The Meanings of Connectives

R. E. JenningsSimon Fraser University

jennings@sfu.ca

1 The Puzzle About Semantics

Every act of speech and every inscription is a physical intervention with physical consequences.If during a lecture I emit the stream of sounds «will-someone-please-open-a-window», that

emission is a physical event. If I repeat the emission sufficiently many times, it will cause atleast one medium-sized mammal to raise itself to something approaching erect stature, shuffle tothe side of the room and struggle with a latch. Again, since only organisms produce language,anything that counts as language belongs to the phenomenology of biology. And even the

linguistic activities of speech-generating machines, seen in the proper descriptive scale, are biological phenomena, as are the machines that generate them. It is a puzzling thing, therefore,

that when we study language we should find ourselves constructing semantic theories rather thanphysical or more specifically biological ones. Seen in the light of my opening, admittedly banalobservation, language can be understood as a remarkably versatile switch or relay: an exercise ofit is a low-energy interaction that triggers similar or larger expenditures of energy at a spatial ortemporal distance. So, to put my puzzlement a different way, it is as though alien engineers,

charged with acquiring an understanding of a television remote control, should content themselves with figuring out no more than which combinations of buttons produced which channels. Now to be sure, in the sense in which those alien engineers would have failed in answering

the more perplexing questions about the remote control, it is false that the totality of languageengineers have neglected the corresponding questions about language. The physics, the

physiology, and the neuro-science of language all have their active investigators. Progress is slow but assured. What remains a puzzle is that semantics should be thought to occupy anywhere

near so large a part as it is thought to occupy of an otherwise serious explanatory enterprise. Merely to say that the satisfaction conditions of the string «will-someone-please-open-a- window», require that someone open a window does not explain the capacity of repeated productions of the string to move organisms about the room, and cause them to struggle with latches. The corresponding capacity of the remote control is, after all, not explained by the observations that “12” is the name of the ordinal of channel 12. Now in the case of the remote

control a plausible rejoinder is that the correlation honoured in the labelling of the buttons is conventional. But there is no convention, in any ordinary understanding of the word that correlates the phonemic string of my example with that student’s fiddling with a latch or with his

nearly erect stature, nor indeed with any of the particularities of opening a window on any singleoccasion. There is however one feature genuinely conventional and ordinary linguistic causalityshare, namely that, unlike other physical connections, the explanation of the event lies in the

history of the causal nexus itself. In broad terms, our linguistic interventions have the consequences that they do because ancestral linguistic interventions had the consequences that

they did, and because of the facts of linguistic transmission.Again, this is not to deny anything of what we ordinarily say in explanation of linguistic

success, that the student heard what I said, understood it as an intentional utterance originating ina desire that a window should be opened, and so on. Nor is it to deny that the student would havegiven some such explanation of his having opened the window. W may say therefore that thateexplanation gives us an understanding of what has happened in the case at least to the extent thatwe already have an understanding of beliefs, intentions, and desires. The problem, if it is one, isthat although every competent speaker of a language might confidently wield its vocabulary ofbelief, intention and desire, that fact does not require any speaker to be able to say what beliefs,intentions or desires are; nor have philosophers and others been notably successful in their

attempts to do so. Speaking for myself, my understanding of that vocabulary consists entirely inmy being able to use it in ways that do not startle my interlocutors. I suppose that the explanation

– 2 –

for my using the vocabulary as I do is to be sought in the facts of my linguistic ancestors’ uses ofit and its ancestors together with the facts of linguistic transmission.

Now so far this is merely trite linguistics, a commonplace of our ordinary unreflective understanding of the history of language. I speak the English that I speak because it is the English I have learned and to some extent cultivated. The same can be said of my parents, and

theirs before them. Y t the English of the nineteenth century is markedly different from that ofethe twentieth or the twenty-first, and both are just recognizably prefigured in the English of

Chaucer. F cts of ancestral uses and facts of transmission would be of interest to the semanticistaonly if they yielded a more informative account than semantics can of a sufficiently broad rangeof quite specific kinds of linguistic behaviour and their effects. It would seem at first blush thatthe level of detail required for such an explanation would be unattainable, and the facts of thecase virtually inaccessible. Of course none of this would constitute an argument against the

claims of such an account were one available, only an argument against spending valuable research time in the hopes of satisfying a semanticist. But for those of us who have been dissatisfied with the offerings of the semanticists and the analysts, and who simply want an explanatory physical theory of language, a theory, that is, of the ordinary experimentally confirmable and predictive sort, there is no alternative. Semantics has not so far succeeded and

there is no reason to suppose that it can succeed. In these circumstances an explanatory theorymight be all we can have. If in addition its offerings satisfy our cravings for understanding withinsome range of linguistic behaviours, it may be as much as we want. As to the question whetherthe accessible data are reliable grounds for such a theory, that must await the outcome. In anycase, we would be doing no more than following the ordinary path of scientific investigation ifwe proposed an early theory that eventually gave way to a more expressive or more

comprehensive one, confirmable in the measure of its greater refinement.

2 Where Semantics Defeats Us

2.1 The case of or

Since we have no difficulty in using our language, but, in certain sectors of it, have great difficulty in giving a non-trivial semantic account of it, it is a fair conclusion that our use of a

language does not require us to possess a semantic theory for it. As I have already remarked, nosatisfactory semantic theory has been given for the vocabulary of folk-psychological explanation.T engage in such explanation requires nothing beyond an ordinary conversational understandingoof the vocabulary. That, I take it, is what makes it a folk-theory: that one is in possession of it invirtue of being, in the linguistic sense, one of the folk. W exercise it well or badly as we attendeto the nuances of human interaction and have bothered to master the language in which it is

described. Such a one as George Eliot wields the theory with noticeable genius, most of us withlacklustre ease, some with clumsy and painful imprecision. Much the same can be said of thenatural language counterparts of logical connectives. It constitutes the language of a folk-logic.The very intelligent and widely read use it well; for some of us the task of acquiring it is moredifficult than for others; for many its rudiments are never reliably mastered. There is howeverthis difference: that the fundamentals of the theory, at least as it applies to an artificially narrowband of uses of an artificially constricted range of the vocabulary, can be acquired with a

modicum of diligence by the study of academic logic. The well-instructed student of logic, is better off than his counterpart in the philosophy of mind in that he has a more confident mastery

of the logical vocabulary of natural language. And even the meagre store of connectivevocabulary that logic studies can, when suitable mathematical methods are applied, be made togive up a vast lode of abstract theory. Nothing I have to say here is intended as a diminution of

– 3 –

the magnificent achievements of logical theorists. But the very success of logical theory presentsdangers to our understanding of natural language. An immersion in the traditions of logic andformal semantics and a just appreciation of their successes seems to have inspired in some recentwriters what Mr Greenspan would no doubt call an irrationally exuberant investment of effort inapplying its methods to natural language. My aim in what follows is no more than a sober

analysis of the state of the semantic market, in the hope that those who have bought on metaphysical rumour can be persuaded to sell on empirical news. F rtunately for the analyst, theo

delusion has had such a hypnotic grip that its tricks of fancy lie in the open, invisible to the mesmerized, but evident to the casual inspection of any dispassionate observer. Here I illustrate

with a single example: that of English or.It is a curious fact of logical history that until the advent of the truth-table, there was no

noticeable unanimity about the meaning of or, and much perplexity. V nn (1894) says of thee connection between and and or

This must rank among the many perplexities and intricacies of popular speech, but it doesnot seem at variance with the statement that regarded as mere class groupings, independentof particular applications, ‘A and B’ , ‘A or B’ must as a rule be considered as equivalent.(45)

Philosophers of the nineteenth century puzzled diffusely over the nature of disjunctive judgement, but their questions was only rarely put in the form of queries about the meaning of

the word or. But the character of that academic discussion became noticeably more focussed inthe twentieth century as the advent of the truth-table re-presented the central question as that ofthe connection between the or of English on the one hand and 1110 and 0110 disjunctions on theother. The clarity and simplicity of truth-tabular semantics mainly accounts for the simplicity andunclarity of logicians’ opinions as to the meaning of or. (I say ‘opinions’ , not ‘understanding’ ,for they unselfconsciously use or in the full range of its natural roles in their texts. Expectedly,their explicit explanations and prescriptions are usually at odds with their own practice elsewhere

1on the page. ) Nevertheless, according to the explicit accounts of the great majority of late twentieth-century introductory logic textbooks, virtually all semantical questions about and and

or can be referred to truth-tables. Moreover, truth-tables have confirmed for many textbook authors that there are two meanings of or in English, the meaning corresponding to the truth- conditions of 1110 disjunction (∨ ), and that corresponding to the truth-conditions of 0110 disjunction (∨ or xor). Now we ought to have known at least since Reichenbach (1947) that there__

is no single piece of English connective vocabulary that corresponds to ∨ , and that it is extremely__improbable that any natural language should have evolved such a connective. The reason is thatin the general case ∨ (α , . . . , α ) will be true when an odd number of its component sentences__ 1 nare true, and false otherwise. Thus ∨ (α , α , α , α , α ) is true when either exactly one or exactly__ 1 2 3 4 5

three or all of its component sentences are true.There is of course a more fundamental reason why or of English cannot be identified with

either the ∨ or the ∨ of logic, namely that ∨ and ∨ are binary connectives. W may tolerate P ∨ Q_ _ e_ _∨ R as an abbreviation because its syntactic ambiguity is semantically benign, but the

abbreviation is nevertheless syntactically ambiguous. He’s dead or he’s asleep or he’s comatoseis not syntactically ambiguous. W do not regard it as an abbreviation of Either either he’s deadeor he’s asleep or he’s comatose or of Either he’s dead or either he’s asleep or he’s comatose.Now that either of these deficiencies might escape the notice even of authors of logic texts,

consciously in the grip of their subject matter ought to be expected; it merely confirms an important thesis that holds for all of us: Without conscious investigation we can have no studied,

