en beoordeling van conditionele uitspraken die worden gebruikt in argumentatie. Ik richt me daarbij primair op conditio-nele uitspraken die argumentatief worden gebruikt. Dit betekent dat conditionele zinnen als ‘als je het niet erg vindt, zou ik eerst even mijn gedachte af willen maken’ niet aan de orde komen, hoezeer ze ook van nut kunnen zijn voor een goed verloop van de discussie. De conditio-nele uitspraken die in deze dissertatie besproken worden, fungeren in de discussie ofwel als standpunt, ofwel als argument. Daarbij is gekozen voor een pragma-dialectische benadering van argumentatie, zoals die is ontwikkeld door Van Eemeren en Grooten-dorst. Kenmerkend voor deze benadering is dat argumentatie gezien wordt als een middel om een verschil van mening op te lossen (Van Eemeren & Grootendorst 1992, 2004). Volgens van Eemeren en Groo-tendorst ontstaat een verschil van mening op het moment dat iemand een standpunt naar voren brengt dat door de wederpartij niet (direct) wordt aanvaard. Door middel van argumentatie probeert de spreker vervolgens de twijfel bij de wederpartij weg te nemen. De pragma-dialectische benadering beschrijft onder meer welke stappen nodig zijn om het verschil van mening op een redelijke wijze op te lossen en welke discussieregels een goed verloop van een discussie waarborgen.

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De zoektocht naar een analyse- en beoordelingsmodel voor argumenta-tief gebruikte conditionele uitspraken begint in hoofdstuk 2 bij de hier-bovengenoemde stelling van Philo van Megara, die bekend is geworden als de ‘definitie van materiële implicatie’. Paragraaf 2.2 beschrijft deze definitie en de problemen die traditioneel met deze definitie en met de daarmee samenhangende logische operaties ‘contrapositie’, ‘hypothe-tisch syllogisme’ en ‘strengthening the antecedent’ worden geassocieerd. Omdat critici tegenvoorbeelden hebben geformuleerd die op het eerste gezicht zeer overtuigend zijn, is het begrijpelijk dat een aantal logici de definitie van materiële implicatie hebben verworpen als een adequate beschrijving van de betekenis van ‘als-dan’ en alternatieven hebben voorgesteld. In paragraaf 2.3 wordt een aantal van dergelijke alterna-tieve logische systemen beschreven. Het verwerpen van de definitie van materiële implicatie en de bij-behorende logische operaties heeft echter ook nadelen. In paragraaf 2.4 stel ik daarom voor om de definitie van materiële implicatie niet te overhaast te verwerpen maar te behouden voor conditionele uitspraken waarvoor deze definitie en de logische operaties onproblematisch zijn. Voor de problematische gevallen kan dan een alternatief beoordelings-model worden ontwikkeld. Dit betekent echter wel dat er een manier gevonden moet worden om de problematische conditionele zinnen te onderscheiden van de onproblematische gevallen.

In hoofdstuk 3 is nagegaan of de linguïstische traditie in het onderzoek naar conditionele uitspraken een bijdrage kan leveren aan de ontwik-keling van een systematische methode om problematische en onpro-blematische conditionele uitspraken van elkaar te onderscheiden. De paragrafen 3.2 en 3.3 beschrijven verschillende classificaties van conditi-onele zinnen en in paragraaf 2.4 wordt beoordeeld welke classificaties voor het maken van dit onderscheid van nut kunnen zijn.Helaas blijkt geen van de classificaties bruikbaar om op een syste-matische wijze een onderscheid te maken tussen problematische en onproblematische conditionele uitspraken, zij het dat ze niet om dezelfde reden te kort schieten. De classificaties van Funk, Dudman en Davies lijken een aanknopingspunt te bieden omdat daarbij het belangrijkste struikelblok is dat een aantal conditionele zinnen ambigu is: deze zinnen kunnen in meerdere klassen worden ondergebracht. De ambiguïteit van deze uitspraken verdwijnt echter zodra de zinnen in een context worden geplaatst. De conclusie van hoofdstuk 3 is dan ook dat de aandacht verlegd moet worden van de eigenschappen van de conditionele uitspraak naar de eigenschappen van de context waarin deze uitspraak voorkomt.

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Hoofdstuk 4 beschrijft een context die het mogelijk maakt de conditi-onele zinnen die onproblematisch zijn met betrekking tot de definitie van materiële implicatie te specificeren. De centrale stelling van hoofd-stuk 4 is dat de definitie van materiële implicatie beperkt dient te wor-den tot conditionele uitspraken die de rol vervullen van verbindend argument in een modus ponendo ponens redenering of in een modus tollendo tollens redenering. Het volgende voorbeeld kan verduidelijken wat met een verbindend argument wordt bedoeld:

1 Ikram drinkt geen alcohol, want ze is moslima.

1.

