the context principle and dummett

7/22/2019 The Context Principle and Dummett

1/26

The Context Principle andDummett 's Argum ent fo r Anti-realismbyKAR EN G REEN

Monash University

Abr/ruct: In his earlier writings, Dumm ett mad e a distinction between deep and shallowarguments for being suspicious of bivalence. Deep argum ents brought with them a com -mitment to an ti-realism, shallow arguments did not. This distinction was m otivated by acertain understanding of the significance of the con text principle, according to which itis the sentence wh ich is the primary vehicle of mean ing. In later writings Dumm ett hasdespaired of making clear the d istinction between deep and shallow argumen ts for reject-ing bivalence. He has adop ted the position that all deviations from bivalenc e involveanti-realism of som e kind. In this paper I argue that this in effect remove s any clear con-nection between D umm ettian anti-realism and idealism. A suspicion of bivalence shouldoften be interpreted as the result of an a nti-realim of the error theoretic kind.Keyword!:anti-realism, bivalence, contex t principle, D umm ett, error theory.

1. IntroductionANTI-REALISMS NOT a single doctrine, but comes in a number of vari-eties. There are forms of idealism, which deny that the furniture of theworld exists independently of our epistemic capacities, and make whatexists in some sense mind-dependent. There are error theories, which arehappy to recognise some classes of independently existing entities, butwhich claim that others, apparently presupposed in certain areas of dis-course, do not in fact exist. Last, there are forms of expressivism, whichclaim that certain sentences which appear to be fact stating are really serv-ing some other function (Wright 1992, pp. 1-7). Dummettian anti-real-ism, defined as a refusal to endorse bivalence, is generally thought tocapture a variety of idealism. In this paper I will argue that while this isan accurate characterisation of the anti-realism of the early Dummett, ina later manifestation Dummettian anti-realism can be seen to have morein common with anti-realisms of an error-theoretic kind.' Dummett doesnot explicitly signal the fact that two apparently different forms of anti-' I t goes beyond th e aims of this paper to give a full exegesis of Dumm ett's argum ents fo r anti-realist semantics. Fo r that the reader should consult, Weiss, B. (2002) or Green, K. (2001).


2/26

T HE C O N T E X T PRINCIPLE AND DUMMETTS A R G U M E N T P O R A N T I - R E A L I S M 9 3realism are captured by a refusal to endorse bivalence, but their existenceraises questions for the overall interpretation of Dummetts philosophy.The main purpose of this paper is to demonstrate the existence of thisshift of emphasis in Dummetts writing and to elucidate the way that it ismediated by his changing attitude to the context principle.

The locus classicus for the statement of an error-theoretic point of viewis John Mackies Ethics: Inventing Right and Wrong where he denies thatmoral discourse is objective, while admitting that the apparent semanticsof ethical assertions presupposes the existence of moral values. There hecharacterises an error theory as:... theory that al though most people in making moral judgments implici t ly claim,among othe r things, to b e point ing to someth ing object ively prescr ipt ive, these claimsare all false. It is this that make s the nam e moral scept icismap propriate . (Mackie 1977,P. 3 5 )Hartry Field has also developed an error-theoretic position in relation tomathematics, and his characterisation of the position has an advantageover Mackies. For Mackies formulation can be read as asserting thatall moral claims are false, and this has led to the accusation that it rel-egates moral discourse to bad faith (Wright 1996, p. 2).2 Field argues thatmathematics does not constitute a body of truths, but this is not to saythat there is something wrong with mathematics; its simply to say thatmathematics isnt the sort of thing that can be appropriately evaluated interms of truth and falsehood (Field 1980, p.viii). Or we might say forshort, mathematics is neither true nor false. The fundamental idea guid-ing an error theory with regard to some sentence, or area of discourse,is that we are led into error about the real semantics of the sentence, orarea of discourse, by a naive semantic theory which takes syntactic fea-tures such as assertoric force and predication as a reliable guide to seman-tics. But the error theorist will claim, with regard to some sentence orclass of sentences, that although they are syntactically assertions, whichinvolve singular terms and predicates, they are not genuinely fact stat-ing. These sentences are in some sense neither true nor false. It is notthe aim of this paper to endorse error theories in either the mathematicalor the ethical case. Nor will we be able to examine the varieties of error

In fact, in the quoted passage, M ackie may only be intending to assert that all claims to bepointing to so meth ing objectively prescriptive are false , not that all moral claims are false , buthis formulation is ambiguous.


3/26

94 K A R E N G R E E N

theory, a substantial task worthy of an extended treatment. The aim ofthe paper is merely to argue that there is a precise point in the develop-ment of Dummetts anti-realism, represented by him as merely an exten-sion and simplification of his views, which in fact represents a substantialreorientation. This reorientation represents a shift from an idealist to anerror-theoretic anti-realism and is bound up with his changed attitude toFreges context principle.Freges context principle has had an important influence on twentiethcentury analytic thought. However, it has undergone a number of subtletransformations in the hands of analytic philosophers. The context prin-ciple found in Dummetts early writings is not quite Freges, and the firsttwo sections of the paper will discuss the historic transformations whichled to a strong reading of the context principle, which I will call the suf-ficiency reading. This reading, though not clearly justified by Fregestexts, played an important part in Dummetts early arguments for a con-nection between the refusal to assert bivalence and a version of moderateidealism. The bulk of the paper will argue that, implicitly, Dummett hasbeen forced to give up the strong reading of the context principle, andthat once the sufficiency reading of the principle is abandoned there is noreason to conclude that the failure to assert bivalence will, by itself, bringwith it a commitment to idealism. Instead, refusing to accept bivalencewill, at least in many cases, capture what is central to an anti-realism of anerror-theoretic kind, and should be congenial to those who are thoroughrealists about the objects and properties of the causal realm.Dummetts acceptance of a version of the context principle justifiedhis early adherence to the claim that it is the sentence that is the primaryvehicle of meaning. This view is closely associated with, though not iden-tical to, the linguistic priority thesis, the thesis that an account of thoughtmust go by way of an account of language - a thesis that Dummett alsoaccepts. This thesis is itself somewhat ambiguous, but for the sake of thispaper we can ignore these complications. Following the principle that thesentence is the primary vehicle of meaning, Dummett attempted, in hisearly writing, to distinguish between deep and shallow reasons for beingsuspicious of bivalence. Deep reasons led to a refusal to assert bivalenceand fell out of an account of the use that is made of sentences. Shallowreasons led to the denial of bivalence, and it was suggested that this denialwas only required in order to tidy up certain logical complexities internalto sentence^.^ At this stage Dummett deemed the intuitionists reasons


4/26

T H E C O NT E X T P R I N C I P LE A N D D U M M E T T S A R t i U M E N T F O R A N T I - R E A L I S M 95for failing to endorse bivalence to be deep, and to be the expression of ananti-realist attitude, while he claimed that Strawsons arguments for say-ing that some sentences are neither true nor false were shallow, and lednot to anti-realism, but to a more complex form of realist logic which dis-tinguished among undesignated truth values (Dummett 1978, pp. 1-28).In its earliest form, the deep argument for failing to endorse bivalence ledto an anti-realism allied to idealism, because the idea that the sentence isthe primary vehicle of meaning was supplemented with the thought thattruth for sentences should be explained in terms of the use that is made ofthem. Together these two thoughts led to the replacement of truth by war-ranted assertibility. Even at this stage, Dummett wanted to distinguish hisposition from that of subjective idealism, but because he replaced truthwith warranted assertibility, it was natural to equate the refusal to assertbivalence with a form of moderate idealism (Dummett 1978, pp. 17-1 8).Later Dummett decided that it was better, instead of replacing truth withwarranted assertibility, to speak of giving a substantive account of truthin terms of warranted assertibility, but while this made his idealism evenmore moderate, by allowing a greater gap between truth and assertibility,the position was still idealistic; at least, i t embodied a form of linguisticidealism, as I will clarify below (Dummett 1978, p. xxii).