1. F r examples, see Jennings 1994 pp. 70—71.o

– 4 –

but only a conversational understanding of the connective vocabulary of English. English speakers do sometimes use or to form sentences semantically akin to constructions with ∨ of formal logic. Neverthless, the exercises of logic texts are a more reliable source of examples than

speech or literary texts, where such formations represent a only very small proportion of the usesof or, perhaps five percent. Most of the other uses to which English or is put both in literatureand in common speech are semantically quite remote from disjunction. So it may be entered aseven more dramatic evidence of my thesis that textbook authors regularly draw upon non-

disjunction-like uses of or to illustrate the differences between what they take falsely to be themain divisions of its uses, giving non-disjunctive examples to illustrate a non-existent contrast

2between 1110 and 0110 uses. Thus, for example, P trick Suppes (1957) :a

When people use ‘or’ in the exclusive sense to combine two sentences they are asserting thatone of the sentences is true and the other is false. This usage is often made explicit byadding the phrase ‘but not both’ . Thus a father tells his child, ‘Y u may go to the movies oroyou may go to the circus this Saturday but not both’ . (6)

Now since the child is entitled to infer from this pronouncement that he may go to the moviesthis Saturday, and is likewise entitled to infer from it that he may go to the circus this weekend,the sentence could not be a disjunction of any kind, in fact must be some sort of conjunction.From a disjunction one is not entitled to infer the disjuncts. Evidently, the qualification but notboth can be applied to non-disjunction-like sentences. W can consistently say such things ase

‘Y u may go to the movies; you may go to the circus; you may not do both’ .oNow I stress that the point of these remarks is not to advance any positive thesis about or

in particular or connectives in general, nor yet to impugn the authors of logic texts for inattentionto detail. The whole point of the observations is to underline a fact about natural language: that aconversational knowledge of its vocabulary does not require or provide, and therefore does notguarantee the existence of a semantic theory. There is no reason to suppose that the authors ofEnglish logic textbooks speak English worse than anyone else, and much evidence to suggest

that they speak it better than many. But their ability to speak and write the language, like that ofthe rest of us, does not confer an explicit understanding. And they are Socratically worse off thantheir pre-tabular predecessors. Before the advent of truth-tables theorists struggled without

success for an understanding of the connective vocabulary of English; the effect of the tables hasbeen that since their introduction the theorists feel no need to struggle at all.

Even P ul Grice, singular as are his contributions to our understanding of conversationalauses of connectives, insisted upon the sufficiency of truth-tables for the semantics of connectives.Of course, on the Gricean view we require more than the truth-tabular semantics to explain theuses of or: for this we rely upon a kind of background savvy about conversational exchanges, anacquaintaince, not necessarily conscious, with conversational conventions. As Grice sees the

matter, a proper understanding of the role of these conventions should forestall suggestions thatthe natural language correspondents of logical connective vocabulary sometimes have meaningsother than those given truth-conditionally by the tables. Grice (1989) does consider one putative‘strong sense’ of or, that in which is conveyed not only that at least one of the disjuncts is true,but also that the assertion does not rest upon knowledge as to which disjunct is true. This

additional information conveyed is not, he says, evidence of a strong sense of or, but rather ofinformation extracted from the manner of the utterance according to some general rules that

regulate conversation. That it is not a part of some strong meaning of or is evident from the factof its cancellability. The reading can be coherently cancelled or forestalled by the addition of

some some such codicil as ‘ . . . and of course I know which.’

2. F r a more extensive sampling see Jennings 1994.o

– 5 –

Now a for-instance is not an argument. That there is no such strong meaning of or does notestablish that there are no uses of or other than those to which the standard truth-tabular

satisfaction conditions apply. In fact the examples mistakenly given in most of the logic texts aregood examples of such uses, and Suppes’ illustration ‘Y u may go to the movies or you may gooto the circus this Saturday . . .’ is a case in point. Of course the father could add somewhat

surrealistically ‘but I don’ t know which’ . (Much would be explained should it be discovered thatFranz Kafka’s father had been given to such conversational tropes.) The effect would be to

cancel the hearing according to which assent is given to the film-going and assent is given to thecircus visit, in favour of a hearing according to which a disjunction of assents is reported, butaccording to which it is not reported which assent is actually given. In fact we must weigh theoddness of forcing disjunctivity by the cancellation clause against the naturalness of fixing theconjunctive reading by the clause ‘so you decide which’ .

W can set beside this the fact that phrases of the same sort as ‘but I don’ t know which’ecan also be used with less oddity to cancel truth-tabular disjunctive readings of or, as in ‘ If

Elizabeth speaks to him or Margaret speaks to him, Martyn will blush, but I honestly don’ t remember which of them has that effect on him’ , just as the disjunctive reading can be enforced

by the clause ‘so you decide which to ask.’ These clauses and others can certainly be used tocancel readings, but they can also be used to differentiate meanings, and make explicit the

intended relative scopes of sentence elements.It seems merely to be a fact of the English language that or can sometimes be read

adsententially as alternatively, as in

1. Even once you’ve banished a message to your on-screen garbage, it can be pulled from the trash like aday-old sandwich. Or it can be recovered from your hard drive by someone with the know-how. TheV ncouver Sun 1997-02-15a

It seems a mere fact that it will sometimes bear the reading otherwise as in

2. The indictment was wrongly drawn, or I could have flogged the man (Hare 1946, 170)

and again, the fact that one could vex one’s interlocutor by insisting in either such case that onedoesn’ t know which is neither here nor there. If there is an argument capable of showing thatcancellability proves that these are really ordinary disjunctive uses of or, Grice has not presentedit.

There is evidence, in any case, that ought to make us suspicious of any view that wouldgive the truth-conditions of disjunction as the central historical explanation of the uses of or inEnglish,— even of those uses that superficially accord with the truth-tabular account. In the firstplace there are points of continuity between uses of or in which the equivalence to conjunctionseems explainable by reference to truth-conditions of disjunction, and sentence constructions

involving or in which truth-conditional equivalence to conjunction cannot be so explained. I refer to what could be called the ut nunc (or ‘as things are now’ ) character of the conjunction.

Suppes’ illustration is an example. ‘Y u may ϕ or you may ψ’ is such a conjunction. It is its utonunc character that is reinforced formulaically by the addition of but not both. It is to be

understood as saying ‘As things are now, you may ϕ; as things are now you may ψ; but it notguaranteed that once you do one or the other, you will still be permitted to do the other. It is acharacteristic shared with some if-clause occurrences of or. Consider ‘ If Elizabeth or Margaretoffers a suggestion I’ ll be surprised.’ It will be taken to be the claim that if Elizabeth offers asuggestion, I’ ll be surprised and if Margaret offers a suggestion, I’ ll be surprised, but it will notwarrant the further inference that having been surprised by a suggestion from Margaret I’ ll besurprised again by one from Elizabeth, and that in spite of the logical truth that if the conjunctionis true then the disjunction is. The conjunction of conditionals is another example of ut nunc use.

– 6 –

Indeed a conditional theorist might well want the equivalence of α ∨ β > γ with (α > γ) ∧ (β > γ)− − −among his theorems but reject the monotonicity principle | α > β & | γ → α ⇒ | γ > β. T beo

sure, in the formalism this can be regarded as a property of the > rather than as a property of ∨ ,which retains it normal truth-condition, but there is nothing in the natural linguistic facts of thecase to make us so regard its natural counterpart, and much about the behaviour of or in otherenvironments to make us suspect that such if-clause occurrences of or are more naturally

regarded as conjunctive than as disjunctive, including uses, also ut nunc conjunctive, in then-clauses.

3. I will fight you here in London, or, if you are afraid of that, I will go over to France, or to America, ifthat will suit you better. (Trollope 1864, 748)

A second linguistic fact that ought to cast suspicion upon the doctrine of the centrality oftruth-tabular disjunction as the ultimate explanation for this apparent diversity is historical in

character. The modern English word or is a contraction of other, and seems to be the result of acoalescence of two distinct Old English words ‘o„er’ meaning ‘other’ or ‘second’ (as in ‘everyother day’ ) and ‘o„„e’ , which we usually translate as ‘or’ , but which seems to have a range ofuses similar to that of or in modern English. More generally, it seems to be a fact of linguisticevolution that all functional vocabulary is descended from vocabulary that was lexical in its

earlier deployments. There is simply no reason why we should expect anything but diversity from evolutionary developments, and certainly no reason to suppose, in the case of or, that all the

inherent tendencies of such an item as ‘other’ toward adverbialization, then adsentential uses (otherwise, alternatively), and metalinguistic ones such that of

4. Sometimes, for a minute or two, he was inclined to think — or rather to say to himself, that Lucy wasperhaps not worth the trouble which she threw in his way. (Trollope 1861, 401)

would be absent from the development of its contracted form. One has almost to adopt a creationist’s picture of language development to suppose that there would be one use of or in

English, or of any such connective vocabulary of any natural language, and that use the one corresponding to a truth-conditionally definable item of twentieth-century invention.