Ikram drinkt geen alcohol

↑

1.1 1.1’

ze is moslima − & − [als Ikram moslima is, dan drinkt ze geen alcohol]

In dit voorbeeld bestaat er verschil van mening over het standpunt ‘Ikram drinkt geen alcohol’. De protagonist is van mening dat dit standpunt juist is, terwijl de antagonist betwijfelt of deze stelling klopt. Om de twijfel bij de antagonist weg te nemen voert de protago-nist het directe argument ‘Ze is moslima’ aan. Hij gaat ervan uit dat (1) de antagonist dit argument als waar zal aanvaarden en (2) dat het aanvaarden van dit directe argument ertoe leidt dat de twijfel aan het standpunt wordt weggenomen. De protagonist is daarom niet alleen gebonden is aan het directe argument ‘Ikram is moslima’ maar ook aan het verbindende argument ‘Als Ikram moslima is, dan drinkt ze geen alcohol’. Via dit verbindende argument wordt de ‘waarheid’ van het directe argument overgedragen op het standpunt. De definitie van materiële implicatie beschrijft precies de vier situ-aties die zich kunnen voordoen in een discussie waarin een conditio-nele uitspraak fungeert als verbindend argument. Daarnaast maakt de argumentatieve context het mogelijk om te verklaren dat contrapositie, hypothetisch syllogisme en strenghtening the antecedent intuitief aan-vaardbaar zijn. Contrapositie is noodzakelijk bij een indirect bewijs, een hypothetisch syllogisme kan gebruikt worden om een verbindend argument te ondersteunen dat niet meteen door de wederpartij wordt aanvaard en zonder strenghtening the antecedent kan geen geslaagde aanval op een verbindend argument worden uitgevoerd. De argumentatieve context biedt tevens een systematische verkla-ring voor de problemen die traditioneel met de definitie van materiële

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implicatie en met contrapositie en het hypothetisch syllogisme worden geassocieerd. Wil een conditionele zin als verbindend argument kun-nen fungeren, dan moet zowel het antecedent als het consequent een ‘Gedanke’ bevatten – een propositie die als waar of onwaar beoor-deeld kan worden. Niet alleen algemene conditionele uitspraken zijn daarom uitgesloten van de functie van verbindend argument, maar ook ‘predictive conditionals’, zoals ‘als we onze schulden afbetalen, dan hoeven we geen rente meer te betalen’. Predictive conditionals bevat-ten geen ‘Zeitbestimmung’ waardoor niet kan worden beoordeeld of ze waar of onwaar zijn. De bekende tegenvoorbeelden tegen contrapositie en het hypothe-tisch syllogisme, die besproken zijn in paragraaf 2.2, bevatten allemaal conditionele uitspraken die niet aan dit vereiste voldoen. Ook de paradoxen van materiële implicatie kunnen binnen een argumenta-tieve context worden verklaard. De conditionele uitpraken die hierbij worden afgeleid kunnen wel, maar zullen niet als verbindend argu-ment worden gebruikt omdat de spreker zichzelf dan zal tegenspreken of zich schuldig zal maken aan een cirkelredenering. Tot zover lijkt het nuttig om inzichten uit de argumentatietheorie te combineren met inzichten uit de logica. De waarheidswaarden die in de waarheidstabel van de materiële implicatie zijn uitgedrukt, zouden kunnen worden gebruikt om conditionele zinnen te beoordelen die de functie vervullen van verbindend argument. Wanneer het argumenta-tietheoretisch perspectief consequent wordt toegepast, blijkt echter dat de waarheidswaarden voor de beoordeling van dergelijke zinnen niet bruikbaar zijn. Om een beoordelingsmodel op te stellen voor condi-tionele uitspraken die de functie van verbindende premise vervullen, moet daarom een andere koers worden gevolgd. Gelukkig biedt de argumentatietheorie al een aanwijzing voor de richting die gekozen kan worden. De argumentatietheorie kent na-melijk het concept ‘argumentatieschema’, waarin het verband tussen het argument en het standpunt wordt uitgedrukt en waaraan kritische vragen gekoppeld zijn waarmee dit verband aan een kritische beschou-wing kan worden onderworpen. In paragraaf 4.4 wordt betoogd dat het argumentatieschema moet worden beschouwd als een argument ter ondersteuning van de verbindende premisse. De kritische vragen die behoren tot het argumentatieschema zijn ofwel gericht op dit ar-gument, ofwel op het verband tussen dit argument en de verbindende premisse en kunnen fungeren als beoordelingscriteria voor conditio-nele uitspraken die de rol vervullen van verbindend argument.Hoofdstuk 5 beschrijft conditionele uitspraken die fungeren als

