Philosophy of Logic

Second Edition

Willard Van Orman Quine, W. V. Quine

• Publisher: Harvard University Press
• Year: 1986
• Print ISBN: 9780674665637
• eBook ISBN: 9780674254565
• Topic: Philosophie
• Subtopic: Logik in der Philosophie

With his customary incisiveness, W. V. Quine presents logic as the product of two factors, truth and grammar—but argues against the doctrine that the logical truths are true because of grammar or language. Rather, in presenting a general theory of grammar and discussing the boundaries and possible extensions of logic, Quine argues that logic is not a mere matter of words.

MEANING AND TRUTH

1

Objection to propositions

When someone speaks truly, what makes his statement true? We tend to feel that there are two factors: meaning and fact. A German utters a declarative sentence: ‘Der Schnee ist weiss’ In so doing he speaks truly, thanks to the happy concurrence of two circumstances: his sentence means that snow is white, and in point of fact snow is white. If meanings had been different, if ‘weiss’ had meant green, then in uttering what he did he would not have spoken truly. If the facts had been different, if snow had been red, then again he would not have spoken truly.

What I have just said has a reassuring air of platitude about it, and at the same time it shows disturbing signs of philosophical extravagance. The German utters his declarative sentence; also there is this white snow all around; so far so good. But must we go on and appeal also to intangible intervening elements, a meaning and a fact? The meaning of the sentence is that snow is white, and the fact of the matter is that snow is white. The meaning of the sentence and the fact of the matter here are apparently identical, or at any rate they have the same name: that snow is white. And it is apparently because of this identity, or homonymy, that the German may be said to have spoken truly. His meaning matches the fact.

This has the ring of a correspondence theory of truth, but as a theory it is a hollow mockery. The correspondence holds only between two intangibles that we have invoked as intervening elements between the German sentence and the white snow.

Someone may protest that I am being too severely literalistic about this seeming invocation of intervening elements. He may protest that when we speak of meaning as a factor in the truth of what the German said, we are merely saying, somewhat figuratively, what nobody can deny; namely, that if, for instance, the word ‘weiss’ were applied in German to green things instead of white ones, then what the German said about snow would have been false. He may protest likewise that the seeming reference to a fact, as something over and above the snow and its color, is only a manner of speaking.

Very well; as long as we can view matters thus, I have no complaint. But there has long been a strong trend in the philosophy of logic that cannot be thus excused. It is on meanings of sentences, rather than on facts, that this trend has offended most. Meanings of sentences are exalted as abstract entities in their own right, under the name of propositions. These, not the sentences themselves, are seen as the things that are true or false. These are the things also that stand in the logical relation of implication. These are the things also that are known or believed or disbelieved and are found obvious or surprising.

Philosophers’ tolerance toward propositions has been encouraged partly by ambiguity in the term ‘proposition’. The term often is used simply for the sentences themselves, declarative sentences; and then some writers who do use the term for meanings of sentences are careless about the distinction between sentences and their meanings. In inveighing against propositions in ensuing pages, I shall of course be inveighing against them always in the sense of sentence meanings.

Some philosophers, commendably diffident about positing propositions in this bold sense, have taken refuge in the word ‘statement’. The opening question of this chapter illustrates this evasive use. My inveterate use of ‘statement’ in earlier books does not; I there used the word merely to refer to declarative sentences, and said so. Later I gave up the word in the face of the growing tendency at Oxford to use the word for acts that we perform in uttering declarative sentences. Now by appealing to statements in such a sense, instead of to propositions, certainly no clarity is gained. I shall say no more about statements, but will go on about propositions.

Once a philosopher, whether through inattention to ambiguity or simply through an excess of hospitality, has admitted propositions to his ontology, he invariably proceeds to view propositions rather than sentences as the things that are true and false. He feels he thereby gains directness, saving a step. Thus let us recall the German. He spoke truly, we saw, inasmuch as (1) ‘Der Schnee ist weiss’ means that the snow is white and (2) snow is white. Now our propositionalist saves step (1). The proposition, that snow is white, is true simply inasmuch as (2) snow is white. The propositionalist bypasses differences between languages; also differences of formulation within a language.

