The Meanings of Connectives
R. E. Jennings
Simon 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 at
least one medium-sized mammal to raise itself to something approaching erect stature, shuffle to
the 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 than
physical or more specifically biological ones. Seen in the light of my opening, admittedly banal
observation, language can be understood as a remarkably versatile switch or relay: an exercise of
it is a low-energy interaction that triggers similar or larger expenditures of energy at a spatial or
temporal 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 language
engineers 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-awindow», 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 single
occasion. There is however one feature genuinely conventional and ordinary linguistic causality
share, 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 in
a desire that a window should be opened, and so on. Nor is it to deny that the student would have
given some such explanation of his having opened the window. We may say therefore that that
explanation gives us an understanding of what has happened in the case at least to the extent that
we already have an understanding of beliefs, intentions, and desires. The problem, if it is one, is
that although every competent speaker of a language might confidently wield its vocabulary of
belief, 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 in
my 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 of
it 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. Yet the English of the nineteenth century is markedly different from that of
the twentieth or the twenty-first, and both are just recognizably prefigured in the English of
Chaucer. Facts of ancestral uses and facts of transmission would be of interest to the semanticist
only if they yielded a more informative account than semantics can of a sufficiently broad range
of quite specific kinds of linguistic behaviour and their effects. It would seem at first blush that
the level of detail required for such an explanation would be unattainable, and the facts of the
case 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 theory
might be all we can have. If in addition its offerings satisfy our cravings for understanding within
some range of linguistic behaviours, it may be as much as we want. As to the question whether
the accessible data are reliable grounds for such a theory, that must await the outcome. In any
case, we would be doing no more than following the ordinary path of scientific investigation if
we 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, no
satisfactory semantic theory has been given for the vocabulary of folk-psychological explanation.
To engage in such explanation requires nothing beyond an ordinary conversational understanding
of the vocabulary. That, I take it, is what makes it a folk-theory: that one is in possession of it in
virtue of being, in the linguistic sense, one of the folk. We exercise it well or badly as we attend
to 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 with
lacklustre ease, some with clumsy and painful imprecision. Much the same can be said of the
natural 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 more
difficult than for others; for many its rudiments are never reliably mastered. There is however
this difference: that the fundamentals of the theory, at least as it applies to an artificially narrow
band 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 connective
vocabulary that logic studies can, when suitable mathematical methods are applied, be made to
give 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 presents
dangers to our understanding of natural language. An immersion in the traditions of logic and
formal semantics and a just appreciation of their successes seems to have inspired in some recent
writers what Mr Greenspan would no doubt call an irrationally exuberant investment of effort in
applying 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. Fortunately for the analyst, the
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. Venn (1894) says of the
connection between and and or
This must rank among the many perplexities and intricacies of popular speech, but it does
not seem at variance with the statement that regarded as mere class groupings, independent
of 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 in
the twentieth century as the advent of the truth-table re-presented the central question as that of
the connection between the or of English on the one hand and 1110 and 0110 disjunctions on the
other. The clarity and simplicity of truth-tabular semantics mainly accounts for the simplicity and
unclarity 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
on the page.1) 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 truthconditions 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 that
in the general case _∨(α
_ 1, . . . , αn) will be true when an odd number of its component sentences
are true, and false otherwise. Thus _∨(α
_ 1, α2, α3, α4, α5) is true when either exactly one or exactly
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. We may tolerate P ∨ Q
∨ 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 comatose
is not syntactically ambiguous. We do not regard it as an abbreviation of Either either he’s dead
or 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. For examples, see Jennings 1994 pp. 70—71.
–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 uses
of or, perhaps five percent. Most of the other uses to which English or is put both in literature
and in common speech are semantically quite remote from disjunction. So it may be entered as
even more dramatic evidence of my thesis that textbook authors regularly draw upon nondisjunction-like uses of or to illustrate the differences between what they take falsely to be the
main divisions of its uses, giving non-disjunctive examples to illustrate a non-existent contrast
between 1110 and 0110 uses. Thus, for example, Patrick Suppes (1957)2:
When people use ‘or’ in the exclusive sense to combine two sentences they are asserting that
one of the sentences is true and the other is false. This usage is often made explicit by
adding the phrase ‘but not both’. Thus a father tells his child, ‘You may go to the movies or
you 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 movies
this 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 not
both can be applied to non-disjunction-like sentences. We can consistently say such things as
‘You may go to the movies; you may go to the circus; you may not do both’.