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standpunt. Een spreker kan een conditionele uitspraak gebruiken om zijn standpunt naar voren te brengen wanneer hij de verdedigingslast voor dit standpunt alleen kan aanvaarden indien aan de voorwaarde in het antecedent is voldaan. In hoofdstuk 5 worden drie categorieën van voorwaardelijke standpunten beschreven. Paragraaf 5.2 behandelt ‘conditionele standpunten’: standpunten die voorwaardelijk naar voren worden gebracht omdat er onzekerheid / twijfel bestaat over een feit. Het is kenmerkend voor deze categorie dat beide deelnemers aan de discussie deze twijfel delen. Door in het antecedent van een condi-tionele uitspraak de situatie te schetsen waarin deze onzekerheid is opgeheven, kan de discussie voortgang vinden over het standpunt dat in het consequent is uitgedrukt. In paragraaf 5.3 worden conditionele uitspraken besproken die fun-geren als een ‘voorwaardelijk verweer’. Van voorwaardelijk verweer is sprake wanneer de protagonist een tweede poging om de wederpartij van zijn standpunt te overtuigen inleidt met een conditionele uit-spraak. Het antecedent schetst de situatie waarin een eerdere overtui-gingspoging niet opgaat en het consequent bevat ofwel een herhaling van het standpunt ofwel een alternatief standpunt. Het verschil tussen een voorwaardelijk verweer en een conditioneel standpunt is dat de twijfel aan de propositie die in het antecedent is uitgedrukt niet ge-deeld is. De protagonist is van mening dat deze situatie niet overeen-komt met de werkelijkheid, maar hij laat de mogelijkheid open dat de antagonist daar anders over denkt. Paragraaf 5.4 behandelt hypothetische standpunten. Bij hypotheti-sche standpunten zijn beide partijen het erover eens dat het antece-dent een situatie beschrijft die niet overeenkomt met de werkelijkheid. Toch nemen ze deze situatie voor waar aan, om de discussie over het standpunt die in het consequent is opgenomen, doorgang te kunnen laten vinden.

Hoofdstuk 6 is gericht op conditionele uitspraken die een onderdeel vormen van een argumentatieschema. Binnen de argumentatietheorie bestaat geen overeenstemming over het aantal argumentatieschema’s dat onderscheiden kan worden en over de precieze beschrijving van deze schema’s. Het overzicht dat in hoofdstuk 6 gegeven wordt, is dan ook allerminst uitputtend: er wordt slechts een indicatie gegeven van de wijze waarop de analyse en beoordeling van conditionele uitspra-ken die een deel uitmaken van een argumentatieschema in zijn werk kan gaan. Het hoofdstuk behandelt conditionele uitspraken die een onderdeel uit maken van pragmatische argumentatie, van dilemma’s,

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van autoriteitsargumentatie en van voorbeeldargumentatie. Hoofdstuk 6 maakt opnieuw duidelijk dat het voor de analyse en beoordeling van argumentatief gebruikte conditionele uitspraken van groot belang is om de uitspraak te beschouwen binnen de directe ar-gumentatieve context. Bij de beoordeling van conditionele zinnen die deel uitmaken van voorbeeldargumentatie is het voor de beoordeling zelfs van belang van welk subtype sprake is. Zo is bij inductieve voor-beeldargumentatie het gebruik van ‘hypothetische voorbeelden’ niet toegestaan, terwijl dergelijke voorbeelden in het geval van illustratieve voorbeeldargumentatie juist zeer overtuigend kunnen zijn. De argumentatieve context is ook van belang bij pragmatische argumentatie, waarbij de invoering van een maatregel wordt verdedigd of juist afgeraden op basis van de al dan niet gewenste gevolgen die deze maatregel zal hebben. Conditionele uitspraken die onderdeel uitmaken van dit argumentatieschema, schetsen de gevolgen die optreden wanneer de maatregel is ingevoerd. Een conditionele zin kan deze functie alleen naar behoren vervullen wanneer aan een aantal vereisten is voldaan. Allereerst moet het antecedent een mogelijkheid bevatten: anders is de discussie over de maatregel zinloos omdat de maatregel onuitvoerbaar is. Verder moeten de gevolgen die in het con-sequent worden geschetst niet sowieso optreden. Zou dat wel het geval zijn, dan zou de ratio voor de maatregel verdwijnen – de maatregel zou daarmee overbodig zijn. Deze specifieke vereisten illustreren mis-schien nog wel het duidelijkst dat het voor de analyse en beoordeling van conditionele uitspraken van belang is om aandacht te besteden aan de functie die deze uitspraak in de argumentatie vervult.