My objection to recognizing propositions does not arise primarily from philosophical parsimony—from a desire to dream of no more things in heaven and earth than need be. Nor does it arise, more specifically, from particularism—from a disapproval of intangible or abstract entities. My objection is more urgent. If there were propositions, they would induce a certain relation of synonymy or equivalence between sentences themselves: those sentences would be equivalent that expressed the same proposition. Now my objection is going to be that the appropriate equivalence relation makes no objective sense at the level of sentences. This, if I succeed in making it plain, should spike the hypothesis of propositions.

Propositions as information

It is commonplace to speak of sentences as alike or unlike in meaning. This is such everyday, unphilosophical usage that it is apt to seem clearer than it really is. In tact it is vague, and the force of it varies excessively with the special needs of the moment. Thus suppose we are reporting a man’s remark in indirect quotation. We are supposed to supply a sentence that is like his in meaning. In such a case we may be counted guilty of distorting his meaning when we so much as substitute a derogatory word for a neutral word having the same reference. Our substitution misrepresents his attitude and, therewith, his meaning. Yet on another occasion, where the interest is in relaying objective information without regard to attitudes, our substitution of the derogatory word for the neutral one will not be counted as distorting the man’s meaning. Similar shifting of standards of likeness of meaning is evident in literary translation, according as our interest is in the poetic qualities of the passage or in the objective information conveyed.

The kind of likeness of meaning that is relevant to our present concerns, namely sameness of proposition, is the second of the alternatives mentioned in each of these examples. It is sameness of objective information, without regard to attitudes or to poetic qualities. If the notion of objective information were itself acceptably clear, there would be no quarrel with propositions.

The notion of information is indeed clear enough, nowadays, when properly relativized. It is central to the theory of communication. It makes sense relative to one or another preassigned matrix of alternatives—one or another checklist. You have to say in advance what features are going to count. Thus consider the familiar halftone method of photographic illustration. There is a screen, say six by six inches, containing a square array of regularly spaced positions, say a hundred to the inch in rows and columns. A halftone picture is completely determined by settling which of these 360,000 points are black. Relative to this screen as the matrix of alternatives, information consists in saying which places are black. Two paintings give the same information, relative to this matrix, when they determine the same points as black. Differences in color are, so to speak, purely stylistic relative to this matrix; they convey no information. The case is similar even for differences in shape or position, when these are too slight to be registered in the dots of the halftone. Relative to this matrix, furthermore, a verbal specification of the dots gives the same information as did the painting. (This is the principle of transmitting pictures by telegraph.) And of course two verbal accounts can give the information in very different phrasing; one of them might give the information by saying which positions are white instead of black.

Sameness of information thus stands forth clear against a preassigned matrix of black and white alternatives. But a trouble with trying to equate sentences in real life, in respect of the information they convey, is that no matrix of alternatives is given; we do not know what to count. There is no evident rule for separating the information from stylistic or other immaterial features of the sentences. The question when to say that two sentences mean the same proposition is consequently not adequately answered by alluding to sameness of objective information. This only rephrases the problem.

Ideally, physics does offer a matrix of alternatives and therewith an absolute concept of objective information. Two sentences agree in objective information, and so express the same proposition, when every cosmic distribution of microphysical states over space-time that would make either sentence true would make the other true as well. Each such distribution may be called a possible world, and then two sentences mean the same proposition when they are true in all the same possible worlds. The truths of pure mathematics and logic stand at an extreme, true in all possible worlds. The class of all possible worlds in which a sentence comes out true is, we might say, the sentence’s objective information—indeed, its proposition. But still this idea affords us no general way of equating sentences in real life. In many cases we can clearly see that the sentences would hold under all the same distributions of microphysical states, and in many cases we can clearly see that they would not; but in the case of sentences about purposes, motives, beliefs, or aesthetic values we would scarcely know where to begin.

A different way of reckoning objective information is suggested by the empiricist tradition in epistemology. Say what difference the truth or falsity of a sentence would make to possible experience, and you have said all there is to say about the meaning of the sentence; such, in substantially the words of C. S. Peirce, is the verification theory of meaning. This theory can be seen still as identifying the proposition or meaning of a sentence with the information conveyed; but the matrix of alternatives to be used in defining information is now the totality of possible distinctions and combinations of sensory input. Some epistemologists would catalog these alternatives by introspection of sense data. Others, more naturalistically inclined, would look to neural stimulation; the organism’s triggered nerve endings are the analogues of the halftone’s black dots. Either way, however, a doctrine of propositions as empirical meanings runs into trouble. The trouble comes, as we shall now see, in trying to distribute the sensory evidence over separate sentences.