That the truth-table specifically has been the instrument of seduction, there can be no doubt. There are no parallel claims in Grice’s writings or in those of his followers that in the case

of since or so, both logical words to be sure, the illative uses are primary and their non-illativeuses derivative or the illusory products of conversational conventions. No one denies that the

since of ‘ I’ve a vehicle since I’ve a car’ is different from the since of ‘ I’ve been driving since Iwoke up’ , or that moreover, if either is the more primitive, the non-logical use is. No one deniesthat the so of ‘Fred is happy, so I’m happy’ is different from the so of ‘Fred is happy; so Fred is aconscious being.’ P rallel remarks are warranted by the varieties of uses of therefore, because,afor and so on. Their logical uses are derivative, in ways that are not immediately clear, from theirnon-logical uses. A semantic theory of the former, like a semantic theory of the latter, will notdepend upon truth-conditions, but will rather outline a practice; an explanatory theory will tell ushow one practice gave rise to the other, and thereby what the later practice is.

2.2 The case of but

It is unclear why Grice should have had such faith in the capacity of truth-tables to provide, withthe help of a theory of implicatures, a sufficient semantic account of all uses of or in English,unless he was simply under the spell of a logico-philosophical habit of thinking of or rather thanany other connective vocabulary of natural language as the reading of ∨ . F r if we set that habitoaside, consider what parallel universal claims would be grounded by a similar fit. The sole

– 7 –

premise vis- ̀ -vis the vocabulary is that there is a use of it that truth-conditionally matches theatable. The conclusion is that there are no uses of the vocabulary that do not. By this reasoning wecould infer, for example, that the truth-table for ∨ , if augmented by a theory of implicatures

provides a sufficient semantic account of all of the uses of but in English, since the sentence ‘Heavoids me but he wants to borrow money’ on one reading has exactly the truth-conditions of thetable. In fact the case of but shows remarkable parallels with that of or since each has distinctuses that are approximately in the relationship of duality. The disjunctive use of but, like that ofor is relatively rare; it more commonly found in conjunctive constructions, but as in the case ofor, the whole story of its conjunctive uses cannot be given by a truth-tabular account. Even whenwe have acquired a conversationally sufficient understanding of it, we have great difficulty in

explaining, even to the standards of folk-linguistic explanations what distinguishes the contextsin which it is the right connective to use. Dictionaries resort to providing approximate synonymsthat are both varied and equally difficult. The Concise Oxford Dictionary entry adequately

illustrates those of the rest: on the contrary, nevertheless, however, on the other hand, moreover,yet. P edagogical grammars classify it as adversative. Even speakers of the most exquisitelya

cultivated sensitivity, such as H.W. F wler have a little difficulty ‘ . . . the mere presence of theoopposed facts is not enough to justify but; the sentences must be so expressed that the total effectof one is opposed to that of the other . . .’ (but s.v.) That opposition is not the feature is evidentfrom such examples as ‘He got here, but he got here late’ , and any explanation must be such as toexplain the conversational inequivalence of that sentence with ‘He got here late, but he got here’ .In the end the way to learn how to use but is to become immersed in the practice of its use. Butsuch an immersion does not afford us an articulable account of what we are doing when we useit. That task, I wish to claim, must fall to an explanatory theory of connectives. Indeed any

sufficient explanatory theory must be capable of explaining satisfactorily the distinctive coordinating role of but. It must also yield a unified account of all the uses of but including all of

those exemplified by the following:

1. But for your help I’d be dead

2. No one but his mother calls him that.

3. It never rains but it pours.

4. She wanted to come but she couldn’ t.

5. She was but fifteen years of age.

6. My, but that’s a handsome desk!

Such a theory will also unify those Modern English uses of but with Old English butan (outside),as it will unify uses of or with Old English o„er.

3 The Shape of a Biological Theory

3.1 The representation of meaning

If the physical significance of utterance or inscription lies in its effects, then an explanatory theory will make of a meaning an effect-type. F r purposes of outline it wouldn’ t matter where ino

the physical world those effect-types were located, but as a convenient first approximation, theycan be thought of as neurophysiological, and more specifically as types of neurophysiological

– 8 –

effects that are accessible to the processes that give rise to speech production and other overt intervention. That restriction at least accommodates the fact that speech and inscription sometimes gives rise to speech- or inscription-production, but need not do so. But it also occasions future inconvenience, since any such theory must eventually settle upon a theoretical

language capable of typing such neurophysiological effects in such as way as to accommodatethe facts of multiple neurophysiological realization. As will become evident in the sequel,

ultimately such a theory must be capable of distinguishing between two kinds of differences: (a)the differences between two realizations by two different recipients of a single syntactic

structure, and (b) the differences between realizations by two different such recipients when onesuch realization agrees with that of the producer of the string, and the other does not. That is tosay, it must eventually provide the means of distinguishing the class of realizations that are

correct from the class of those that are in error. Certainly at this stage we can say little or nothingabout the fine structure of that language or the details of the effects. Nor do I intend any guessesas to their nature in labelling such effects inferential effects, a label intended here simply to

locate rather than to characterize the effects in question. The biological theory to be outlined is atheory at the level of population biology, and although even at this level it applies the languageof cellular biology, it applies that language to the syntax of sentences, and not to the human

brain.Now the facts of linguistic transmission and change are such that the types of what I am

labelling inferential effects must constitute species, where the notion of a species is that of a union of populations temporally ordered by a relation of engendering. The facts of change lend

such species features that are also features of biological species. First, virtually every such species is a non-classical set: every member of it has ancestors for which there is principled way

of deciding whether they are members or not. Second, every member of it has ancestors that arenot members of it. Of course the earliest linguistic species are temporally compressed, as are theearliest biological species, and artificially engineered species (those engendered by convention)require a different story from that of those naturally occurring, but for an explanatory theory ofthe connectives of English, the language of evolutionary biology is a good fit: if meanings areidentified with inferential effect types, then meanings can be spoken of as evolving, and

historical changes in the range of uses of words as evolutionary changes. The utility of the identification must be judged when the theory has attempted some explanatory work.

3.2 The picture

Two points serve to give concreteness and a sense of scale to what must here be no morethan a schematic account. They are not premises of an argument for the account, but they are partof the picture of things upon which the schema to some extent relies. The first remark is a globalone: this representation, though it is constructed for detailed and temporally local explanation, isalso promising as a theoretical framework for couching an account of how human or pre-humanlanguage began. It is a fair assumption that linguistic inferential effects have ancestors that arenon-linguistic inferential effects and even earlier ancestors that are non-inferential effects, suchas those consisting in a tendency to detect motion and visually track moving objects. It is

plausible to suppose that the earliest steps toward language involved the opportunistic exploitation of such effects.

At the other extreme of scale, the theory invites us to think of a syntactically structuredstring as a complex system, in fact in much the way that a microbiologist might think of a

polypeptide chain or a larger component of genetic material. The parallels, as they apply to connectives are striking, but again to be judged by the standards of explanatory usefulness, rather

than by competing disanalogies with the biological case. The parallels come to light only as they

– 9 –

are revealed by the conjectured facts of linguistic evolution; they are conclusions; not premises. Iregister them beforehand only to give concreteness to the picture the account presents.

Biological organisms come in a great variety of shapes and sizes, from viruses to whales.The cells of medium-sized organisms also vary over a wide range of sizes. But by and large,

smaller organisms are not smaller because their cells are smaller, but because they have fewer ofthem, and if we descend to the level of the nuclei of cells, there is remarkably little difference innuclear size between the smallest and the largest cells of medium-sized organisms and even

between the smallest and the largest organisms. It is not a coincidence that nuclei are uniformlyso small: it is an essential feature of a method of chemical synthesis that depends upon the

coincidence of weak molecular forces and therefore upon the orientation and proximity of molecules. That is the first point. The second is that the ultimate molecular components of the

products of this synthesis have their informational significance, not in themselves, but in the combinations into which they enter, and ultimately in the places of those combinations in the higher order combinations that constitute the whole. DNA has a syntax. Finally, the uncorrected

reading frame errors that give rise to biological mutations are essentially syntactic in character.The emerging linguistic parallels, which are only general in character, seem to be these:

the smallest verbal components have their inferential significance only as they occur within sentences and are dependent for their inferential effects upon a hierarchy of structural features of

the sentence. Thus for example, the or of ‘He is asleep or comatose’ will be read disjunctively;the or of ‘He may be asleep or he may be comatose’ will be read conjunctively. W do not writeelonger novels by writing longer sentences, but by writing more sentences within a relatively

narrow range of lengths. There is some evidence that in conversation we set durational targets forthe sentences we produce. There are limitations upon our capacities to be reliably affected by

complexities of syntax, and those limitations mainly enforce these durational restrictions. Our apprehension of syntactic structure is prosodically assisted. Thus, for example, we distinguish the

two syntactic readings of ‘But for my son I’d stay and fight’ by differences of lengthening, pitchcontour and stress. Prosodic control of syntax apprehension also enforces limitations of sentencelength. Finally, mutations occur in the meanings of connective vocabulary through undetected

and therefore uncorrected misapprehensions of syntax.