Over the years Dummetts own attempts to distinguish between deepand shallow reasons for being suspicious of bivalence ultimately dissatis-fied him, and in the early 199Os, he apparently simplified his philosophy,and claimed that every rejection of bivalence involves some form of anti-realism (Dummett 1991a, pp. 322-7). Strawsons denial of bivalence,as well as the intuitionists refusal to assert bivalence, now both countaccording to Dumrnett, as forms of anti- rea li~m.~n what follows I will

In his recent Dewey lectures Dummett argues that these complexities demonstrate differ-ences in the ingredient senses of sentences which have the same assertoric content. He thereacknowledges ingredient sense as a feature of the sense ofsentences of which a theory ofmeaning needs to give an account, Dummett, M . (2003) ,pp . 16-2 I,

Dummett has had a similar change of heart with regard to the denial of bivalence brought onby cases of vagueness. Having once thought that such denials are not evidence of an anti-real-ist attitude, he now thinks that they do involve a version of anti-realism, Dummett, M. (1996).This raises the interesting question of whether what is involved in this case is also a form oferror theory. My initial thought is that it may be, but that the person who denies bivalence onaccount of vagueness is offering an error- theoretic account of the semantics of certain predi-cates, whereas the error theory discussed below involves attributing an error with regard to thesemantics of some singular terms.


5/26

96 K A R E N GREEN

argue that motivating Dummetts renunciation of the distinction betweendeep and shallow reasons for being suspicious of bivalence are misgiv-ings about the doctrine that the primary unit of meaning is the sentence.This is the central insight captured by the context principle. However, itwas the fact that the primary unit of meaning was deemed to be the sen-tence, plus, either an explanation of truth in terms of assertibility, or thereplacement of truth by warranted assertibility, that underpinned the ideathat to refrain from asserting bivalence was to adopt a form of idealism.Dummetts later view, according to which any kind of refusal to assertbivalence brings with it a form of anti-realism with regard to some kindof entity has therefore severed the most obvious link between Dummet-tian anti-realism and idealism. Once one gives up the context principle, asexpressed in the idea that the sentence is the primary unit of meaning, therefusal to assert bivalence turns out, in many cases, to be something thatthe realist about common-sense material objects can adopt with equanim-ity. Indeed, I believe that Dummettian anti-realism should be adopted bythose who do not want to be committed to the more bizarre denizens ofthe metaphysicians jungle or paradise.

2. The C ontext Principle in Frege, Dummett and Wright:In Freges writings the context principle is one of three fundamental prin-ciples that are laid down in the introduction to Freges Grundlagen. Thefirst is to always separate the psychological from the logical, the third isnot to lose sight of the distinction between concept and object, and the sec-ond is: never to ask for the meaning of a word in isolation, but only in thecontext of a proposition (Frege 188411950, p. x). There has been consid-erable discussion about the interpretation of the principle, partly becausethe distinction between sense and reference was not made in Grundlagen,and so it is open to at least two readings. One makes it a principle aboutsense, the other a principle about reference (Resnik 1967, 1976, 1979). Inthis paper I will assume that it is initially most plausible to read Frege ashaving had reference in mind when he formulated the context principle,at least in a confused way. I also prefer to use the word sentence ratherthan proposition to translate Freges word Satz, because this avoidsthe implication that Frege is speaking of propositions, thought of as themeanings of sentences. Frege makes it clear in his correspondence with


6/26

T H E C O NT EX T P R I N C I P L E N D DUMMETTS A R G U M E N T FO R A N T I - K ~ A L I S M 97

Russell that he uses the word Satz for a group of visible or audible signsexpressing a thought, not for the thought itself (Frege 1980, p. 149). Readthus, the context principle is the injunction, never to ask for the referenceof a word in isolation, but only in the context of a sentence. This readingis in line with the gloss on the context principle that is provided by Frege:if [it] is not observed, one is almost forced to take as the meanings [ref-erents] of words mental pictures or acts of the individual mind, and so tooffend against the first principle as well. Taking number words to refer toideas is also the fault that he is primarily attempting to avoid in $60 wherethe context principle is reiterated. There he suggests that it is because weask for the reference of a word in isolation that we are led to accept an ideaas its meaning. Read thus, the context principle is a constraint on askingafter the reference of a word. One should only do this in the context of asentence, because it is when we consider the contribution that particularwords are making to the truth conditions of sentences in which they occurthat we can avoid the dead end of mentalistic psychologism succumbed toby those who ask after the meaning of number words in isolation. Whenthe context principle is read as a mere constraint on asking after the refer-ence of an expression it is at least prima facie compatible with the realismthat Frege intended it to secure, though it does not deliver it.5

Following one of Freges other formulations, Dummetts early inter-pretation of the context principle made it sound less like a constraint onassigning reference, and more like a suj$cient condition for conferringreference. In one place Frege expresses the context principle by saying,It is enough if the sentence as a whole has a sense; it is this that conferson its parts also their content (Frege 1884/1950, p. 71e). Early on Dum-mett interpreted this as showing that for Frege, once we have laid downthe truth conditions for mathematical sentences, we are committed to rec-

This is not the place to attempt an analysis of Freges own intentions in introducing thecontext principle. It is clear, however, that while he suggested that one shou ld only ask afterthe reference of an expression in the context o f a senten ce, he did not think that a contextualdefinition of numerical identity w as sufficient to secure a unique reference fo r each numeri-cal expression. See Demopoulos, W. (1998), particularly pp.489-93, for a clear account ofFreges reservations ab out contextual definition . Michael B eaneys discussion of the contextprinciple also makes it a mere constraint, but in his case he suggests that Frege intends it asan epistemological constraint on a sking after the meaning of num ber words, which he arguesFrege thinks of as referring to numbers conceived of as having independent existence, Beaney,M. (1 996), p. 243.