Now 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 inattention
to detail. The whole point of the observations is to underline a fact about natural language: that a
conversational knowledge of its vocabulary does not require or provide, and therefore does not
guarantee the existence of a semantic theory. There is no reason to suppose that the authors of
English 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 of
the rest of us, does not confer an explicit understanding. And they are Socratically worse off than
their 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 has
been that since their introduction the theorists feel no need to struggle at all.
Even Paul Grice, singular as are his contributions to our understanding of conversational
uses 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 the
uses of or: for this we rely upon a kind of background savvy about conversational exchanges, an
acquaintaince, not necessarily conscious, with conversational conventions. As Grice sees the
matter, a proper understanding of the role of these conventions should forestall suggestions that
the natural language correspondents of logical connective vocabulary sometimes have meanings
other 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 of
information 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 fact
of 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. For a more extensive sampling see Jennings 1994.
–5–
Now a for-instance is not an argument. That there is no such strong meaning of or does not
establish 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 are
good examples of such uses, and Suppes’ illustration ‘You may go to the movies or you may go
to 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 that
Franz 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 the
circus visit, in favour of a hearing according to which a disjunction of assents is reported, but
according to which it is not reported which assent is actually given. In fact we must weigh the
oddness of forcing disjunctivity by the cancellation clause against the naturalness of fixing the
conjunctive reading by the clause ‘so you decide which’.
We can set beside this the fact that phrases of the same sort as ‘but I don’t know which’
can 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 to
cancel 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 a
day-old sandwich. Or it can be recovered from your hard drive by someone with the know-how. The
Vancouver Sun 1997-02-15
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 one
doesn’t know which is neither here nor there. If there is an argument capable of showing that
cancellability proves that these are really ordinary disjunctive uses of or, Grice has not presented
it.
There is evidence, in any case, that ought to make us suspicious of any view that would
give the truth-conditions of disjunction as the central historical explanation of the uses of or in
English,— even of those uses that superficially accord with the truth-tabular account. In the first
place there are points of continuity between uses of or in which the equivalence to conjunction
seems 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. ‘You may ϕ or you may ψ’ is such a conjunction. It is its ut
nunc 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 not
guaranteed that once you do one or the other, you will still be permitted to do the other. It is a
characteristic shared with some if-clause occurrences of or. Consider ‘If Elizabeth or Margaret
offers a suggestion I’ll be surprised.’ It will be taken to be the claim that if Elizabeth offers a
suggestion, I’ll be surprised and if Margaret offers a suggestion, I’ll be surprised, but it will not
warrant the further inference that having been surprised by a suggestion from Margaret I’ll be
surprised again by one from Elizabeth, and that in spite of the logical truth that if the conjunction
is 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. To be
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 the
case to make us so regard its natural counterpart, and much about the behaviour of or in other
environments 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 thenclauses.
3.
I will fight you here in London, or, if you are afraid of that, I will go over to France, or to America, if
that will suit you better. (Trollope 1864, 748)
A second linguistic fact that ought to cast suspicion upon the doctrine of the centrality of
truth-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 a
coalescence of two distinct Old English words ‘o„er’ meaning ‘other’ or ‘second’ (as in ‘every
other day’) and ‘o„„e’, which we usually translate as ‘or’, but which seems to have a range of
uses similar to that of or in modern English. More generally, it seems to be a fact of linguistic
evolution 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 was
perhaps 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-illative
uses 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 I
woke up’, or that moreover, if either is the more primitive, the non-logical use is. No one denies
that the so of ‘Fred is happy, so I’m happy’ is different from the so of ‘Fred is happy; so Fred is a
conscious being.’ Parallel remarks are warranted by the varieties of uses of therefore, because,
for and so on. Their logical uses are derivative, in ways that are not immediately clear, from their
non-logical uses. A semantic theory of the former, like a semantic theory of the latter, will not
depend upon truth-conditions, but will rather outline a practice; an explanatory theory will tell us
how 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, with
the 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 than
any other connective vocabulary of natural language as the reading of ∨. For if we set that habit
aside, consider what parallel universal claims would be grounded by a similar fit. The sole
–7–
premise vis-a` -vis the vocabulary is that there is a use of it that truth-conditionally matches the
table. The conclusion is that there are no uses of the vocabulary that do not. By this reasoning we
could 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 ‘He
avoids me but he wants to borrow money’ on one reading has exactly the truth-conditions of the
table. In fact the case of but shows remarkable parallels with that of or since each has distinct
uses that are approximately in the relationship of duality. The disjunctive use of but, like that of
or is relatively rare; it more commonly found in conjunctive constructions, but as in the case of