Diffuseness of empirical meaning

Suppose an experiment has yielded a result contrary to a theory currently held in some natural science. The theory comprises a whole bundle of conjoint hypotheses, or is resoluble into such a bundle. The most that the experiment shows is that at least one of those hypotheses is false; it does not show which. It is only the theory as a whole, and not any one of the hypotheses, that admits of evidence or counter-evidence in observation and experiment.

And how wide is a theory? No part of science is quite isolated from the rest. Parts as disparate as you please may be expected to share laws of logic and arithmetic, anyway, and to share various common-sense generalities about bodies in motion. Legalistically, one could claim that evidence counts always for or against the total system, however loose-knit, of science. Evidence against the system is not evidence against any one sentence rather than another, but can be acted on rather by any of various adjustments.

An important exception suggests itself: surely an observation is evidence for the sentence that reports that very observation, and against the sentence that predicted the contrary. Our legalist can stand his ground even here, pointing out that in an extreme case, where beliefs that have been supported overwhelmingly from time immemorial are suddenly challenged by a single contrary observation, the observation will be dismissed as illusion. What is more important, however, is that usually observation sentences are indeed individually responsive to observation. This is what distinguishes observation sentences from theoretical sentences. It is only through the responsiveness of observation sentences individually to observation, and through the connections in turn of theoretical sentences to observation sentences, that a scientific theory admits of evidence at all.

Why certain sentences are thus individually responsive to observations becomes evident when we think about how we learn language. Many expressions, including most of our earliest, are learned ostensively; they are learned in the situation that they describe, or in the presence of the things that they describe. They are conditioned, in short, to observations; and to publicly shared observations, since both teacher and learner have to see the appropriateness of the occasion. Now if an expression is learned in this way by everyone, everyone will tend uniformly to apply it in the presence of the same stimulations. This uniformity affords, indeed, a behavioral criterion of what to count as an observation sentence. It is because of this uniformity, also, that scientists who are checking one another’s evidence gravitate to observation sentences as a point where concurrence is assured.

We learn further expressions contextually in ways that generate a fabric of sentences, complexly interconnected. The connections are such as to incline us to affirm or deny some of these sentences when inclined to affirm or deny others. These are the connections through which a theory of nature imbibes its empirical substance from the observation sentences. They are also the connections whereby, in an extremity, our theory of nature may tempt us to ignore or disavow an observation, though it would be regrettable to yield often to this temptation.

The hopelessness of distributing empirical information generally over separate sentences, or even over fairly large bundles of sentences, is in some sense widely recognized, if only by implication. For, look at it this way. It will be widely agreed that our theory of nature is under-determined by our data; and not only by the observations we actually have made and will make, but even by all the unobserved events that are of an observable kind. Briefly, our theory of nature is under-determined by all “possible” observations. This means that there can be a set H of hypotheses, and an alternative set H’ incompatible with H, and it can happen that when our total theory T is changed to the extent of putting H’ for H in it, the resulting theory T’ still fits all possible observations just as well as T did. Evidently then H and H’ convey the same empirical information, as far as empirical information can be apportioned to H and H’ at all; but still they are incompatible. This reflection should scotch any general notion of propositions as empirical meanings of sentences.

Why then is the notion so stubborn? Partly because the separate sentences of science and common sense do in practice seem after all to carry their separate empirical meanings. This is misleading, and explicable. Thus suppose that from a combined dozen of our theoretical beliefs a scientist derives a prediction in molecular biology, and the prediction fails. He is apt to scrutinize for possible revision only the half dozen beliefs that belonged to molecular biology rather than tamper with the more general half dozen having to do with logic and arithmetic and the gross behavior of bodies. This is a reasonable strategy—a maxim of minimum mutilation. But an effect of it is that the portion of theory to which the discovered failure of prediction is relevant seems narrower than it otherwise might.

Probably, moreover, he will not even confront the six beliefs from molecular biology impartially with the failure of prediction; he will concentrate on one of the six, which was more suspect than the res...

Table of contents

• Cover
• Title
• Copyright
• Preface
• Contents
• 1: Meaning and Truth
• 2: Grammar
• 3: Truth
• 4: Logical Truth
• 5: The Scope of Logic
• 6: Deviant Logics
• 7: The Ground of Logical Truth
• For Further Reading
• Index