Truth (Princeton Foundations of Contemporary Philosophy) Read online

  While deflationists about truth may also be deflationists about reference, it must not be automatically assumed, just because some doctrine has come to be labeled “deflationism about X” in the literature, that deflationists about alethic notions will be committed to it. Deflationism about truth is subject to enough criticisms of its own, without saddling deflationists about truth with any and every doctrine to which the “deflationist” label has been applied. The label has become rather fashionable of late, so there are quite a few such doctrines, not all of which are even consistent with each other.

  Criticism of any one form of deflationism about truth is implicit in advocacy of any other, and we have already seen many issues about whether this or that version can account for this or that use of the truth predicate (to endorse or repudiate or query, to do so blindly or generally or fractionally, and in inflected form and transcendently and for placeholders). Deflationist sloganeering has provoked criticism going far beyond such issues, so that deflationism finds itself embattled on many fronts. But there is at least this much to be said for it: that its opponents are by no means agreed what is supposed to be wrong with it.

  CHAPTER FOUR

  Indeterminacy

  THE EQUIVALENCE PRINCIPLE (“Saying something is true is equivalent to just saying it”) has been less controversial than deflationism's other theses, but it has been challenged by examples of what we will call indeterminacy. These are cases where we have a question “Are things thus?” to which neither the affirmative nor the negative answer seems appropriate, and not just because of ignorance on our part. If the question “Are things thus?” cannot be answered “Yes” or “No,” then it seems the corresponding declarative “Things are thus” cannot be called “true” or “false,” and so it seems we have a counterexample to the bivalence principle, according to which every proposition is either true or false. And any threat to the bivalence principle is a threat to the equivalence principle.

  For if we were to assume (A) things are thus, then applying the equivalence principle, in the form of the rule of T-introduction, it would follow that (B) it is true that things are thus. But we are supposed to be dealing with a counterexample to bivalence, hence a case where (~B) it is not true that things are thus (and also not false). It follows that (~A) things are not thus (here using the rule of classical logic that allows us, having seen a conclusion B to follow from an assumption A, to infer the negation ~A of the latter given the negation ~B of the former). From this intermediate conclusion that things are not thus, it then follows by T-introduction that it is true that things are not thus, which is to say, that it is false that things are thus. But again we are supposed to be dealing with a case where it is not false that things are thus (and also not true). And so we have a contradiction.

  Thus it is that indeterminacy threatens the equivalence principle, a central thesis of deflationism, and so centrally threatens deflationism. This threat does not depend on any distinctively realist or antirealist assumptions. On the contrary, since the equivalence principle is at least a peripheral thesis of most forms of inflationism, indeterminacy at least peripherally threatens them, too (though inflationists, whose theories are generally more elaborate than deflationist theories, may claim to have more resources available for warding off such threats).

  In this chapter we will concentrate mainly on two alleged classes of examples, involving phenomena of presupposition and vagueness, on each of which there is a vast literature in linguistics and philosophy of language. We first briefly describe the two phenomena, and then enumerate various conceivable lines of response to the problems they raise. Finally we examine a purported third type of case, involving a purported special kind of relativity.

  4.1 PRESUPPOSITION

  The fallacy of many questions was illustrated in antiquity by the example “Have you stopped beating your father?” This question is said to have been addressed by one Alexinus to one Menedemus, son of Cleisthenes, who refused to give a yes-or-no answer. It really should be two questions, “Did you ever beat your father? If so, have you stopped?” where if the answer to the first is negative, the second does not arise. Either answer, yes or no, to the original question “Have you stopped?” seems to involve an admission of father-beating, and thus to be inappropriate. Eubulides, to whom the pseudomenos (liar) is attributed, is also credited with another paradox, the keratines (horned one), turning on this phenomenon: What you have not lost, you have; you have not lost horns; therefore, you have (cuckold's) horns.

  Modern linguistics and philosophy of language discuss the same phenomenon under the rubric “presupposition.” Thus one says that

  (1) The phlogiston has been removed from the air under the bell jar.

  presupposes that there was phlogiston in the air under the bell jar to be removed, and hence that there is such stuff as phlogiston. Since, contrary to eighteenth-century chemical opinion, there is not—what early chemists described as the presence of phlogiston modern chemists would describe as the absence of oxygen, and vice versa—we have a case of presupposition failure.