3.3 Compositionality

It will already have become evident from the account I am presenting, that only some weakenedversion of the compositionality thesis will be true of natural languages. But some weak versionwill survive. On whatever account we give of meaning, the meaning of a sentence has somethingto do with the meanings of its component vocabulary together with its syntax even if the

connection between the two is a little murky. As I have already remarked, which meanings elements of component vocabulary have must sometimes be gathered from an apprehension of

syntax in the prosodic presentation. Consider the difference between ‘What is this thing calledlove?’ and ‘What is this thing called, Love?’ Sometimes, prosodic clues having been missed, thedetermining syntactic judgement must depend upon the comparative plausibility of the

alternative construals, as in ‘ I’ ll have breakfast only if we are short of food.’ Again, I hope that Ihave already said enough to counter any such suggestion as that semantic problems can arise

only for readings of notional vocabulary, that compositional problems arise for connective vocabulary, only through insufficiently marked syntax, that since the semantics is fixed, ambiguities must be ambiguities of scope. As we have seen, even that modest view cannot survive attention to human speech. W might reade

5. It will be useful or it will be harmful

– 10 –

as a disjunction. But we would not give a disjunctive reading to

6. It could be useful or it could be harmful (Gilbert 1976, 187)

except under very unusual contextual pressure, and then we would be at a loss how to take thesignificance of the disjunction.

In fact there is something unrealistically hypothetical and itself ut nunc about the usual basis for claims of compositionality. Some such principle is claimed to be required to explain our

capacity to produce novel constructions in speech production and understand them in the speechof others. This may be so, but the fact is that in the course of a day’s compositions, we neitherproduce nor process that many constructions, novel or otherwise. More importantly, such

composition as does go on must in fact be a vehicle of meaning change. Else how, for example,did the word internecine come to have anything essentially to do with matters within a family, orspecious anything essentially to do with spuriousness? That notional meanings undergo changesis hardly news, though the details of these changes probably deserve more philosophical studyand interest than they naturally excite. Of greater significance for this study is the global fact

about connective vocabulary:

All the connective vocabulary of any natural language has descended from lexical vocabulary, inmost cases, from the vocabulary of temporal, spatial and other physical relationships.

Thus, as we have remarked, the English or is a contraction of other, but descends from butanmeaning outside, if probably from a coalescence of Old English gif (if ) itself a descendent fromthe language of doubt and the verb giefan (give). Much of the vocabulary retains, in modern

English, residual non-logical physical uses (since, then, therefore, yet, for, as); some such as orhas evolved a distinct morphology that masks its provenance. These facts have philosophical

significance beyond the trivial remarking of etymologies. If we think that every meaning is themeaning of something, then we will conclude from this that at least all naturally occurring logicalmeanings descend from non-logical meanings. And if I may interject a further large-scale

remark, we will also conclude that human intellectual capacities that reveal themselves in propositionally expressed reasoning have their roots in the natural non-linguistic propensities of

human and pre-human organisms, and we will have some concrete clues as to how the one mighthave given rise to the other.

As a topic of study, the descent of connective vocabulary from its physical forbears mightbe called logicalization, in imitation of the related topic that linguists call grammaticalization,the process by which lexical vocabulary acquires functional uses (as the have and will auxiliariesin English tense structure, –abo and –ibo endings of Latin past and future verbs, and so on.)

Logicalization, in being confined to connective vocabulary, is narrower in scope than grammaticalization, but it is also more protracted as a temporal development, since for much of

the vocabulary, connective meanings continue to multiply, even after logicalization. Moreover,these diversities are, on the face of things, sufficiently systematic that any theory of

logicalization with pretensions to completeness had better provide the means of explaining them.Now there is sufficient justification for a study of logicalization in its showing us things aboutour languages that we did not know. The promise that, if it gets matters approximately right, itstheoretical framework might shed light upon the origins of language, ought to earn it passive

tolerance. But it will have more immediate philosophical cash value also, for if a plausible theoryof logicalization individuates multiple meanings of connectives in virtue of its assigning them

distinct causal histories, then the theory is an advance on the Gricean theory that connectives have only one meaning, and that the apparent diversity is attributable to conversational implicatures. It will at any rate have provided an argument where Grice has provided none.

– 11 –

4 Evolutionary tendencies

4.1 Usative relations

On a standard semantic account, an n-place predicate ϕ is interpreted as a n-ary relation, [ ϕ ][ ] understood extensionally as a set of ordered n-tuples. The intuitive understanding of the interpretation is that the meaning of an n-place predicate, ϕ is given extensionally by the set:

{<x , . . . , x > | ϕx . . . x }.1 n 1 n

that is, the set of ordered n-tuples of which it is correctly predicated. Thus for example, a meaning of the preposition between is the set of triples <x, y, z> of which it is true that x is between y and z. Since we are interested in the evolution of meanings, that standard semantic

account will not quite do for our purpose. The representation we require is, not that of a putativeestablished meaning, but that of the establishing of it. F r this we must broaden our purview tooinclude what I shall call the usative relation, «ϕ» of a predicate, ϕ. «ϕ» includes the set of n-tuples <x , . . . , x > of items of which it has ever been claimed that ϕx . . . x . Statistically it1 n 1 n

would make little difference if it it also included the set of n-tuples of items <x , . . . , x > of1 nwhich ϕx . . . x has been denied. And it also ought to include the set of n-tuples of items of1 n

which ϕx . . . x has been enjoined, and so on. Our purposes do not require a precise or even1 n detailed definition of a usative relation, only mention of its intended role, namely that it should

be the relation that records the accumulated historical uses of the item of speech, that is to say,the set of compositions in which the predicate has played a part. In the case of between, it may besaid, the record would not be a relation, but a hyper-relation, since it would contain n-tuples andm-tuples for m =/ n. In particular, it would include a set of quadruples, each of which comprisesa speaker, a hearer, a lamp post, and a piece of information. Neither will it be uniformly spatialor temporal, but will include a set of triples each of which contains two alternative conditionsand a choice, as in

7. The choice was between five hundred pounds a year . . . or penal servitude. (Trollope 1871, 181)

It will include another set of triples each containing two items and a relation, as in

8. . . . the difference between sinking or floating. (Engel 1990, 252)

It will also record all of the accumulated nonce uses and misuses of the vocabulary, not marking,other than statistically or incidentally, any distinctions among misrepresentations of fact, correctuses, and incomprehensible ones.

A usative relation «ϕ» is the union of a temporally ordered set of relations {«ϕ» | t ∈ T}.tEach «ϕ» can be defined by «ϕ» = ∪ «ϕ» }. Hence, if t ≤ t′, then «ϕ» (SS) «ϕ» . This{t t i t t′

i t

temporal monotonicity is a potent instrument of semantic innovation, since, in general, the morethe n-tuples in the relation, the less the n-tuples have in common, and more particularly the morevaried the compositions experienced by any given speaker of the language of which it is an

element. Again, the more varied the uses, the fewer the inferential effects that all of the experienced uses have in common, and the more frequent the instances of use for which none of

the subspecific inferential effects of previous spatial uses is forced or expected. Examples of vocabulary that, without having acquired logicalized meanings, have acquired non-spatial meanings partly through extensional saturation and consequent inferential dilution are just,

straight, right, flat, even, downright. But prepositions such as but, without and outside that have

– 12 –

now acquired logicalized meanings also have antecedently acquired non-logical but also schematized non-spatial meanings.

The point, once appreciated, should make us skeptical of the place of metaphor in thesedevelopments. No doubt explicitly metaphorical, non-spatial extensions of physical vocabularydo occur. But we ought to resist the temptation to lay very much at all of the generalizing workof schematization to their influence. The gradual wearing away of the capacity, independently ofother cues, sometimes even with them, to occasion particularistic relational inferences can for themost part be regarded as a natural effect of ordinary non-metaphorical use. The effect has a

counterpart in the model-theoretic slogan that the wider the class of models, the fewer the validformulae, simply because the broader the class of models, the more opportunities there are forany particular formula to be falsified. The larger the usative relation (or hyperrelation) the fwerthe particularistic inferential effects supported.

What schematization amounts to in particular cases depends upon the character of the ancestral vocabulary. V cabulary that supports inferences as to spatial relationships will acquireo

despatialized uses in which no such inferences are supported; temporal vocabulary will acquirede-temporalized uses, and so on. There is no reason to suppose, nor does my account require,that the traffic of evolution is all one way in this regard. Plenty of examples come to hand ofspatial meanings with temporal ancestors or the reverse and of temporal meanings whose

ancesters are inferences of relationship of manner or character. The word as alone furnishes sufficient examples.