7/26

98 K A R E N GRhkNognizing the singular terms in those sentences as referring to objects andso:._ .f an expression functions as a singular term in sentences for which we have provideda clear sense, ... then that expression is a term (proper name) and accordingly has a refer-ence: ...So, then, to assert that there are, e.g., natural n umbers turns ou t to be to assert nomore than that we have correctly supplied the sentences of number theory with determi-nate truth conditions; ._ _Dummett 1978, p.212)He continued to interpret the principle in this strong way, and to appar-ently endorse the context principle at least until the 1980s;

if a sense has been fixed for all possib le sentenc es in which an exp ression m ay occur,then no additional stipulation is needed to confer a reference on that expression. (Dum-mett 198 , p. 380)

However, more recently, he has voiced considerable doubts about thetenability of the context principle so interpreted (Dummett 1995). Part ofthe problem arises from the fact that, since Frege did not at this early stagedistinguish sense from reference, the above reading is tendentious.Dummetts doubts were also inspired by Crispin Wrights 1983discus-sion of Freges conception of numbers as objects (Wright 1983). In thatbook Wright appeared to be closely following Dummetts interpretationof the context principle and he drew from it the conclusion that:If ... certain expressions in a branch of our language function as singular terms, anddescriptive an d identity co ntexts contain ing them are true by ordinary criteria, there is noroom for any ulterior failure of fit between those c ontexts and the structure of the statesof affairs which make them true. So there can be no philosophical science of ontology,no well founded attempt to se e past our categories of expression and glimpse the way theworld is truly furnished. (Wright 1983, p. 52)

This formulation places a rather minimal requirement on existence andencourages a profligate Platonism, since i t seems to imply that talkingabout something in true sentences is sufficient to secure its existence.A s well as expressing the claim that if an expression functions as a sin-gular term this is sufficient for it to refer to an object, the passage alsomakes clear how the context principle leads to what I referred to earlieras linguistic idealism. Ontological categories are taken to be derivativefrom syntactic categories, such as singular term. This results in a lin-guistic Kantianism. This is not subjective idealism, because the rnean-ings of words are not ideas. But just as Kant avoided subjective idealism,


8/26

THE CONTEXT PRINCIPLE A N D DUMMETTS A R G U M E N T OR A N T I - R E A L I S M 99

but argued that the categories determine the limits of our thought, so thelinguistic idealist avoids subjective idealism, but accepts that the logicalstructure of language determines the limits of our thought. Dummett hasstated in a number of places that from the point of view of the contextprinciple the possession of reference is wholly internal to the language.He has also associated it with Putnam, and the internalist strain in Fregesthinking thus implying that he recognised at least a distant connectionbetween Freges context principle and Kantian idealism (Dummett 1973,p.499; Dummett 1991b, p.211n.; Dummett 1995, pp. 10-11, 18).6Withdrawing from his earlier apparently unqualified endorsement ofthe context principle, Dummett argued in Frege: Philosophy of Muth-emutics that problems arise for it, because it lies behind the method thatFrege adopted for determining what the numbers are, and so i t resultedin contradiction and the collapse of Freges project (Dummett 1991b,pp. 2 2 3 ~ I O ) . ~ut these arguments do not by themselves constitute a com-plete retreat from something like the view expressed by Wright, and theearly Dummett. For they could be taken to hinge on a disagreement overthe conditions under which a sense will have been determined for all thesentences in which a singular term occurs. Indeed, Dummett has beenloath to give up the context principle, for he has always seen it as pro-viding the basis of an account of our reference to abstract objects whichavoids, on the one hand, the extreme of nominalism and psychologismor, on the other, a crude Platonism which makes a mystery of our epis-temic access to truths about numbers (Dummett 1995, p. 19). Dummettsdisagreement with Wright shows that when the sufficiency reading of thecontext principle is taken to justify the introduction of numbers by themethod of contextual definition, the resultant impredicativity constitutesa prima facie objection to the strong construal of the principle. This dis-cussion opens a space for considering a much simpler objection to thecontext principle. We will deal with this in 55 below. First, it will beinstructive to look at the history of the context principle to see why Dum-mett initially fastened on a strong formulation that takes it to be a suf-ficient condition for reference, rather than merely accepting the principle

For a discussion of Dummett as a linguistic Kantian see Matar, A . (1997) pp.9-I0 and4&3. If the argument of my paper is correct, D ummett has progressively moved away froman endorsement of anything like the linguistic idealism there attributed to him.

The debate between Dumm ett and Wright continued in D ummett, M. (1995), pp. 17-1 8, and(1998) and in W right, C. (1998a) and (1998b).


9/26


as a constraint on asking after reference. Since some readers may feelthat Freges texts provide a stronger case for the sufficiency reading thanI have allowed, I should note that we shall return to this question in 97.Frege himself moves from the observation that numerals play the role ofsingular terms to the conclusion that numbers are objects, and this is evi-dence that he did not consider the context principle to be a mere constraint(Frege 188411950,957).

3. The context principle in Wittgenstein and QuineI surmise that the transformation of the context principle from an apparentconstraint on asking questions about reference into a sufficient conditionfor determining reference went by way of Wittgenstein. At Tractatus 3.3Wittgenstein echoes Freges formulation, with a subtle difference. Witt-genstein says that only a sentence has a sense, and it is only in the con-text of a sentence that a name has Bedeutung (Wittgenstein 1961, p. 24).Thus he forged an implicit connection between the context principle andRussells theory of descriptions. It is often claimed that Russells theoryshows that in the context of a sentence a definite description contributesto the meaning of the sentence, although it does not mean something, anobject, when taken in isolation (Quine 1963, p, 6). In the paragraphs 3.26-3.263, which immediately precede his echo of Freges context principle,Wittgenstein had introduced names as primitive signs which are incapableof being defined, and whose use can only be illuminated through elucida-tions. A defined sign signifies by way of the signs used in the definition,and a primitive and defined sign can never signify in the same way. Thisis highly reminiscent of Russells distinction between logically propernames and definite descriptions. Apage later, at 3.318,an explicit connec-tion between Frege and Russell is made when Wittgenstein says that likeFrege and Russell he takes a sentence to be a function of the expressionsthat it contains (Wittgenstein 1961, p. 26).The connection that is suggested in the Tractatus, between the ideathat i t is only in the context of a sentence that a name has meaning andRussells theory of descriptions is taken up in various writings by Quine.Quine, following the general direction of other followers of the ViennaCircle, such as Ayer, sees Russells theory as providing a paradigm of amethod for analysing away unwanted ontological commitments and mak-


10/26

T H E CONTEXT P R I N C I P L EAND D U M M E T T S A R G U M E N T FO R A N T I - R E A L I S M 101

ing sense of negative existential statements (Ayer 1946, pp. 59-62). Earlyon, the method of descriptions provided some hope for the empiricistprogram of translating theoretical sentences into sense datum language,for it showed that it was only necessary that, our statements as wholesbe translatable into sense-datum language, but not that they be translat-able term by term (Quine 1963, p. 39). Quine goes on; the reorientationwhereby the primary vehicle of meaning came to be seen no longer inthe term but in the statement .. seen in Bentham and Frege, underliesRussells concept of incomplete symbols defined in use; i t is also implicitin the verification theory of meaning, since the objects of verification arestatements. This connection between Frege and Russell is reiterated inEpistemology Naturalised (Quine 1969, p. 72).