or, the whole story of its conjunctive uses cannot be given by a truth-tabular account. Even when
we 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 contexts
in which it is the right connective to use. Dictionaries resort to providing approximate synonyms
that 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. Paedagogical grammars classify it as adversative. Even speakers of the most exquisitely
cultivated sensitivity, such as H.W. Fowler have a little difficulty ‘. . . the mere presence of the
opposed facts is not enough to justify but; the sentences must be so expressed that the total effect
of one is opposed to that of the other . . .’ (but s.v.) That opposition is not the feature is evident
from such examples as ‘He got here, but he got here late’, and any explanation must be such as to
explain 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. But
such an immersion does not afford us an articulable account of what we are doing when we use
it. 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. For purposes of outline it wouldn’t matter where in
the physical world those effect-types were located, but as a convenient first approximation, they
can 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 accommodate
the 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 one
such realization agrees with that of the producer of the string, and the other does not. That is to
say, 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 nothing
about the fine structure of that language or the details of the effects. Nor do I intend any guesses
as 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 a
theory at the level of population biology, and although even at this level it applies the language
of 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 are
not members of it. Of course the earliest linguistic species are temporally compressed, as are the
earliest 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 of
the connectives of English, the language of evolutionary biology is a good fit: if meanings are
identified 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 more
than a schematic account. They are not premises of an argument for the account, but they are part
of the picture of things upon which the schema to some extent relies. The first remark is a global
one: this representation, though it is constructed for detailed and temporally local explanation, is
also promising as a theoretical framework for couching an account of how human or pre-human
language began. It is a fair assumption that linguistic inferential effects have ancestors that are
non-linguistic inferential effects and even earlier ancestors that are non-inferential effects, such
as 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 structured
string 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. I
register 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 of
them, and if we descend to the level of the nuclei of cells, there is remarkably little difference in
nuclear 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 uniformly
so 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. We do not write
longer 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 for
the 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, pitch
contour and stress. Prosodic control of syntax apprehension also enforces limitations of sentence
length. 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 weakened
version of the compositionality thesis will be true of natural languages. But some weak version
will survive. On whatever account we give of meaning, the meaning of a sentence has something
to 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 called
love?’ and ‘What is this thing called, Love?’ Sometimes, prosodic clues having been missed, the
determining 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 I
have 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. We might read
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 the
significance 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 speech
of others. This may be so, but the fact is that in the course of a day’s compositions, we neither
produce 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, or
specious anything essentially to do with spuriousness? That notional meanings undergo changes
is hardly news, though the details of these changes probably deserve more philosophical study
and 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, in
most 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 butan
meaning outside, if probably from a coalescence of Old English gif (if ) itself a descendent from
the 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 or
has 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 the
meaning of something, then we will conclude from this that at least all naturally occurring logical
meanings 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 might
have given rise to the other.
As a topic of study, the descent of connective vocabulary from its physical forbears might
be 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 auxiliaries
in 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 about
our languages that we did not know. The promise that, if it gets matters approximately right, its
theoretical 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 theory
of 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:
{<x1, . . . , xn> | ϕx1. . . xn}.
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 putative
established meaning, but that of the establishing of it. For this we must broaden our purview to
include what I shall call the usative relation, «ϕ» of a predicate, ϕ. «ϕ» includes the set of ntuples <x1, . . . , xn> of items of which it has ever been claimed that ϕx1 . . . xn. Statistically it
would make little difference if it it also included the set of n-tuples of items <x1 , . . . , xn> of
which ϕx1 . . . xn has been denied. And it also ought to include the set of n-tuples of items of
which ϕx1 . . . xn has been enjoined, and so on. Our purposes do not require a precise or even
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 be
said, the record would not be a relation, but a hyper-relation, since it would contain n-tuples and
m-tuples for m =/ n. In particular, it would include a set of quadruples, each of which comprises
a speaker, a hearer, a lamp post, and a piece of information. Neither will it be uniformly spatial
or temporal, but will include a set of triples each of which contains two alternative conditions
and 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, correct
uses, and incomprehensible ones.