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Adams; 32Anderson & Belnap; 27argument from authority; 117-119, 148, 162-165, 181argument from example; 147, 165-167, 181argument scheme; 114, 147, 176-177, 179, 182-183austin-conditional; 9Bennett; 35Comrie; 51, 64, 154concession; 20, 108, 175conditional defence; 124, 133-138, 178conditional proof; 128conditional standpoint; 48, 123, 126-135, 143, 161, 165, 168, 177, 183connecting premise; 86, 88-90, 104, 115-119, 173, 176, 183contraposition; 19-21, 42, 43, 93-95, 107, 171, 174counterfactual; 34, 41, 47, 51, 71, 72, 73, 105, 106Dancygier; 48, 58-61, 68, 76Davies; 68-74, 78-79, 80, 172definition of material implication; 16, 90-93, 113, 172, 174, 176dilemma; 148, 157-162, 180direct premise; 88, 173Dudman; 53-58, 75, 80,102, 172fallacy of denying the antecedent; 135Fisher; 7, 185Frege; 8, 90, 93, 100, 102, 103, 174 Funk; 52-53, 74, 80, 172Gedanke; 100, 103, 174general conditional; 100-101, 106, 174Gibbard; 44Grice; 24hypothetical standpoint; 125, 138-140, 142, 168, 179, 183hypothetical syllogism; 21, 42, 43, 96-97, 106-107, 171, 174hypothetisches Gedankengefüge; 101, 102illustrative argument from example; 166-167indirect proof; 93-95inductive argument from example; 165-166Johnson; 110Johnson-Laird; 50, 62, 76, 96judgeable content; 99Kienpointner; 148-149, 166knowledge conditionals; 73, 78-79, 83, 172Lewis, C.I.; 23, 26

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Lewis, D; 31,44, 106logical minimum; 111Mackie; 18modal logic; 26, 41modus ponendo ponens; 87, 92, 107, 109-110, 120, 143, 174, 176, 183modus tollendo tollens; 90, 92, 94, 108, 109-110, 120, 142,173, 176, 183Moore; 23Nieuwint; 40, 42, 62, 76non-monotonic logic; 36-39, 185Noordman; 63, 77paradoxes of material implication; 18, 108-110, 175Perelman & Olbrechts-Tyteca; 148, 149, 157, 165, 166Philo of Megara; 8, 15, 171possible world semantics; 29-32, 40, 185pragma-dialectics; 9-11, 182pragmatic argumentation; 147, 150-157, 169, 179pragmatic optimum; 111,115predictive conditional; 58-61, 103, 143, 174probability theory; 32-36, 40, 185ramsey test; 29, 156relevance logic; 27-28Schellens; 149, 157speech act conditional; 66, 130speech act theory; 10Stalnaker; 29, 31, 106, 141stock issues; 152strenghtening the antecedent; 22, 42, 43, 97-98, 171, 174strict implication; 26Sweetser; 65-67, 77transitivity; 21Van Belle, Horst & Schaeken; 67Van Eemeren & Grootendorst; 9, 111-113, 114, 135, 192Zeitbestimmung; 102, 174

Frans van Eemeren had not initiated the NWO- project on argumentative indicators and had not offered me the freedom and the confidence that he did, Agnes van Rees had not lent me her sharp eye, Erik Krabbe had not shown his genuine inte- rest, had not provided his many critical remarks on both content and grammar and had not shared his valuable proposals for improvement, Tjark Kruiger and Erik Viskil had not first raised my interest in argumentation theory and had not by means of their lectures defied me to think, Rob Grootendorst had not encouraged me to start this research and had not pointed out to me that research can take its own direction, the members of the ‘promoteam’, especially Mas Fopma and Jan Albert van Laar, had not had the endurance to hear me out on many occasions, Menno van de Koppel, Elliott Eisenberg and Melle Hammer had not supported me in the production of the book, Stefanieke Veenstra had not been so utterly uncritical, Egon had not lovingly given me all this room for manoeuvre, my parents had not been my parents ...

I would never have succeeded in writing this thesis.

Janne Maaike Gerlofs

If

then