One needs, however, to add one more element, also to be found inQuine, and this time with antecedents in the work of the later Wittgen-stein, to get the strong sufficiency interpretation of the context principle.In the Philosophical Investigations the context principle is referred toexplicitly only once, at 549, but Wittgensteins discussion of ostensivedefinition operates on the assumption that some form of context prin-ciple is true (Wittgenstein 1967, $92840). We cannot tell from a simpleact of ostension what a word refers to. It is only after we have learnedwhat role it plays in a number of sentences that we can distinguish thename of a particular object from a common noun or a predicate. Strictlyspeaking, we have here also only a necessary condition for determiningreference. But the insistence on use, and the way in which Wittgensteinclaims that the sentence is the smallest unit that makes a move in thelanguage game, suggest the sufficiency view. Once we have laid downthe uses of the sentences of the language, and given that some expres-sions are being used as singular terms, that is as terms which function topick out objects, there appears to be nothing more required in order forthose words to pick out objects. Wittgensteins critique of ostension sug-gests that confrontation with reality, which might have been thought tounderpin a difference between singular terms which genuinely refer, andothers which only apparently do so, is in fact irrelevant, since i t is fromthe logical structure of sentences that the ontological category of beingan object derives. Wright makes this connection explicit in his discussionof the context principle and his strong defence of the sufficiency reading(Wright, 1983, pp.41-7).

This thought is also explicit in Quine, who depicts the stimulations that


11/26

102 K A R E N G R E E Nimpinge on our nerve endings as underpinning stimulus meanings thatcan be interpreted ontologically in various ways, relative to a language. Itis only with the introduction of a language that has quantifiers and iden-tity that reference to objects is introduced. Nothing but language deter-mines the range of the quantifiers, for languages can differ with regardto the ontological structure they impose on reality (Quine 1969, pp. 1-1 6;Quine 1995). Thus for Quine, ontology is relative to theory. It was, I sur-mise, because of these intervening developments that Dummett initiallyaccepted the sufficiency reading of the context principle. Yet from thebeginning he was aware of a tension between the reading of Frege whichmakes reference internal to a theory, implied by the context principle, andthe realism implicit in Freges use of the namehearer relation as the pro-totype of reference (Dummett 1973, pp. 498-9). By the time the secondedition of Frege: Philosophy of Language appeared, he admitted that hehad perhaps gone too far in attributing to Frege the view that our graspof ontological distinctions depends entirely on language (Dummett 1981,p. 235).

This background elucidates Dummetts former reasons for thinkingthat shallow arguments for giving up bivalence are realist in character.They are realist because they implicitly accept the namehearer relationas the prototype of reference. Strawsons arguments are a paradigm ofsuch arguments. When Dummett extended the application of the termanti-realist and assimilated these arguments with the arguments thathe initially deemed deep, he severed any necessary link between refus-ing to endorse bivalence and the linguistic idealism that resulted froman internalist perspective. One moral that one could take from this is thatDummett had more cogent grounds than he himself now recognises formaintaining the distinction between deep and shallow reasons for beingsuspicious of bivalence. A different moral, and the one which interestsme, is that in a large class of cases the failure to endorse bivalence haslittle to do with idealism, but rather issues from an anti-realism that hasan error-theoretic motivation.

4. Deep versus shallow argum ents for failing to accept bivalenceThe argument against bivalence that Dummett initially deemed to be shal-low is that found in Strawsons treatment of sentences containing proper


12/26

T H E C O N T E X T P R I N C I P L E AND D U M M E T T S A R G U M E N T F O R A N T I - K ~ A L I S M 103

names that fail of reference (Strawson 1950). Like Frege, Strawson wasinclined to say that sentences that contain non-denoting terms are neithertrue nor false. Duminett pointed out that this leads to the denial of biva-lence, and the introduction of a third truth value, a position quite differentto that of the intuitionists, who rejkain,from asserting bivalence, and forwhom the law of excluded middle is not a theorem, but who accept thatthe negation of the law of excluded middle implies a contradiction. Whenone asserts that some sentences are neither true nor false, the introduc-tion of a third truth value becomes necessary in order to side-step thiscontradiction, and in order to make negation behave in a regular fashion.Dummett argued that the introduction of a new truth value disassociatestruth and falsity from the basic notions of correctness and incorrectness ofan assertion, and so from the uses that we make of sentences.

Dummett attempted to demonstrate the shallowness of this argumentby asking what the point is of categorizing certain sentences as neithertrue nor false, and how our categorizing them thus would show up asrequiring a different use from our simply categorizing them as false. Astatement is either correct or incorrect. Here there is no place for a thirdoption. In this regard, an assertion is different from a conditional bet. Iftwo people make a conditional bet such as If France gets into the WorldCup final it will lose there are three possible outcomes. Either one or theother wins the bet, or, in the case where France does not get into the final,the bet is off. Dummett uses examples of this kind as an illustration ofwhat would be required in order for there to be a third option in the case ofassertion (Dummett, 1978, pp. 8-10; Dummett, 1973, pp.341-2). But inthe case of assertion, and in the case of conditional assertion, we need tointroduce a third truth value, not because there is a definite third outcometo the assertion of a sentence, but in order to give an account of the waycertain simple sentences behave in more complex sentences (Dummett1978, pp. 12-14; Dummett 1973, p.347). To say The King of France isbald when there is no King of France is to mislead, and so is to say some-thing incorrect. The pressure to say that it is neither true nor false, comesfrom the fact that The King of France is not bald is just as misleading.A third truth value needs to be introduced, but from the point of view ofusage, uttering a sentence which has the third truth value is just a way ofsaying something incorrect.

The reason why such objections to the principle of bivalence weredeemed to be shallow was because the third truth value that is introduced


13/26


is unrelated to the use that we make of sentences when they are assertedon their own. Dummett claimed, indeed, that every other feature of mean-ing must consist in its contribution to what is conveyed by the utteranceof some complete sentence (Dummett 1973, ~ . 4 4 9 ) . ~e can see behindthis an adherence to the context principle as discussed above. However, itis worth trying to say more clearly exactly why Dummett refused at thisstage to take three-valued logic as being any less realist than two-valuedclassical logic. The thought appears to have been something like this:the strong construal of the context principle brings with it the view thatreference is internal to a language. It is true that some philosophers wouldreject the principle thus construed, and see it as already an abandon-ment of realism, but Dummett did not see the issue in this light. Havingaccepted that the context principle implies that the sentence is the primaryvehicle of meaning, the dispute between realists and idealists became adispute over the notion of truth for sentences. Realists adopted classicallogic. Dummett saw anti-realists as tying the notion of truth to the useswe make of sentences, and this led him to take the refusal to assert biva-lence as the mark (from an internalist perspective) of anti-realism. Likethe realists, advocates of many-valued logic severed the connection oftruth with use, and thus brought in a conception of truth as unacceptableas the classical logicians.Dummetts deeper argument for the failure to assert bivalence had twodistinct elements. The first, which Dummett continues to adhere to, wasthe claim that if we are going to give an account of meaning in terms oftruth conditions we will need a notion of truth that is more substantivethan that provided by the redundancy theory which says that the completeexplanation of the meaning of is true is captured in the equivalence, pis true iff P . ~ he second element, which Dummett has modified, wasthat the substantive notion of truth that could turn the trick of providingan account of what it is to manifest a grasp of truth conditions would beone according to which the truth of a sentence was explained in terms ofsome kind of potential verifiability. Once we have tied substantive truthto potential verifiability there is an argument for refraining from assertingbivalence for undecidable statements. Since this account of truth makes

It is instructive to contrast this with Dummetts current view as expressed in his DeweyDummett, M. (2003) pp . 5-25.

lectures referred to in note 3 .