4.2 Schematization, spatial and temporal examples

Much of the logical connective vocabulary of natural language is descendent from ancestral vocabulary whose explication would require mention of spatial relationships, and much of that

same connective vocabulary have existent homonymic cousins carrying on in much the originalfamily business and others in related branches of trade. But at an early stage of its evolutionarydevelopment, schematized, in these cases, despatialized meanings must have emerged. Thus, forexample, the subordinator where as

9. He was four years younger than Donovan with the same fair hair. Where Donovan’s was glossy,Bennet’s was coarse . . .. (Grafton 1996, 30)

Here, though there are spatial, locational implications expressible using where they are incidentalto this fully logicalized use. Again, the conjunction but of

10. Mrs. Pipkin’s morals were good wearing morals, but she was not strait-laced (Trollope 1875 i, 399)

since it takes a sentential filling may be regarded as a logicalized use even if it is unclear which.Nevertheless it has a distant but homographic Scottish cousin labouring as an adjective meaningphysically outside, and often seen in company with ben meaning inside:

11. It cannot be brought But, that is not the Ben. (OED. BUT s.v.)

12. Gae but, and wait while I am ready. (OED. BUT s.v.)

Elsewhere, adverbial/prepositional but is present only in schematized non-spatial uses. Such a remark as

13. There is no one but the house

– 13 –

would seem a curious, perhaps precious, personalization, if not a selection error. The reason isthat outside of the much constricted geographical regions in which but retains its spatial uses, theresidual prepositional use is that of representing schematized relations: categorial outsideness:

14. I could see nothing but sunshine caught in leaves . . . (Cornwell 1992, 8)

or circumstantial outsideness:

15. But for the storm he would have given way. (Trollope 1875, 354)

Though schematic, these are not yet logicalized uses. They do, however, take us close, since circumstances can be specified sententially or gerundially. Thus But though prepositional, could

be labelled proto-logical in

16. But for the fact that there was a storm he would have given way

as it could in

17. But that there was a storm he would have given way

a use that takes us to a stage only an ellipsis away from one of the completely logicalized usessuch as that of

18. It never rains but it pours.

W re this the only logicalized use of but the story could perhaps stop with that explanation. But,eas we have seen, and as this sentence bears witness, it is not. It is relatively easy to see how butmay have become logicalized as a disjunctive connective; the account of its conjunctive logicaluses must await a later discussion.

More familiar than the surviving Scottish but, which, had its original spelling survived tojustify its sense, would be spelled by out (as ben would be spelled by in), is the orthographicallymore forthright without of:

19. There is a green hill far away, Without a city wall . . .

a use corresponding to within. This spatial without has acquired and in turn nearly lost certainquasi-spatial prepositional uses

20. A very violent and painful heat cannot exist without [≈ outside] the mind. (Berkeley 1713, 533)

that can of course be party to spatial metaphors:

21. . . . he would be beyond the reach of law, and regarded even as without the pale of life. (Trollope1882a, 26)

This metaphorical spatiality is palpably present in:

22. I cannot hold myself without abusing him. (Trollope 1882b, 134)

but is all but absent in the most usual uses of the word:

23. . . . I shall always do as I like in such matters without reference to you . . . (Trollope 1859, 499)

These are schematized, but not logicalized uses. Y t even without can do duty as a sententiale connective:

24. She could not write the letter without some word of tenderness should go from her to him (Trollope1882b, 133)

– 14 –

or more crudely

25. He’s a local lad and he won’ t get far without he’s noticed (Hare 1938, 123)

in which some trace of the ancestral meaning is still discernible.The curious dualization that, in the case of but is apparent only in its fully logicalized uses,

emerges in the schematized but still proto-logical uses of without. Whereas the but dualizationhas yielded an and/or split, the without-meanings, are roughly distinguishable as and not and ifnot. The divergence is apparent in the two following:

26. He’ ll die without help (if not)

and

27. He’ ll die without fear. (and not)

And it is worth mentioning as an aside that not only without, but with has a proto-logical uses,with a meaning approaching that of because of:

28. W haven’ t formally started to review it, but with it hitting the news . . . hopefully we’ ll be gettingetogether next week and bring our findings to Caucus on Sept. 19 (Coquitlam, P rt Coquitlam, P rto o

Moody Now, 1994,09,03)

and, like without, both conjunctive and conditional uses

29. With frugality we’ ll get by (if)

30. W ’ ll get by with plenty to spare (and)e

English likewise puts outside to schematized, non-spatial uses, as Groucho Marx noticed

31. Outside of a dog, a book is man’s best friend; inside of a dog it’s too dark to read.

Compare,

32. His driver’s license says he’s Hulon Miller, Jr., but I doubt if there’s anyone outside of his mother callshim Hulon. (Leonard 1992, 153)

Even under has found schematized uses, as

33. Manners were all that could be safely judged of, under a much longer knowledge than they had yet hadof Mr. Churchill. (Austen, 1816, 129)

English also affords many examples of schematized meanings that descend from previously temporal ones. I present here only two illustrations, yet, and still. Homographic descendents of

giet find themselves employed in work, some at greater, some at less remove from the earlier meaning of before. Some have meant something like in all the time before that time:

34. She had no plan of revenge yet formed. (Trollope 1875 i, 255)

others mean something like despite that circumstance.

35. . . . he need not fear the claws of an offended lioness:—and yet she was angry as a lioness who had losther cub. (Trollope 1875 i, 254)

Again, the obsistive still of:

36. Mr. O’Callaghan was known to be condescending and mild under the influence of tea andmuffins—sweetly so if the cream be plentiful and the muffins soft with butter; but still, as a man and apastor, he was severe. (Trollope 1859, 277)

– 15 –

is cousin to the adjective meaning unmoving:

37. Mr. Bertram sat still in his chair. (Trollope 1859, 307)

and to the persistive adverb of:

38. He still kept rubbing his hands . . . (Trollope 1859, 307).

Having illustrated developments at the earliest stages of logicalization, we move to a much laterstage, without pretending that there is no more to be said of stages in between. In fact a completeaccount must mention the process by which certain origiunally multivalent vocabulary acquirestrivialized, that is two-valued readings, and must explain how words that are originally

prepositions or relative adjectives come to punctuate acts of speech. Here I offer only what I hope is sufficient evidence of the explanatory usefulness of the approach. So we move to what is

perhaps the most intriguing finding of the research.

4.3 Allotropy

The label, allotropy is intended to suggest the physical use of the term and its cognates, that is, asdenoting or pertaining to a variation in physical properties without variation of elementary

matter. Diamonds and coal are allotropic forms of carbon; ozone an allotrope of oxygen. As applied to a natural language, it picks out classes of sentences capable of presenting themselves

as of one syntactic kind to one user and of a different syntactic kind to another, while being assigned the same satisfaction-conditions by both. As a nearly trivial example we may consider

the following. A speaker says,

39. No trees have fallen over here

expecting the words of the sentence to be taken as having the roles that they have in ‘Over hereno trees have fallen’ , and a hearer understands the sentence as ‘Here no trees have fallen over’ .They agree on the satisfaction-conditions of the sentence, but disagree on its syntax. The near-triviality of the example lies in the semantic idleness of the over. Of course, one might argue thatthe over of fallen over must therefore have a different meaning from that of the over of over

here. But the effect of over in both constructions is at best vestigial, and the difference falls below the threshold of interest for this study. Non-trivial examples present themselves. Consider

the two forms

(x)(ϕx → α)

and

(∃ x)ϕx → α.

where α contains no free occurrence of x.

They are both formalizations of the schema

If any x ϕ’s, then α

and either represents a way of understanding the structure of that schema. F r some instances ofothe schema for which the different structural understandings corresponding to the two

– 16 –

formalizations require no difference in the understandings of the satisfaction-conditions. The alternative formalizations correspond to allotropes of the schema. Notice that in one allotrope the

work of any in the original schema is that of a long-scope universal quantifier; in the other it isthat of a short-scope existential quantifier. Now for some α’s, in particular, for those in whichthere is anaphoric reference to the whole if-clause, a satisfaction-conditionally significant

syntactic ambiguity persists. The sentence

40. If any student touches my whisky, I’ ll know it

remains ambiguous as between

41. If any student touches my whisky, I’ ll know that some student has touched my whisky

and

42. If any student touches my whisky, I’ ll know that that student has touched my whisky.

Indeed the availability of the former reading should sufficiently tarnish the sometime-expressedthesis that any is just a natural language long-scope universal quantifier. But, such examples

aside, such conditionals are generally capable of distinct but allotropic representations of the sortgiven. The ambiguous anaphora of 40 confirms that neither allotrope is a uniquely correct

representation, and that the contrary assumption for particular cases buys no greater simplicityoverall.

Negative environments also can be allotropic. Consider

43. . . . I will not be brought under the power of any (I Corinthians, 6:12)

which could be represented by the form

¬ (∃ x)Bx

or by the form

¬(x) Bx

By contrast, interrogatives, which together with hypotheticals and negations make up all of theoccurrences of any in the Authorized V rsion, are non-allotropic, requiring something akin to aneexistential reading.

The allotropy hypothesis, as applied to the evolution of meanings, is the hypothesis thatcertain meanings of certain connective vocabulary are the product of a development that dependsupon allotropy in the sense given. In the generation of such meanings there is a stage in whichidentical sequences of words, with identical or sufficiently similar satisfaction-conditions,

presents one syntactic structure to one subpopulation of their users, and a distinct syntactic structure to another. The evolutionary significance of allotropy is that by its means the earliest

populations of a new meaning can be hidden, and therefore protected from correction, by maturepopulations of an older one. F r convenience I shall refer to new meanings allotropicallyo

nurtured in this way as succubinal meanings and distinguish them by overlining. This suggeststhat the older, fostering meaning should be called incubinal and marked by underlining. W re theeaccount to be applied directly to any, and were the case as simple as an examination of the

Authorized V rsion might suggest, it would regard the uses that tempt or require representationeby existential quantifiers as having common ancestors with incubinal, any, those, such as “ free___choice” any that seem to require representation by universal quantifiers as descendents of

– 17 –

---------succubinal, any. In fact if some such developments account for the existential/universal dual personality of any, they must have occurred in much earlier than Jacobean times. The duality of

use is likely inherited from aenig, which, in written remains, occurs predominantly in allotropicand interrogative environments earlier than the eight century, but in its normal universal role incomparisons as well. Beowulf boasts to Unferth that he has more strength in swimming ‘„onne--- ---- -- aenig o„er man.“ (534)

It will be evident that the adjective succubinal refers to a stage in the generation of a newmeaning. At that stage the population of users can be classified accordingly as their parsings

require the incubinal or succubinal representation. So while that stage persists, there may be nogenerally accessible evidence that a new meaning is emerging. It is only when the new meaningis out from under the old that there can be said to be two meanings in the ordinary way of

speaking, which is to say, two meanings equally available to both populations of users. The newmeaning must migrate to non-allotropic environments in which commonly recognizedsatisfaction-conditions demand the formerly succubinal meaning. In the case of any, such an

environment might be permissive or probabilistic or the use may be triggered by adjacent vocabulary as

44. Those people probably saw things much stranger any given day of the week (Grafton 1995, 171)

where perhaps the comparative ‘stranger’ triggers the use of any because comparatives normallytake any (as stranger than any fiction. W will return to the matter later, but the point deserves aelittle flag here. The evidence suggests that adjacent vocabulary triggers use, rather than that

conscious consideration of the meanings of adjacent vocabulary gives rise to deliberate deployments. As we shall see, this involuntary feature of speech-production quickly gives rise to

hybridizations as vocabulary with formerly succubinal, now migratory, meanings combine withsurrounding connectives as though still bearing their formerly incubinal meanings. This to theconfounding of any simplehearted compositionality doctrine.