A usative relation «ϕ» is the union of a temporally ordered set of relations {«ϕ»t | t ∈ T}.
Each «ϕ»t can be defined by «ϕ»t = ∪{«ϕ»i}. Hence, if t ≤ t′, then «ϕ»t (SS) «ϕ»t′. This
i t
temporal monotonicity is a potent instrument of semantic innovation, since, in general, the more
the n-tuples in the relation, the less the n-tuples have in common, and more particularly the more
varied 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 these
developments. No doubt explicitly metaphorical, non-spatial extensions of physical vocabulary
do occur. But we ought to resist the temptation to lay very much at all of the generalizing work
of schematization to their influence. The gradual wearing away of the capacity, independently of
other cues, sometimes even with them, to occasion particularistic relational inferences can for the
most 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 valid
formulae, simply because the broader the class of models, the more opportunities there are for
any particular formula to be falsified. The larger the usative relation (or hyperrelation) the fwer
the particularistic inferential effects supported.
What schematization amounts to in particular cases depends upon the character of the
ancestral vocabulary. Vocabulary that supports inferences as to spatial relationships will acquire
despatialized uses in which no such inferences are supported; temporal vocabulary will acquire
de-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 of
spatial 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 original
family business and others in related branches of trade. But at an early stage of its evolutionary
development, schematized, in these cases, despatialized meanings must have emerged. Thus, for
example, 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 incidental
to 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 meaning
physically 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 is
that outside of the much constricted geographical regions in which but retains its spatial uses, the
residual 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 uses
such as that of
18.
It never rains but it pours.
Were this the only logicalized use of but the story could perhaps stop with that explanation. But,
as we have seen, and as this sentence bears witness, it is not. It is relatively easy to see how but
may have become logicalized as a disjunctive connective; the account of its conjunctive logical
uses must await a later discussion.
More familiar than the surviving Scottish but, which, had its original spelling survived to
justify its sense, would be spelled by out (as ben would be spelled by in), is the orthographically
more 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 certain
quasi-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. (Trollope
1882a, 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. Yet even without can do duty as a sentential
connective:
24.
She could not write the letter without some word of tenderness should go from her to him (Trollope
1882b, 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 dualization
has yielded an and/or split, the without-meanings, are roughly distinguishable as and not and if
not. 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.
We haven’t formally started to review it, but with it hitting the news . . . hopefully we’ll be getting
together next week and bring our findings to Caucus on Sept. 19 (Coquitlam, Port Coquitlam, Port
Moody Now, 1994,09,03)
and, like without, both conjunctive and conditional uses
29.
With frugality we’ll get by (if)
30.
We’ll get by with plenty to spare (and)
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 calls
him 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 had
of 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 lost
her 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 and
muffins—sweetly so if the cream be plentiful and the muffins soft with butter; but still, as a man and a
pastor, 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 later
stage, without pretending that there is no more to be said of stages in between. In fact a complete
account must mention the process by which certain origiunally multivalent vocabulary acquires
trivialized, 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, as
denoting 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 here
no 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 neartriviality of the example lies in the semantic idleness of the over. Of course, one might argue that
the 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. For some instances of
the 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 is
that of a short-scope existential quantifier. Now for some α’s, in particular, for those in which
there 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-expressed
thesis 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 sort
given. 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 simplicity
overall.
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 the
occurrences of any in the Authorized Version, are non-allotropic, requiring something akin to an
existential reading.
The allotropy hypothesis, as applied to the evolution of meanings, is the hypothesis that
certain meanings of certain connective vocabulary are the product of a development that depends
upon allotropy in the sense given. In the generation of such meanings there is a stage in which
identical 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 mature
populations of an older one. For convenience I shall refer to new meanings allotropically
nurtured in this way as succubinal meanings and distinguish them by overlining. This suggests
that the older, fostering meaning should be called incubinal and marked by underlining. We re the
account to be applied directly to any, and were the case as simple as an examination of the
Authorized Version might suggest, it would regard the uses that tempt or require representation
by 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 –
----- In fact if some such developments account for the existential/universal dual
succubinal, ---any.