14/26

TH E C O N T E X T P R I N C I P L ~A N D DUMMETTS A R G U M E N T ~ O K N T I - R E A L I S M I05

truth epistemic, and so relative to our capacities to judge truth, thereis every reason to think that something close to traditional idealism isimplied. The objects and states of affairs that exist are just those that wecan potentially recognize as existing. o

5. A sim ple-mind ed ob jection to the sufficiency interpretationof the context principle

When Dummett was committed to the truth of the sufficiency readingof the context principle, he had a persuasive argument for distinguish-ing deep from shallow reasons for failing to endorse bivalence. But onceone gives up the strong reading of the principle this argument founders.One reaction would be to conclude that Durnmett erred by his own lightswhen he allowed his belief in the strong construal of the context prin-ciple to waver. I will argue by contrast that there was never good rea-son for accepting the sufficiency reading of the context principle, whichwas deeply flawed from the outset, as Dummett has come to recognize.Without it we have lost Dummetts primary reason for thinking that theoutright denial of bivalence and the adoption of a three valued logic is ashallow or flawed position relative to intuitionism. Of course, there maybe other reasons for preferring intuitionist logic to the three valued kind,but these need not detain us here. If the denial of bivalence is neverthelessdeemed to be a form of anti-realism, this should not make us concludethat it is automatically a form of idealism. Only the refusal to assert biva-lence that could be justified from the deeper perspective deserved thatname. Without this deeper perspective the natural way to interpret manycases where bivalence is questioned is to see them as expressions of ananti-realism of an error-theoretic kind.When Frege articulated the context principle he had not clearly dis-tinguished sense and reference. But once that distinction is available, theprinciple appears to conflict with Freges later view that an expressionmay have a sense but no reference. We might well think, for instance,

. .~l o In his Dewey lectures Dummett replaces the term verificationist with justificationistand argues, in particular, that a justificationist can adopt with regard to statements about thepast a distinction between what they assert is the case (some past fact or event) and what veri-fies them (present evidence).As he says, this brings the justificationist position much closerto realism. Ibid. pp.36-7.


15/26

106 K A R E N G R E F Nthat a sense has been fixed for all the possible sentences in which SantaClaus or Athena can occur, but that no reference is thereby fixed forthese terms. Or at least, since it really isnt very clear what is meant bysaying that a sense has been fixed for all (even the meaningless ones?) thepossible sentences in which a term can occur, we might think that as gooda sense has been fixed for the possible sentences in which these termsoccur as has been fixed for the sentences in which referring terms such asJesus Christ and Hypatia occur. Dummett when he discussed this diffi-culty said that here the question is no longer of a philosophical character(Dummett 1978, p. 40; Dummett 1981, p. 383). But what did he mean?

Early on Dummett expanded on what he meant, by saying that there is adifference between giving an account of the kind of reference that belongsto some class of expressions, and giving an account of the reference ofone particular expression of that class. To say that singular terms referto objects is to say that expressions that fulfill the syntactic role of sin-gular terms are apt for referring to objects. ] I Similarly, to say that predi-cates refer to concepts (in Freges sense of functions from objects to truthvalues) is to say that predicates are apt for referring to concepts. It maynevertheless be that in natural language a term which plays one or otherof these syntactic roles is not functioning normally, and hence fails ofreference. Dummett suggests, therefore, that the context principle shouldbe read as applying to classes of expressions. Once a sense is determinedfor all the sentences in which an expression of a class can meaningfullyoccur, there is no further question to be asked concerning the kind ofreference which expressions of that class can have. In the case of numberwords, if number words behave syntactically like singular terms, and ifsingular terms are apt for referring to objects, then number words refer toobjects, if they refer to anything.

Yet this returns us to a context principle that provides only a neces-sary and not a sufficient condition for determining whether any particu-lar expression has a reference. Although singular terms may be apt forreferring to objects there will always be the possibility of mock singularterms. Such terms appear to refer to objects but do not do so. In at least

In order to be non-circular this formulation requires the formulation of a syntactic criterionfor being a singular term.A considerable literature has developed following Dummetts initialattempts in Dummett, M. (1973) pp.54-80 to provide such a criterion. See, in particular,Wright, C. ( 1 983) #ix and Hale, B. (1994).


16/26

T H E C O N T E X T P R IN C I P L E A N D D U M M E T T S A R G U M E N T FOR A N T I - R t A L I S M 107

one place, this is the way in which Frege treats names such as Scyllaor the name Odysseus as it occurs in the sentence, Odysseus was setashore at Ithaca while sound asleep (Frege 1979, p. 130). From a fairlynatural point of view (though perhaps not Freges) this sentence is cor-rect, and so on one interpretation true, but only given that one reads itas implicitly governed by a proviso such as, in the story of Odysseussadventures. Although Odysseus is a name, it is usually assumed thatit does not refer. It might be called a mock name. Once we recognizethe possibility of mock names we will have to have some criterion fordistinguishing such mock names (expressions which are syntacticallynames but fail of reference) from genuine names (expressions which infact contribute to the truth values of the sentences in which they occur byintroducing an object which is asserted to fall under some concept). Giventhe distinction between genuine and mock names, it is not enough to saythat number words play the role of singular terms in order to conclude thatthey refer to objects. We need to be given a principled case for treating thewhole class of numerals as genuine rather than mock names.The preceding claims may be somewhat controversial, but they pro-vide prima facie support for thinking that, read in the strong way, thecontext principle is highly implausible, and that therefore Dummett isright to have expressed his doubts about it. Having undercut the distinc-tion between the deeper and shallower arguments, in the next sectionI will argue that it is in fact the shallower style of argument that liesbehind a wide variety of reasons for being suspicious of bivalence, andthus in many cases Dummettian anti-realism arises out of error-theoreticintuitions rather than being a form of idealism.

6. Further consequences of rejectingthe deep/shallow distinctionWe have seen that once Dummett gives up the distinction between deepand shallow reasons for being suspicious of bivalence he no longer hasa case for finding a necessary connection between the refusal to assertbivalence and a commitment to idealism. The crux of the argument is asfollows. Dummett himself recognised a tension between Freges tendencyto treat the namehearer relation as the prototype of reference, and thetendency, apparently implied by the context principle, to treat reference


17/26

I08 K A R E N G R E E Nas internal to a language. Once reference is made internal to language thedispute between realists and anti-realists comes to hinge on the notion oftruth that is adopted for sentences. Yet, if we resolutely hold to the viewthat reference is internal, there is no simple route back from the notionof correctness for sentences to the idea that some singular terms fail ofreference, and so are only mock singular terms. By attributing a form ofanti-realism to those who take sentences containing non-referring singu-lar terms to be neither true nor false, Dummett has reintroduced a notionof robust reference of which the namehearer relation may be taken to be aparadigm, and so has moved away from the perspective that makes refer-ence internal to language. By his own earlier account, realism is closelyassociated with the view of reference that takes it to be a relation betweenwords and independently existing things, and so there appears to be noprincipled reason to forge a necessary link between this kind of anti-real-ism, which derives from failure of reference, and idealism.