5 Mutations

Usually, we may assume, the syntax produced by a speaker is the syntax received by the hearer.Sometimes, however this is not so. On such occasions, one of two conditions must prevail: eitherthe error is syntactically negligible, as in 39, or the error is not. If the error is not syntacticallynegligible, then we might suppose that one of two conditions must obtain: either the error is

satisfaction-conditionally negligible or it is not. W need not set the standards of negligibilitye puristically high. If a speaker says ‘ I don’ t think she’s there yet’ and the hearer mistakenly takes

this to be the claim ‘ I think that she’s not there yet’ the satisfaction-conditional difference between the two, though not formally negligible, may nonetheless make no practical odds. This

may sufficiently explain why the English language tolerates negation-raising verbs (though Griceans might insist upon explanatory elaborations.) If the difference is not satisfaction- conditionally negligible, then one of two conditions must arise: either the syntactic error is eventually corrected or the hearer persists for a while in satisfaction-conditional error as to what

was said. This, I say, is how one might have thought the cases would bifurcate. In fact there seems to be an intermediate case: namely that, roughly speaking, the syntactic error should be

satisfaction-conditionally compensated for by a semantic one. A more precise account of whathappens in the misconstrual of 39 might be made in these terms: the speaker’s syntax of ‘ fallen(over here)’ is imperfectly replicated as hearer’s syntax ‘ (fallen over) here’ but the error is

compensated for by a semantic error in which the otiose over of the construction over here isunderstood as the non-otiose over of the construction fallen over (as distinct from fallen in, fallenthrough, and so on.) Under certain conditions, when the syntactic error is compensated for by a

– 18 –

novel or non-standard semantic construal, new meanings can be introduced, which are appropriately thought of as mutations in something very close to the molecular biological sense

of the word.

The replacement of a codon specific for a given amino acid by another codon specific foranother amino acid is called a missense mutation. On the other hand, the change to a codonthat does not correspond to any amino acid is called a nonsense mutation. The existence ofextensive degeneracy means that most mutations are likely to cause missense rather thannonsense. Missense mutations produce proteins changed in only one location, and so thealtered proteins which they produce frequently possess some of the biological activity of theoriginal proteins. The abnormal hemoglobins are the result of missense mutations. (W tsona1965, 374)

Mistakes in reading the genetic code also occur in living cells. These mistakes underlie thephenomenon of suppressor genes. Their existence was for many years very puzzling andseemingly paradoxical. Numerous examples were known where the effects of harmful

mutations were reversed by a second genetic change. (378)

Those mutations which can be reversed through additional changes in the same gene ofteninvolve insertions or deletions of single nucleotides. These shift the reading frame so that allthe codons following the insertion (or deletion) are completely misread. (379)

Now some of the nonsense mutations produced by such ‘ reading frame’ errors of English havebeen recognized as nonsense by sensitive listeners without having been diagnosed as mutations.Consider this exchange between the naive and immature Catherine and the better educated HenryTilney (Northanger Abbey)

. . . ‘Have you had any letter from Bath since I saw you?’‘No, and I am very much surprized. Isabella promised so faithfully to write.’‘Promised so faithfully!—A faithful promise!—That puzzles me.—I have heard of a

faithful performance. But a faithful promise—the fidelity of promising! It is a power littleworth knowing however, since it can deceive and pain you.’ (Austen 1818, 209−10)

There need be no doubt (since Henry has put his finger on it) that Austen could see how this nonsense use of faithfully has come into English: through some earlier misreading of the adverb

as applying to the finite verb where it had applied to the succeeding infinitive. T promiseo faithfully to write makes some sort of pleonastic sense; T promise faithfully to write makeso none. Nevertheless, the legacy of this syntactic misconstrual is the idiomatic coupling of faithfully and promise as

45. I promise faithfully not to explore. (Milne 1922, 143)

It would seem that, in the case of notional vocabulary, the distinct meaning that arises throughsuch an error persists as an idiom only within the very restricted environment that gave rise to theerror, and does not propagate through migration to others. In this case the reason is perhaps thatfaithfully does not seem to have any non-perplexing new meaning when attached to forms of

promise. Something along the same lines could be said about negation-raiser verbs. Suppose theverb think were to acquire a distinct succubinal meaning through the construal of

46. I don’ t think she’ ll come

as

47. I think she won’ t come

-------------the succubinal think would bear the relation to the standard think represented in the equivalence_____

– 19 –

-------------I think that α iff I do not think that not α_____

That there is no such non-committal meaning of think in English is sufficient proof that no suchdevelopment has taken place. And we might suppose a priori that any such development wouldbe unlikely. One reason might be that positive verbs of attitude are too well established in theirrange of uses for such a non-committal use to persist uncorrected in negation-free environments;another is that the negation-raising reading is sufficiently robust that I do not think that not-α will____be read as I think that α. Again, one might look to some such development to explain the____anomalous doubt but as

48. I do not doubt but that the Viet Cong will be defeated (Richard Nixon)

This venerable construction was already current in Jacobean English.

49. No doubt but ye are the people, and wisdom shall die with you (Job 12:2)

But the anomaly is explained by the presence in English of a use of doubt having approximatelythe force of fear or suspect as in

50. There I found as I doubted Mr. P mbleton with my wife (P pys 1663-5-26)e e

51. . . . she could not forbear telling me how she had been used by them and her mayde, Ashwell, in thecountry, but I find it will be best not to examine it, for I doubt she’s in fault too . . . (1663-8-12)

52. . . . he is not so displeased with me as I did doubt he is (1663-12-8)

and so on. In fact for most of the biblical occurrences of doubt there is sufficient contextual evidence, sometimes quite explicit, to support some such “middle voice” reading as be in perplexity about or weigh the evidence for and against, rather than the “active voice” reading as

think improbable. In fact, at least seven distinct Greek verbs and nouns are translated as ‘doubt’in the KJV New T stament. And the preferred construction doubt whether is itself evidence that a___ e_

distinct middle voice reading, now largely superseded, was once standard. If the doubt but construction is explained as an isolated survival of an earlier weak positive doubt, then it may be

that the standard (suspect-that-not) use of doubt is the product of just the sort of mutation thatstronger positive verbs of attitude so robustly resist; for the standard use approximates the usethat one would predict as likely to arise, through mutation, from negated negation-raising uses ofthe P pysian doubt. A strong verb’s modus tollens is perhaps a weaker verb’s modus ponens.e

5.1 Metanalysis

Jespersen (1922) introduced the term metanalysis as a label for a phenomenon in the process ofword-formation.

Each child has to find out for himself, in hearing the connected speech of other people,where one word ends and the next one begins, or what belongs to the kernel and what to theending of a word, etc. In most cases he will arrive at the same analysis as the former

generation, but now and then he will put the boundaries in another place than formerly, andthe new analysis may become general. (174)

Thus we have an umpire from a numpire, an apron from a naperon, a nickname from an ickname and so on. In such cases the mutation comes about through a misapprehension of the

divisions between words. Jespersen is rather vague in the matter of how such a mutated form survives, but we can note here at least the prime condition for such a survival, that the discrepancy between speakers and audience in alternating roles should go for a time undetected,

– 20 –

and therefore that it should make no or sufficiently little difference in the satisfaction-conditionsof sentences in which the discrepancy occurs. And of course, as the difference is undetected, the

3metanalytic population has a chance to become established.

5.2 Scope Evasion

The term metanalysis, transposed to the level of syntactic structure, would serve equally well tolabel the initial stage of the development that I label scope evasion, for it too springs from a

misapprehension of divisions within sentences, though at the clausal level. The more importantdifference is a dimensional one. F r Jespersen the significance of metanalysis lies in theo

introduction of a new verbal expression of an existing meaning: in the course of the developmentumpire came to mean what numpire had meant. F r us, its significance lies in the introduction ofoa meaning that did not previously exist. In the physicalist idiom adopted here, Jespersen’s

observation can be couched in semantic language as well, since, for example, umpire comes tohave a meaning where previously it had none. But in all but one of the cases we consider, theoutcome of the metanalysis is that a word that previously had n meanings comes to have n + 1. Ibegin with the exception.