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 allotropic
and interrogative environments earlier than the eight century, but in its normal universal role in
comparisons 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 new
meaning. 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 no
generally accessible evidence that a new meaning is emerging. It is only when the new meaning
is 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 new
meaning must migrate to non-allotropic environments in which commonly recognized
satisfaction-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 normally
take any (as stranger than any fiction. We will return to the matter later, but the point deserves a
little 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 with
surrounding connectives as though still bearing their formerly incubinal meanings. This to the
confounding 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: either
the error is syntactically negligible, as in 39, or the error is not. If the error is not syntactically
negligible, then we might suppose that one of two conditions must obtain: either the error is
satisfaction-conditionally negligible or it is not. We need not set the standards of negligibility
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 satisfactionconditionally 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 what
happens 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 is
understood as the non-otiose over of the construction fallen over (as distinct from fallen in, fallen
through, 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 for
another amino acid is called a missense mutation. On the other hand, the change to a codon
that does not correspond to any amino acid is called a nonsense mutation. The existence of
extensive degeneracy means that most mutations are likely to cause missense rather than
nonsense. Missense mutations produce proteins changed in only one location, and so the
altered proteins which they produce frequently possess some of the biological activity of the
original proteins. The abnormal hemoglobins are the result of missense mutations. (Watson
1965, 374)
Mistakes in reading the genetic code also occur in living cells. These mistakes underlie the
phenomenon of suppressor genes. Their existence was for many years very puzzling and
seemingly 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 often
involve insertions or deletions of single nucleotides. These shift the reading frame so that all
the codons following the insertion (or deletion) are completely misread. (379)
Now some of the nonsense mutations produced by such ‘reading frame’ errors of English have
been 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 Henry
Tilney (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 little
worth 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. To promise
faithfully to write makes some sort of pleonastic sense; To promise faithfully to write makes
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 through
such an error persists as an idiom only within the very restricted environment that gave rise to the
error, and does not propagate through migration to others. In this case the reason is perhaps that
faithfully 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 the
verb think were to acquire a distinct succubinal meaning through the construal of
46.
I don’t think she’ll come
47.
I think she won’t come
as
-----------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 such
development has taken place. And we might suppose a priori that any such development would
be unlikely. One reason might be that positive verbs of attitude are too well established in their
range 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 approximately
the force of fear or suspect as in
50.
There I found as I doubted Mr. Pembleton with my wife (Pepys 1663-5-26)
51.
. . . she could not forbear telling me how she had been used by them and her mayde, Ashwell, in the
country, 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 Testament. And the preferred construction doubt whether is itself evidence that a
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 that
stronger positive verbs of attitude so robustly resist; for the standard use approximates the use
that one would predict as likely to arise, through mutation, from negated negation-raising uses of
the Pepysian doubt. A strong verb’s modus tollens is perhaps a weaker verb’s modus ponens.
5.1 Metanalysis
Jespersen (1922) introduced the term metanalysis as a label for a phenomenon in the process of
word-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 the
ending 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, and
the 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-conditions
of sentences in which the discrepancy occurs. And of course, as the difference is undetected, the
metanalytic population has a chance to become established.3
5.2 Scope Evasion
The term metanalysis, transposed to the level of syntactic structure, would serve equally well to
label 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 important
difference is a dimensional one. For Jespersen the significance of metanalysis lies in the
introduction of a new verbal expression of an existing meaning: in the course of the development
umpire came to mean what numpire had meant. For us, its significance lies in the introduction of
a 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 to
have a meaning where previously it had none. But in all but one of the cases we consider, the
outcome of the metanalysis is that a word that previously had n meanings comes to have n + 1. I
begin with the exception.
Unless is a striking example of a connective for which the original meaning, which had a
conjunctive 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 α
with the condition that β unmet, that is α without β, that is, α and not β.4 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 and
the introduction of negators such as It’s not the case that, with long scope intonationally made
explicit.
It is plausible to suppose that the conditional and of middle and Jacobean English, the and
that, 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 . . ., the
and 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 Passus VII. 288-290)
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 the
holding of an election. The draw up of the formulaic announcement has been heard as drop, with the result that it is now standard usage to
speak of the Prime Minister as in course of dropping the writ or as having finally dropped the writ. The absurdity of the construction is
evidently 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 medical
attention and she’ll die without betraying her friends.