What then is the relationship between the failure to endorse bivalence,error theories and idealism? Mackie suggests a connection between theerror-theoretic attitude and subjectivism. He says that a reason whyone might become a subjectivist in ethics is because one assumes thatthere are no objective values and so will be led to look elsewhere foran account of the truth conditions of moral statements (Mackie 1977,p. 18). Similarly, in the mathematical realm, the psychologist mathema-ticians, against whom Frege railed, thinking that numbers could not beobjectively existing objects, turned them into subjective ideas. But whilethe move to subjectivism or idealism is motivated by the same suspicionof the apparent semantic commitments of a discourse as is error theory,the positions should be distinguished. The subjectivist or idealist thinksthat the surface syntax of some discourse is misleading. A reduction orreformulation of the subject matter is then offered in which new referents(subjective sensations or ideas) are supplied. The error theorist thinks thatthere is no reduction that shows that the sentences of the disputed classreally concern some entities other than those misleadingly referred to. Anintermediate position is possible which takes some sentences to be reduc-ible, but in which others, for which no reformulation is forthcoming, aredeemed neither true nor false.

Berkeley, for instance, believes that expressions apparently referringto material substances should be understood as really referring to ideas.According to this kind of subjective idealism it is only when perceived


18/26

T H E C O N TE X T P R I N C I P L E A N D D U M M E T T S A R G U M E N T I-OR ANTI-RhALISM 109

that a thing exists, and hence only then that there are facts as to the way itis. On this view one would expect truths to come into existence as thingscome to be perceived. Berkeley only avoids this consequence of his phe-nomenalism by postulating that ideas are eternally perceived by God. Onthe unmodified phenomenalist view, the existence of an object with deter-minate properties, of a kind appropriate for making a sentence true, is asdependent on our perception as is the existence of a fictional fact on theinvention of its author. Such subjective idealism naturally leads to therejection of bivalence. For, just as fictional entities only have the qualitiesthey are described as having, mental items will only have the qualitiesthey are perceived as having. There is no fact of the matter as to whetherOdysseus did or did not have a mole on his left shoulder. Nor, arguably,is it the case that either his nurse was a redhead or she was not. EquallyBerkeley might accept that the unperceived tree, since it does not exist, isneither deciduous nor evergreen.When excluded middle is claimed to fail as a result of this form of argu-ment, it is the lack of an independently given referent for the singular termwhich is to blame. Thus there is a strong parallel with Strawsons viewthat sentences containing non-denoting singular terms are neither true norfalse. For, in each case it is the fact that an item does not exist which leadsto the conclusion that sentences apparently referring to that item lack atruth value. In both these cases our intuitions are guided by a prior notionof existence for things of a mental or fictional kind, rather than falling outof a prior notion o fcorrectness for sentences. The situation with mental,fictional and mythical entities differs subtly. Mental entities exist only inminds, so an idea that is unperceived, since it exists in no mind, does notexist. This is similar to the case of non-referring singular terms. Relativeto a notion of existence for material things we judge that some singularterms fail to pick out any existing thing.Fictional and mythological sentences are slightly different, for there isa notion of correctness for sentences of this kind, even though it is quitenatural to say, as Frege was inclined to, that the singular terms that appearin them are only mock singular terms. The sentence Zeus was a god ofthe ancient Greeks is correct, whereas Zeus was a god of the pre-colonialAustraliansis incorrect. The sentence Odysseus tricked the Cyclops iscorrect, while Odysseus captured the Golden Fleece is incorrect. Thereare other cases in which sentences involving singular terms that fail ofreference are intuitively correct. The novel I might have written would


19/26

110 K A R E N GREEN

have been based on history is a modal example. Such sentences may onlybe true-in-the-fiction, true-in-mythology, or true in virtue of how thingsmight have been (sometimes called true in virtue of the way things arein another possible world). But, if one retains the view that reference isinternal to language, and maintains the sufficiency reading of the contextprinciple, then it would seem to follow that Zeus, Hera, Odysseus and thenovel I might have written exist (though perhaps we would have to saythey have only fictional or possible existence). If the correctness of someof these sentences is analogous to truth, and so requires the existence(even if it is only in fictional or possible worlds) of the entities referred toin them, then why not allow that these entities exist in fictional, mythicalor possible worlds? This profligate position is resisted by anti-realists whoargue that we should not take the referring terms at face value, but shouldreformulate the sentences to reflect their real subject matter: texts, or theconsistency of sentences, or whatever actually comes into play when weattempt to justify our assertion of these sentences.

The profligate introduction of expanded domains of quantification inorder to provide a semantics for sentences that contain singular terms thatrefer to no actual entities, and the introduction of quantifiers that rangeover non-actual existents is well known and surprisingly popular. Thestrategy is broadly Meinongian. Dummett now argues that when Straw-son and Frege argued that sentences containing non-denoting singularterms are neither true nor false, their position involved a form of anti-real-ism with regard to such Meinongian non-existent objects. Meinongs real-ism; consists in his treating singular terms as always denoting objectseven though some of these objects dont actually exist (Dummett 1991a,p. 324). But Meinongs realism appears to be very much in accord withthe perspective that falls out of the context principle. If we start from anotion of truth for sentences, grounded in an intuitive conception of thecorrectness of an assertion, and we say that it is sufficient, in order for aterm to have a reference that a sense has been laid down for the possiblesentences in which it occurs, then the conclusion that some singular termsrefer to fictional, mythical and merely possible entities appears unavoid-able. If we refuse to accept that these terms refer to these entities becausethe entities are non-existent, we appear to be falling back on a prior notionof existence. This may be something like causal efficacy, or it may besomething vaguer, such as being a potential object of public inter-sub-jective scrutiny with regard to any of its properties. The first notion is


20/26

T H E C O N T E XT P R I N C I P L E A N D D U M M E T T S A R G U M E N T FO R A N T I - R F A L I S M 111

that which lies behind the intuitions of those who want to deny genu-ine existence to abstract obje cts. Th e se con d is mo re generous a nd mightallow the attribution o f existence to well defined abstract objects, withoutadmitting the w hole m otley possible, fictional an d even impossible crew.Falling back on a criterion of existence of this kind will involve giving upthe centrality of the con text principle.