Unless is a striking example of a connective for which the original meaning, which had aconjunctive component, has become extinct in favour of a disjunctive one, and apparently

through evasion of the scope of negative sentence elements. The evidence for this lies in two features of its early development. The first is that its earliest uses are found exclusively in negative constructions; the second that it represents the surviving coalesced core of on [a] less

[condition than that]. Setting aside the scalar feature, the ancestral meaning of α unless β is α4with the condition that β unmet, that is α without β, that is, α and not β. Thus the ancestral,

elementary meaning of not . . . unless . . . is that of not(. . . and not _ _ _)}. The ancestral, elementary meaning of that construction, of course, gives the truth-conditional meaning of not . . . unless _ _ _ in its current use, but its elementary meaning is not( . . .) if not _ _ _. or not( . . .) or _ _ _, the unless being represented by the if not or the or. The establishment of a reading in which the negative element has foreshortened scope sponsored uses in which the negative element was absent. And over that enlarged field of use we may regard unless as univocal provided that the negating elements, when they occur, are always given a short-scope

reading. The disjunctive reading of unless is sufficiently robust to withstand repositionings andthe introduction of negators such as It’s not the case that, with long scope intonationally madeexplicit.

It is plausible to suppose that the conditional and of middle and Jacobean English, the andthat, in Shakespeare, early editors clipped to an, had been speciated by an earlier parallel

development in which in certain constructions not(. . . and . . .). was read not( . . . ) and . . ., theand being construed conditionally to make up the construal of the whole.

.53. Ich nolde cope me with thy catell ne oure kirke amende,.Ne take a meles mete of thyne and myne herte hit wiste

.That thow were such as thow seist; ich sholde rathere sterue: (Langland. C P ssus VII. 288-290)a

Compare such a construction as

3. Canadian English furnishes an charming example of metanalysis. The drawing up of a writ is a constitutionally dictated preliminary to theholding of an election. The draw up of the formulaic announcement has been heard as drop, with the result that it is now standard usage tospeak of the Prime Minister as in course of dropping the writ or as having finally dropped the writ. The absurdity of the construction isevidently sufficiently masked by the presumption of antique obscurity that attends parliamentary language generally.

4. In fact without has undergone a similar mutation, except that in the case of without both uses survive. Compare She’ll die without medicalattention and she’ll die without betraying her friends.

– 21 –

54. I do not think that you should go and she stay behind.

or

55. Could he have come out and we didn’ t see him? (Wingfield 1995, 261)

or

56. Why am I a redhead and you have dark hair? (@discovery.ca 1995-12-26)

where the structure of the clause following the and is such as to permit a foreshortening of thescope of the negation or the modal could or interrogative why with substitution of if for and, atransformation skeletally recognizable in the PL equivalence:

¬ ¬− −(α ∧ β ) || α ← β

It seems likely that the adversative but including its arrogative use, (as in not black but dark blue) was engendered from the propositionally exceptive but by scope evasion. At the initial stage we would expect to find despatialized but in its propositionally restricted use inside the scope of a negative or modal sentence element:

57. He had not been long upon the scout but he heard a noise. (Defoe 1722b, 147)

where what is denied is that the subject had been long on the scout without hearing a noise. If thescope of the negation is foreshortened and the sentence taken to imply absolutely that the subjecthad not been long upon the scout, then the sentence as a whole can have approximately the sameconversational effect if it is taken, in virtue of its second clause, to imply that the subject heard anoise, and this quite independently of any understanding of the force of its but on this reading.Once a non-exceptive use is introduced, it can shelter beneath the exceptive use for all verbs thatcan be made non-trivially subject to exceptive clauses, but it must force a non-exceptive readingfor verb phrases not plausibly so subject. Thus, for example, the but of

58. He wasn’ t given to literary exercises, but he was neat and methodical (Snow 1974, 252)

even without the comma, would have no plausible exceptive reading. The foreshortened scopemade explicit, the non-exceptive reading, however to be understood, persists even in the

presence of preceding negations and exceptively modifiable verb phrases :

59. In the mystery itself there is not the slightest interest. But the mysteriousness of it is charming.(Trollope 1867, 398)

The exceptive but of this development as we have so far discussed it is a multivalent one, theexceptive clause limiting the range of some multivalent magnitude or manner of engagement ofsome activity. Exceptive but has also a bivalent use in certain conditional constructions:

60. . . . I should not now have spoken to you at all, but that since we left England I have had letters from asort of partner of mine (Trollope 1876 i, 236)

Here a number of elements are individually significant. First, the exceptive reading is reinforcedby the subordinating that. Secondly, the sentence is reliably factive at its second clause; that is, itinvites (through the perfect tense of its verb) the inference that the content of the second clause isbeing asserted. In the presence of the second of these factors, the omission of that mightgenerally prompt a non-exceptive reading, though even in the absence of that an exceptive

reading, at least for an audience of any but recent literary experience, will be prompted by an

– 22 –

indefinite present tense. My informal surveys of introductory logic students find very few whoneed not struggle to understand the central example

61. It never rains but it pours

disjunctively.The puzzling character of the adversative coordinator is the product of the scope foreshorteningof the negative or modal sentence element. Certainly the effect is as in other similar

developments, that the connective loses its disjunctive reading in favour of a conjunctive one, butthe historical connection with the despatialized, outside reading of but is rather obscured than

lost. That that connection shapes the conjunctive use of but is, I think, undeniable. With a properly attuned theoretical language we can account for the puzzling adsentential character of

the new use. But a fine-grained account of how speech production adjusts to such new uses requires a detailed neuro-theoretical understanding that we simply have not got.

Inspection reveals a similar development in the case of for which, from an earlier ‘because’ meaning,

62. . . . the crew were beginning to get very much the worse for drink. (Dexter 1989, 53)

has evolved a later ‘ in spite of ’ reading

63. And yet she was alert, for all the vagueness of her manner. (P tter 1986, 149)o

But as a final example, I observe that English has a dualized if that seems to have come about bythis process of scope-evasion. The diathetic condition that rendered propositional if susceptibleof this kind of mutation seems to have been the difficulty in English of negation-placement in if-constructions, and possibly the obscurity of satisfaction conditions for conditionals, an obsurityinherited by their denials. In general, dualized if can be marked by even, but just as frequently itis marked only prosodically. The A if, we think of conveniently as the sufficiency if. The B if wecan label the insufficiency if. The two following examples illustrate them in that order. Contrast

64. If he wins the lottery, he’ ll be MISERABLE(Winning will make him miserable)

with

65. If he wins the LOTTERY, he’ ll be miserable(Winning won’ t cure his misery)

Even in their material representation, the two are distinct, the material representative of the latterbeing deductively stronger than that of the former. That is:

¬ ¬ − (α → β) | α → βPL

but

¬ ¬ /−α → β | (α → β).PL

The conjectured origin of this if is the misapprehended scope of a negation placed in the mainclause as if in

66. I wouldn’ t do that, if the QUEEN (herself ) asked me.(Her asking me would be insufficient)

– 23 –

a short-scope sufficiency if with long-scope negation (n’t) is read as a short-scope negation withlong-scope if. The satisfaction-conditions being kept constant, the if must be given an

insufficiency reading.The dualized, insufficiency if (sometimes marked as even if, sometimes only prosodically)

has, from a formal point of view, the appearance of a sort of hybrid. The reason seems to involvethe triggering phenomenon mentioned earlier. In the production of speech, the choice of

conjunctive connective, whether and or or is determined by habituation rather than the anticipations of interpreted manipulation. Since sufficiency if-clauses with or are effectively conjunctive, so are those of insufficiency if-clauses. But since English sufficiency conditionals

distribute conjunctively over a disjunctive if-clause, a negated conditional ought, at least by thestandards of logic, to be read as a disjunction. Nevertheless, insufficiency conditionals also

distribute conjunctively over disjunctive if-clauses. So, for example,

67. If the King OR the queen asked me I wouldn’ t do it

will be read as

68. If the K. asked I wouldn’ t, and if the Q. asked I wouldn’ t

but does not commit us to:

69. If the King AND the queen asked me I wouldn’ t do it

since though they might be insufficient severally, their requests might be jointly sufficient. Sodualized if is left-downward non-monotonic.

6 The Stages of Mutation

6.1 Genesis

In the case of mutation by scope-evasion the first stage in the production of a new connectivemeaning is the initiating scope misapprehension (by members of population B), typically

involving negative and modal sentence elements (in the speech of population A), with the resulting combination of approximately correct (or at least indetectably incorrect) apprehension

of satisfaction conditions on the one hand and undetected incorrect processing of syntax on theother, that forces an incorrect (or at least novel) apprehension of the use of the connective.

6.2 Incubation

The primary association intended by the label as used here is with the period during which a population of viruses establishes itself in a host organism, rather than with the hatching of a single organism from an egg. But there is a respect in which the process resembles the second: if

we regard the novel reading as a misconstrual, then it is a misconstrual that is protected fromcorrection by the practical overall synonymy of the proper and improper construals of the

sentence as a whole. The new construal is in this way sheltered by the old one, and converselydependent upon it, since there is no guarantee at this stage that the connective in the incorrectlyapprehended use is viable in environments outside those of the highly specific kind in which itwas engendered.

– 24 –

6.3 Autonomy

At this stage the newly engendered reading can be obtained for the connective even in the absence of a sentence element of the kind given a scope-foreshortened reading at an earlier stage.