– 21 –
54.
I do not think that you should go and she stay behind.
55.
Could he have come out and we didn’t see him? (Wingfield 1995, 261)
56.
Why am I a redhead and you have dark hair? (@discovery.ca 1995-12-26)
or
or
where the structure of the clause following the and is such as to permit a foreshortening of the
scope of the negation or the modal could or interrogative why with substitution of if for and, a
transformation 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 the
scope of the negation is foreshortened and the sentence taken to imply absolutely that the subject
had not been long upon the scout, then the sentence as a whole can have approximately the same
conversational effect if it is taken, in virtue of its second clause, to imply that the subject heard a
noise, 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 that
can be made non-trivially subject to exceptive clauses, but it must force a non-exceptive reading
for 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 scope
made 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, the
exceptive clause limiting the range of some multivalent magnitude or manner of engagement of
some 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 a
sort of partner of mine (Trollope 1876 i, 236)
Here a number of elements are individually significant. First, the exceptive reading is reinforced
by the subordinating that. Secondly, the sentence is reliably factive at its second clause; that is, it
invites (through the perfect tense of its verb) the inference that the content of the second clause is
being asserted. In the presence of the second of these factors, the omission of that might
generally 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 who
need 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 foreshortening
of 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, but
the 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. (Potter 1986, 149)
But as a final example, I observe that English has a dualized if that seems to have come about by
this process of scope-evasion. The diathetic condition that rendered propositional if susceptible
of this kind of mutation seems to have been the difficulty in English of negation-placement in ifconstructions, and possibly the obscurity of satisfaction conditions for conditionals, an obsurity
inherited by their denials. In general, dualized if can be marked by even, but just as frequently it
is marked only prosodically. The A if, we think of conveniently as the sufficiency if. The B if we
can 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 latter
being deductively stronger than that of the former. That is:
¬ (α → ¬ β) |−PL α → β
but
α → β |−/PL ¬ (α → ¬ β).
The conjectured origin of this if is the misapprehended scope of a negation placed in the main
clause 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 with
long-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 involve
the 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 the
standards 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. So
dualized 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 connective
meaning 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 the
other, 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 from
correction 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 conversely
dependent upon it, since there is no guarantee at this stage that the connective in the incorrectly
apprehended use is viable in environments outside those of the highly specific kind in which it
was 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 of
negation, 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 migrate
from 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 to
other if positions, as:
71.
Faith, and your foreman go, dame, you must take a journey to seek a new journeyman; if Roger remove,
Firk follows. (Ibid.)
In such a migration, the new reading is still protected, but now by the presence of positional and
modal 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 the
connective.
6.6 Marking
In the fifth stage, the new meaning is disambiguated from the old by order or by the addition of
markers generalized from particular cases or types. At this stage we find the ‘in spite of ’ for at
this stage marked by the addition of all, detached from content, and attached to the connective:
72.
To him Zeus handed over the power, ‘for all he was young and but a greedy infant’ (Guthrie 1935, 82)
We find universal any and anticipative in case marked by just:
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 the
men 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 be
understood and explained — not run away from. (1981, 102)
But having said that, I must confess that the investigation of the principles of linguistic change
would not be of such interest to me if it did not also dissolve puzzles about the present state of
things. This, I think, this approach does accomplish: it explains both the fact and the details of
the diversity of connective uses, of which I have here offered only a few examples. And where
folk-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 of
connectives. It says nothing of that aspect of the theory with which I began, that is, its being, as
far as possible, a physical theory, rather than a semantical one. Since I seem to have made free
with semantical notions such as satisfaction and satisfaction-conditions and so on throughout the
exposition, it will be as well to say something about that here. I have said that acts of speech are
physical 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 to
say 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 is
part 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 to
hypothesise 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 butclause (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 explains
the non-commutativity of such constructions, that is, why ‘He got here, but he got here late’ is
not 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’. Notice
that such constructions are not compositional as that term is usually understood. The effect of the
subtrahend is the subtraction of effects, but the effects to be subtracted are not determinable from
the subtrahend clause independently of particularities of the minuend.