In his later writing D umm etts o wn reading of the source o f the contra-diction in Freges system puts pressure on th e acceptability of the con textprinciple. Dum mett co nclude s that the contex t principle should not beread as justify ing the assump tion that ob jects automatically exist jus t incase we have laid down a sense for the sentences in which names forthem occur, and it is possible to lay d ow n a criterion of identity for them.Further, he has distinguished a thin notion of reference for number wordsfrom a robust notion acc ord ing to w hich fo r numbers to exist is for them tobe the objects which are semantically relevant to th e determination o f thetruth or falsity o f sentence s in which their n ame s occu r (Dum me tt 1991b,pp. 189-99). We might think that, in the cases we have been discussing,the impetus towards den ying bivalence com es from the prior thought thatthe non-actual objects that might be thought of as being referred to bynames such as Zeus, Hera and Odysseus are irrelevant to the determi-nation of the truth or falsity o f the sentences in which these nam es occur.So, the syntactic role that words play in sentences is not sufficient for usto determine wh ethe r or not they ar e gen uine referring expressions. It isonly when that role can be b acked u p by an account o f the w ay in whichthe objects the w ord s refer to are relevant to d eterm ining the correctnessor incorrectness of the sentences in which th ey oc cur that we hav e genu-ine referring. The context principle then places a constraint on questionsof reference to objects, but does not provide a sufficient condition forthe existence o f a referent. A sem antics will have to be enriched by anepistemological a cco un t of ho w the existence o f the postulated objects isrelevant to the determination o f the correctness o r incorrectness o f sen-tences. This brings D um me tt closer to those w ho have found it odd thatquestions of existence should be determined via questions of truth, forit allows that where causal interaction with a physical object is relevantto determining the truth or falsity of a sentence in which a name of thatobject occurs, we will ha ve a paradigm for assuming the existence of thatobject. By contrast, when o ne makes an assertion a bo ut a fictional object,it is not the ob ject, but a text or s et of texts that is relevant for determining


21/26


the correctness of ones assertion.If these arguments are persuasive one might conclude not just thatDummettian anti-realism encompasses anti-realism of both the error-the-oretic and the idealist kinds, but that those features of Dummetts earlythought which took him in an idealist direction were ungrounded, sincethey derived from a reading of Freges context principle neither justifiedby Freges texts nor intuitively plausible. However, before looking intothe consequences of these arguments for the interpretation of Dummettsphilosophy it is worth heading off the objection that the relatively simple-minded objections that have been raised againt the context principle glossover a central caveat.