At this stage, we find occurrences of conjunctive unless, or suppositional and in the absence ofnegation, but otherwise in roughly the same sentence position, as,

70. He shall be glad of men, and he can catch them (Dekker 1600, II. iii)

6.4 Migration

Among the early sites to which one would expect the connective in its new construal to migratefrom the environment that engendered it to sites normally occupied by the connectives with

which it has been newly construed as synonymous. In this stage, suppositional and migrates toother if positions, as:

71. F ith, and your foreman go, dame, you must take a journey to seek a new journeyman; if Roger remove,aFirk follows. (Ibid.)

In such a migration, the new reading is still protected, but now by the presence of positional andmodal cues which defeat a conjunctive and force a suppositional reading.

6.5 Ambiguity

When a meaning engendered by scope evasion is fully established, the re-introduction of the connective into a construction of the kind that engendered the new meaning will give rise to a

semantic ambiguity, either clause of which is expressible by either of the dual readings of theconnective.

6.6 Marking

In the fifth stage, the new meaning is disambiguated from the old by order or by the addition ofmarkers generalized from particular cases or types. At this stage we find the ‘ in spite of ’ for atthis stage marked by the addition of all, detached from content, and attached to the connective:

72. T him Zeus handed over the power, ‘ for all he was young and but a greedy infant’ (Guthrie 1935, 82)o

W find universal any and anticipative in case marked by just:e

73. I’ve never had any time for these women who go out and leave their children all day with just anyone.(Barnard 1980, 18)

74. There was a path up to the summit he felt sure, but it might be as well to keep off it, just in case themen were looking in that direction, expecting someone else. (Barnard 1977, 153)

7 The General Idea

I say nothing more in defence of the evolutionary approach to the study of connectives that I have been advocating. It is essentially an Aristotelian approach, which W.K.C Guthrie sums up

pretty well.

– 25 –

75. Since motion and change are the most characteristic marks of nature, it is precisely these that have to beunderstood and explained — not run away from. (1981, 102)

But having said that, I must confess that the investigation of the principles of linguistic changewould not be of such interest to me if it did not also dissolve puzzles about the present state ofthings. This, I think, this approach does accomplish: it explains both the fact and the details ofthe diversity of connective uses, of which I have here offered only a few examples. And wherefolk-semantical accounts are difficult to give as in the case of but it also explains the difficulty.

That of course speaks only to that aspect of the account that treats of the logicalization ofconnectives. It says nothing of that aspect of the theory with which I began, that is, its being, asfar as possible, a physical theory, rather than a semantical one. Since I seem to have made freewith semantical notions such as satisfaction and satisfaction-conditions and so on throughout theexposition, it will be as well to say something about that here. I have said that acts of speech arephysical interventions, and that they typically have what I have called inferential effects. It

should be added that, typically, acts are speech are interventions in situations in which many features of the environs have inferential effects, in which features have already had effects and in

which effects of expected change are are anticipated. It would, therefore, be equally correct tosay that acts of speech are typically operations on effects. That is they present dynamic

modifications of the effects of other occurrences, spoken, gestural, and non-linguistic. And it ispart of the picture that parts of acts of speech are dynamic alterations and adjustments of the

effects of other parts of the same acts of speech. Within that general viewpoint we are able tohypothesise the roles of connectives understood as discriminating distinct operations on effects.Here I mention, as an illustration, only one connective, conjunctive but.

Conjunctive but is subtractive with respect to inferential effects. The effect of the but-clause (the subtrahend clause) of ‘He got here, but he got here late’ is to cancel or nullify or

reserve some of the expected effects of what could be called the minuend clause. This explainsthe non-commutativity of such constructions, that is, why ‘He got here, but he got here late’ isnot intersubstitutable in conversation with ‘He got here late, but he got here.’ This last subtracts,by the reminder that he got here, from the effects of the utterance of ‘He got here late’ . Noticethat such constructions are not compositional as that term is usually understood. The effect of thesubtrahend is the subtraction of effects, but the effects to be subtracted are not determinable fromthe subtrahend clause independently of particularities of the minuend.

W rks Cited and Sources of Exampleso

Austen, Jane(1816) Emma. Boston, Mass.: Houghton Mifflin (Riverside Edition), 1957.(1818) Northanger Abbey. W re, Herts.: W rdsworth Classics, 1993a o

Barnard, Robert(1977) Death of an Old Goat. Harmondsworth: P nguin Editions, 1983.e(1980) Death in a Cold Climate. New Y rk: Dell Publishing, 1986.o

Berkeley, George(1713) Three Dialogues between Hylas and Philonous. In Smith and Green (1940).

– 26 –

Brooke, C. F. T cker and Nathaniel Burton P radiseu a(1933) English Drama 1580−1642. Boston: D.C. Heath and Company.

Cornwell, P tricia D.a(1992) All that Remains. New Y rk: A on Books, 1993.o v

Defoe, Daniel(1722) A Journal of the Plague Y ar. London: Dent Dutton (Everyman Edition), 1908.e

Dekker, Thomas(1600) The Shoemaker’s Holiday. In Brooke and P radise (1933).a

De Morgan, Augustus(1862) On the Syllogism: IV; and on the Logic of Relations. Transactions of the Cambridge

Philosophical Society X.

Dexter, Colin(1989) The W nch is Dead. London: MacMillan (P n Books), 1990.e a

Engel, Howard(1990) Dead and Buried. T ronto: P nguin.o e

F wler, H.Wo(1937) Modern English Usage. Oxford: Clarendon Press.

Gilbert, Michael(1976) The Night of the Twelfth. London: Arrow (Mysterious Press Books), 1988.

Grafton, Sue(1995) “L” is for Lawless. New Y rk: Henry Holt.o(1996) “M” is for Malice. Markham: Henry Holt.

Grice, P ula(1989) Studies in the W y of W rds. Cambridge, Massachusetts: Harvard University Press.a o

Guthrie, W. K. C.(1935) Orpheus and Greek Religion. Revised edition, New Y rk: W.W. Norton ando

Company, 1952.(1981) Aristotle: an Encounter. Cambridge: Cambridge University Press.

Hare, Cyril(1938) Death is No Sportsman. New Y rk: Harper P rennial, 1991.o e(1946) With a Bare Bodkin. New Y rk: Harper P rennial, 1991.o e

Jennings, R.E(1994) The Genealogy of Disjunction. New Y rk: Oxford University Press.o

Jespersen, Otto(1922) Language: Its Nature, Development and Origin. London: G. Allen and Unwin.

– 27 –

Klaeber, Frederick, Editor(1922) Beowulf and the Fight at Finnsburg. 3d Edition. Boston: D.C. Heath and Company.

Leonard, Elmore(1992) Rum Punch. New Y rk: Dell Publishing, 1993.o

Milne, A.A.(1922) The Red House Mystery. New Y rk: Dell Publishing 1980.o

P tter, Denniso(1986) Ticket to Ride. New Y rk: Random House (Vintage Books), 1987.o

Skeat, Rev. W lter W.a(1886) The Vision of William concerning Piers the Plowman in Three P rallel T xts,a e

T gether With Richard the Redeless by William Langland. 2 vols. Oxford.o

Smith, T. V., & Marjorie Grene(1940) From Descartes to Kant: readings in the Philosophy of the Renaissance and

Enlightenment. Chicago: University of Chicago Press.

Snow, C. P.(1974) In Their Wisdom. Harmondsworth: P nguin, 1977.e

Suppes, P tricka(1957) Introduction to Logic. Princeton: Princeton University Press.

Trollope, Anthony(1859) The Bertrams. Oxford: Oxford University Press (W rld’s Classics), 1991.o(1861) Framley P rsonage. Harmondsworth: P nguin, 1984.a e(1864) Can you forgive her? Harmondsworth: P nguin, 1972.e(1867) The Last Chronicle of Barset. Harmondsworth: P nguin, 1967.e(1871) Sir Harry Hotspur of Humblethwaite Harmondsworth: P nguin, 1993.e(1875) The W y W Live Now. Oxford: Oxford University Press (W rld’s Classics), 1982.a e o(1876) The Prime Minister. Oxford: Oxford University Press (W rld’s Classics), 1983.o(1882a) The Fixed P riod. Oxford: Oxford University Press (W rld’s Classics), 1993.e o(1882b) Kept in the Dark. Oxford: Oxford University Press (W rld’s Classics), 1992.o

V nn, Johne(1894) Symbolic Logic. 2d ed. Bronx, N.Y.: Chelsea Publishing Company, 1971. (First

published 1881).

W tson, James D.a(1965) Molecular Biology of the Gene. New Y rk: W.A. Benjamin Inc.o

Wheatley, Henry B., Editor(1893) The Diary of Samuel P pys. 2 vols. New Y rk: The Heritage Press, 1942.e o

Wingfield, R. D.(1995) Hard Frost. New Y rk: Bantam Books.o

– 28 –

Contents

1 The Puzzle About Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Where Semantics Defeats Us . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 The case of or . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 The case of but . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 The Shape of a Biological Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.1 The representation of meaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2 The picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3 Compositionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4 Evolutionary tendencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.1 Usative relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2 Schematization, spatial and temporal examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.3 Allotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5 Mutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185.1 Metanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.2 Scope Evasion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

6 The Stages of Mutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246.1 Genesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246.2 Incubation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246.3 Autonomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256.4 Migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256.5 Ambiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256.6 Marking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

7 The General Idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

ix