Works Cited and Sources of Examples
Austen, Jane
(1816) Emma. Boston, Mass.: Houghton Mifflin (Riverside Edition), 1957.
(1818) Northanger Abbey. Ware, Herts.: Wordsworth Classics, 1993
Barnard, Robert
(1977) Death of an Old Goat. Harmondsworth: Penguin Editions, 1983.
(1980) Death in a Cold Climate. New York: Dell Publishing, 1986.
Berkeley, George
(1713) Three Dialogues between Hylas and Philonous. In Smith and Green (1940).
– 26 –
Brooke, C. F. Tucker and Nathaniel Burton Paradise
(1933) English Drama 1580−1642. Boston: D.C. Heath and Company.
Cornwell, Patricia D.
(1992) All that Remains. New York: Avon Books, 1993.
Defoe, Daniel
(1722) A Journal of the Plague Year. London: Dent Dutton (Everyman Edition), 1908.
Dekker, Thomas
(1600) The Shoemaker’s Holiday. In Brooke and Paradise (1933).
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 Wench is Dead. London: MacMillan (Pan Books), 1990.
Engel, Howard
(1990) Dead and Buried. Toronto: Penguin.
Fowler, H.W
(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 York: Henry Holt.
(1996) “M” is for Malice. Markham: Henry Holt.
Grice, Paul
(1989) Studies in the Way of Words. Cambridge, Massachusetts: Harvard University Press.
Guthrie, W. K. C.
(1935) Orpheus and Greek Religion. Revised edition, New York: W.W. Norton and
Company, 1952.
(1981) Aristotle: an Encounter. Cambridge: Cambridge University Press.
Hare, Cyril
(1938) Death is No Sportsman. New York: Harper Perennial, 1991.
(1946) With a Bare Bodkin. New York: Harper Perennial, 1991.
Jennings, R.E
(1994) The Genealogy of Disjunction. New York: Oxford University Press.
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 York: Dell Publishing, 1993.
Milne, A.A.
(1922) The Red House Mystery. New York: Dell Publishing 1980.
Potter, Dennis
(1986) Ticket to Ride. New York: Random House (Vintage Books), 1987.
Skeat, Rev. Walter W.
(1886) The Vision of William concerning Piers the Plowman in Three Parallel Texts,
Together With Richard the Redeless by William Langland. 2 vols. Oxford.
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: Penguin, 1977.
Suppes, Patrick
(1957) Introduction to Logic. Princeton: Princeton University Press.
Trollope, Anthony
(1859) The Bertrams. Oxford: Oxford University Press (World’s Classics), 1991.
(1861) Framley Parsonage. Harmondsworth: Penguin, 1984.
(1864) Can you forgive her? Harmondsworth: Penguin, 1972.
(1867) The Last Chronicle of Barset. Harmondsworth: Penguin, 1967.
(1871) Sir Harry Hotspur of Humblethwaite Harmondsworth: Penguin, 1993.
(1875) The Way We Live Now. Oxford: Oxford University Press (World’s Classics), 1982.
(1876) The Prime Minister. Oxford: Oxford University Press (World’s Classics), 1983.
(1882a) The Fixed Period. Oxford: Oxford University Press (World’s Classics), 1993.
(1882b) Kept in the Dark. Oxford: Oxford University Press (World’s Classics), 1992.
Venn, John
(1894) Symbolic Logic. 2d ed. Bronx, N.Y.: Chelsea Publishing Company, 1971. (First
published 1881).
Watson, James D.
(1965) Molecular Biology of the Gene. New York: W.A. Benjamin Inc.
Wheatley, Henry B., Editor
(1893) The Diary of Samuel Pepys. 2 vols. New York: The Heritage Press, 1942.
Wingfield, R. D.
(1995) Hard Frost. New York: Bantam Books.
– 28 –
Contents
1 The Puzzle About Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Where Semantics Defeats Us . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 The case of or . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 The case of but . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 The Shape of a Biological Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1 The representation of meaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 The picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3 Compositionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4 Evolutionary tendencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.1 Usative relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.2 Schematization, spatial and temporal examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.3 Allotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5 Mutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.1 Metanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.2 Scope Evasion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6 The Stages of Mutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
6.1 Genesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
6.2 Incubation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
6.3 Autonomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6.4 Migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6.5 Ambiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6.6 Marking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
7 The General Idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
ix