7. An objection and a replyIt might well be objected to this conclusion that the strongest evidence forattributing what I have called the sufficiency reading of the context prin-ciple to Frege, has been overlooked and that moreover when one readsFreges formulation of the context principle more carefully, it alreadyallows a principled distinction between genuine referring expressionsand mock singular terms to be drawn from within the perspective thattakes reference to be internal to a language.I2 We have been followinga formulation of the context principle that underplays the importance ofstatements of identity. But it will have been objected, by some, that thequote from Wright clearly specified that what was sufficient for referenceto an object was for expressions to function as singular terms and that;descriptive and identity contexts containing them are true by ordinarycriteria. Frege draws attention in 457 of the Grundlagen to the fact thatwe speak of the number one, where the definite article serves to classit as an object. This indicates that he does think that functioning as asingular term is sufficient for referring to an object. In $62, however, hiscomments suggest that this is not sufficient by itself, what must be added

~~~

l 2 Hartry Field objected to Wrights interpretation of Freges context principle, along linessimilar to those developed here, in Field, H. (1984). Wright responded in Wright, C. (1990)placing constraints on the notion of ordinary criteria of truth which were intended to distin-guish between truth and cases where there is a kind of correctness less than truth, pp . 79-80.


22/26

THE CONTEXT PRINCIPL E A N D D U M M E T T S A R G U M E N T FOR A N T I - R E A L I S M 1 13

to the observation that a term takes the definite article is a demonstrationthat a sense has been laid down for statements of identity involving theterm. He says;We have already settled that number words are to be understood as standing for self-subsistent objects. And that is enough to give us a class of sentences which must havea sense, namely those which express ou r recognition of a number a s the same again. Ifwe are to use the symbol a to signify an object we must have a criterion for deciding inall cases whether b is the same as a, even if it is not always in our power to apply thiscriterion. (Frege 188411950,562)

This can be read as supplying a criterion for distinguishing mock fromgenuine proper names. A singular term w ill only count as a genuine sin-gular term if we have provided truth conditions for identity statementscontaining it. That is to say, if we have provided a criterion of identityfor the kind of objec t it refers to. It is jus t such a c riterion that Quinehas always insisted on if we are to admit some class of objects into ourontology. It is this which underpinned his reluctant acceptance of sets asontologically respectable, while he continued to reject possible people,meanings, intensions an d any other purported entity for which there is noclear criterion of identity.

The debate over the adequacy of the neo-Fregean rehabilitation ofFreges Platonism, engag ed in by Dum mett and Wright, hinges on whetherthe Fregean is in the end capable of satisfying this further constraint.Dummett argues that because Freges attempt at a solution to the JuliusCeasar problem -which amou nts to the requirement that the definition ofnumber makes it clear whe ther o r not a particular number is identical withany object - eads to contradiction, the constraint has not been satisfied.Wright argues that the impredicativity of the Fregean method is harm-less (Dum mett 1998; W right 1998a). But from the more naive perspectiveadopted in this paper, a rehabilitation of the sufficiency reading of thecontext principle, that fa lls back on the distinction betw een those entitiesfor which we do, and those for which we do not, have a clear criterion ofidentity, lacks independent motivation.

Superficially it appears too strong. We refer to material objects thatpersist through time, but it is not clear that we have provided clear truthconditions for identity statements that involve reference to persistingmaterial objects. I can surely accept that two singular terms refer, eventhough there is no clear criterion for deciding whether they refer to oneobject that has persisted over time, or to two different objects. Secondly,


23/26


it may be too weak. We may be able to provide a criterion of identity fornon-existent kinds of object. Some of those who seriously quantify overpossible objects think that they can provide criteria of identity for objectsacross possible worlds. And discussions of mythology often contain state-ments such as, The Roman Diana is the same Goddess as the Greek Arte-mis. There seems no reason why principles should not be laid down fordetermining the truth conditions of all such identity statements involvingmythical entities. Even if this could be done, should it convince us thatthese names refer?

Thirdly, one can lay down a criterion of identity for things o f a kind,without this guaranteeing that every term that purportedly refers to a thingof that kind in fact refers. So even if one can say what it is for somethingto be a material object, or a number, and then what counts as being thesame material object, or number, doing this does not serve to distinguishthose terms which actually refer from those that do not. King Arthurrefers, if it does refer, to a man, and we have general, if vague, criteria ofidentity for men, but this does not help us with the question of whetherKing Arthur refers. Sentences containing this name have a sense, andthere are lots of things that it is correct to say about the legendary KingArthur, but this does not secure a reference for the name. Those whothink that the name does refer think that the legends have a source inreal events, but that the account of those events became distorted in theretelling. For King Arthur to exist is for the origin of his legend to be ableto be pinned to some historical figure who existed at a definite place andtime. This brings us back to a notion of existence, at least for materialobjects, which does not fall out of the conditions for the correctness ofthe assertion of sentences. Rather, establishing that King Arthur did exist,and identifying him, will establish a new criterion for the correctness ofassertions about him.

It might be countered that it is just because numbers are abstractobjects, rather than concrete objects, that in their case it is sufficient tohave provided truth conditions for identity statements containing them inorder to have shown that expressions apparently referring to them do infact refer. Yet, in the light of the simple minded objections raised here, itseems that the profligate Platonist needs to say more to motivate the dis-analogy between concrete and abstract objects. One could, for instance,introduce a new class of abstract objects called liairinesses along the fol-lowing lines. First we define equihairiness:


24/26

T H E CONTEXT PRINCIPLE AND DUMMETTS ARGUMFNT bOR ANTI-RtALISM 115

F is equihairy with G =there is a one:one map from the hairs on FsWe can use this to introduce reference to hairinesses:The hairiness of F =the hairiness of G =F is equihairy with GLast, H= will provide us with the identity conditions for hairinesses.H= The hairiness of F =The hairiness of G =there is a one:one map

from the hairs of Fs head to the hairs on Gs head.But does this method really serve to introduce a well defined range ofabstract objects? Is the hairiness of the totally bald man identical with thenumber zero? Or is it another kind of object altogether? Here we haveanother formulation of the Julius Caesar problem, and a different way ofgetting to the conclusion that Dummett now endorses, according to whichthe Platonist needs to do more than give a contextual definition of identityalong these lines in order to secure the existence of abstract objects.

As a result of recognising the need for a more robust conception ofreference than that supplied by such contextual definitions, Dummetthas come to the conclusion that failures of bivalence which result fromnon-denoting singular terms also involve a form of anti-realism. His con-ception of robust reference is more generous than the realist conceptiongrounded in the namehearer relation, but includes it. He suggests thatwe have a notion of reference for singular terms that is robust enough tosupport a realistic interpretation of them when the reference of the termis semantically operative (Dummett 1998, p. 385). However, acceptingfailures of bivalence that result from singular terms which are semanti-cally idle results from a conception of reference as a relation between ourwords and some objects which exist, if they do exist, independently ofour words. Accepting failures of reference of this kind does not by itselfcommit us to any form of idealism, and so the link between Dumrnet-tian anti-realism and idealism is broken. Instead, in many cases we willbe led to deny bivalence because expressions which are apt for referringdo not stand in the reference relation to any existing object, relative tosome realist or idealist criterion of existence. This is the sort of thing anerror theorist will say. Thus once the strong construal of the context prin-ciple is abandoned, Dummettian anti-realism appears to be motivated bythe same set of intuitions as error theory. In so far as an idealist elementremains in Dummetts thinking it is now revealed to be one that emergesout of error-theoretic considerations. In the case of mathematics Dum-mett does not endorse total scepticism as to the truth of mathematics as

head to the hairs on Gs head.


25/26

116 K A R E N G R E E Ndoes Field, but believes that we should follow the constructivists and savejust that indefinite portion of it that is constructible (Dummett 1991b,pp. 3 12-2 1). Nevertheless, his change of heart in relation to the distinc-tion between deep and shallow reasons for being suspicious of bivalencesignals a realignment that makes his current position closer to Fields thanto the linguistic idealism of Wright.

ReferencesA Y E R , . J . (1946). Language, Truth an d Logic. London, Victor Gollancz.B E A N E Y , . (1996). Frege: Making Sense. London, Duckworth.D E M O P O U L O S ,. (1998). The Philosophical Basis of our Knowledge ofDU M M ET T, . (1973) . Frege: Philosophy of Language. London, Duckworth.D U M M E T T , . (1 978). Truth and Other Enigmas. London, Duckworth.D U M M E T T ,. (1 98 1 . The Interpretation of Frege k Philosophy. London, Duck-D U M M E T T ,. (1991a). The Logical Basis ofM etaph ysics. Cambridge, Mass.,D U M M E T T ,. (1991 b). Frege: Philosophy of Mathematics. London, Duckworth.D U M M E T T , . (1995). The C ontext Principle: Centre of Freges Philosophy.

Number. Notis 32: 48 1-503.

worth.Harvard University Press.

Logik und Mathem atik: Frcge-Kolloquium, Jena 1993. I. Max and W.Stelzner. Berlin, de Gruyter: 3-19.D U M M E T T , . (1996). Bivalence an d Vagueness. Theoria 61: 201-16.D U M M E T T , . (1998). Neo-Fregeans: in Bad Company? The Philosophy o Math-D U M M E T T ,. (2003 ). Truth an d the Past. Journal ofphilosophy 100: 5-53.F I E L D , . (1 980). Science Without Num bers. Princeton, Princeton UniversityF I E L D , . (1984). Critical Notice of Fregek Conception ofNu m ber s as Objects.F R E G E , . (1884/1950). The Foundations ofA rithm etic. Oxfo rd, Basil Blackwell.F R E G E , . (1979). Posthumous Writings. Oxfo rd, Basil Blackwell.FREGE, G. (1980). Gottlob Frege: Philosophical and Mathematical Correspond-G R E E N , . (2001). Dummett: Philosophy of Language. Cambridge, Polity Press.H A L E , . (1994). Singular Terms. The Philosophy of Michael Dummett. B.M A C K I E ,. L. (197 7). Ethics: Inventing Right and Wrong. Harmondsworth,

ematics Today. M. Schim . Oxford, Clarendon Press: 369-87.

Press.Canadian Journal ofP hiloso phy 14: 637-62.

ence. Oxfo rd, Basil Blackwell.

McGuinness and G. Oliveri. Dordrecht, Kluwer Academic Publishers: 1 7 4 4 .Penguin.


26/26

T H E C O N T E X T P R I N C I P L E AND D U M M E T T S A R G U M E N T F O R A N T I F R E A L I S M 1 17MATAR,A. (1997). From Dummett k Philosophical Perspective. Berlin, W alter deQUINE,W. V. (1 963). From a Logical Point of Kew. New York, Harper Row.QUINE,W. V. (1 969). Onto logical Relativity and Other Essays. New York,QUINE,W. V. 0. 1995). Assuming Objects. Theoria 60: 171-83.RESNIK,M. (1 967). T he Con text Principle in Freges Philosophy. Philo.mphy

and Phenomenological Research 27: 356-65.RESNIK,M. (197 6). Freges Context Principle Revisited. Studien zu Frege III:

Logik und Semantik. M . Schirn. Stuttgart, Frommann-Holzboog: 3 5 4 9 .RESNIK,M. (1979). Frege as Idealist and then Realist. Inquiry 22: 350-57.STRAWSON,. (1950). On Referring. Mind 59: 3 2 0 4 4 .WEISS,B. (2002). Michael Dum mett. Chesham, B ucks., Acumen.WITTGENSTEIN,. ( 1 961). Tractatus Logico-P hilosophicus. London, RoutledgeWITTGENSTEIN,. (1 967) Philosophical Investigations 3rd Edn. O xford, BasilWRIGHT,C. (1983). Frege j . Conception ofNumbers as O bjects. Aberdeen, Aber-WRIGHT,C. (1990). Field an d Fregean Platonism. Physicalism in Mathematics.WRIGHT, . (1992). Truth and Objectivity. Cambridge, Mass., Harvard Univer-WRIGHT, . (1996). Truth in Ethics. Truth in Ethics. B. Hooker. Oxford, Black-WRIGHT,C. (1998a). On the Harmless Impredicativity o f N=Humes Princi-

Gruyter.

Columbia University Press.

&Kegan Paul.Blackwell.deen University Press.A. D. Irvine. Dordrecht, Kluwer: 73-94.sity Press.well: 1-18.ple). The Philosop hy ofA4athematic.s Today. M . Schirn. Oxford, ClarendonPress: 339-68.Today. M. Schirn. Oxford, Clarendon Press: 3 8 9 4 0 5 .WRIGHT, . (1998b). Response to D umm ett. The Philosophy of Mathematics

the context principle and dummett

Documents