  Being presupposed by a sentence is supposed to differ from being entailed by it, or implied by its meaning, by the fact that the negation of a sentence is supposed to have the same presuppositions as the original, as is the corresponding interrogative. By contrast, a conclusion is never entailed both by an hypothesis and by its negation except in the case where the conclusion is logically valid or analytic. “Phlogiston exists” assuredly is not logically valid or analytic, but it is said to be presupposed both by (1) and by its negation, and by the mere question “Has the phlogiston been removed from the air under the bell jar?” That is why a negative may seem as inappropriate as an affirmative in answer to the interrogative, giving an example of indeterminacy.

  4.2 VAGUENESS

  A stock example of vague predicates is provided by color words. On a simplified model of language-learning, we learn a word like “red” by being given certain paradigms, or samples of red things, and certain foils, or samples of things that are not red but orange or brown or purple or pink, plus certain principles for projecting beyond such examples. On this model, we may be left with certain borderline cases.

  Suppose, for instance, a large number of color chips are placed in a hopper, one is drawn at random but kept covered, and players may bet on whether it is red or not, after which it will be revealed. Then it may happen that after some have guessed “Yes, it is red” and others “No, it is not red,” the chosen chip is uncovered and turns out to be exactly halfway between the most orangish of the red paradigms and the most reddish of the orange foils. In this case it may seem that the only appropriate thing to do is to cancel all bets.

  If one takes the relevant projection principle to be that anything intermediate in color between two red things counts as red, and anything intermediate in color between two nonred things counts as nonred, then the case of the problem chip seems to be underdetermined, and an example of a truth-value gap, something neither true nor false.

  If instead one takes the relevant projection principle to be that anything very similar in color to a red thing counts as red, and anything very similar in color to a nonred thing counts as nonred, then the case of the problem chip seems to be overdetermined, and an example of a truth-value glut, something both true and false. For a paradigmatically red and a paradigmatically orange chip can be connected by a series of intermediates each scarcely (if at all) distinguishable from the next. Numbering the chips from zero (pure red) to a thousand (pure orange), we seem able to argue: Chip #0 is red, so chip #1 is red, so chip #2 is red, and so on, until we reach the conclusion that our problem chip #500 is red; and inversely that chip #1000 is nonred, hence chip #999 is nonred, hence chip #998 is nonred, and so on until the chosen chip #500 is nonred. This puzzle is a version of a pair of paradoxes attributed to the ubiquitous Eubulides. According to the sorites (heap) paradox, since adding one grain of sand won't turn a nonheap to a heap, adding a million one by one won't d
o so either. According to the phalakros (bald one) paradox, since plucking one hair won't turn a nonbald man bald, neither will plucking a million one at a time.

  The phenomenon of vagueness is not limited to “red” and “heap” and “bald,” but is all-pervasive. Frege sometimes wrote as if he took this to show that natural languages are defective, and should ideally be replaced by some perfectly precise artificial language. But actually the vagueness of natural language is more virtue than vice, since if we were forced to say only what could be said perfectly precisely—to describe colors by exact numerical wavelengths, for example—we would hardly be able to say anything at all. The vagueness of ordinary discourse is inseparable from its utility. It does, however, pose problems about what to say in borderline cases, of which the threat to the equivalence principle is only one.

  4.3 DENIAL, DISQUALIFICATION, DEVIANCE

  Denial. We turn next to consideration of possible defenses against the threat posed by borderline cases, and the similar threat posed by presupposition failure. One defense would be simply to deny that “You have stopped” and “Chip #500 is red” or other sentences like them provide examples neither true nor false. This would require denying the reality of the linguistic phenomena—failed presupposition and borderline cases—supposedly illustrated by the examples.

  One might claim, for instance, that so-called presuppositions are simply a subclass of entailments. On such a view, “Have you stopped?” is not a case where neither a yes nor a no answer is appropriate. The answer to the question is a plain “No,” because having stopped entails having started, and you never started. Such denialism is implausible to the degree that the evidence leading linguists and philosophers of language to posit a category of presupposition is convincing.

  The question “Is chip #500 red?” may remain one we are undeniably unable to answer, but it has been claimed that this is just because of ignorance on our part, that in such a case it still is either true or false to call the chip “red,” even though nothing about our usage of “red” enables us to know which. One version of this epistemicist view holds that somewhere between the most orangish paradigm and the most reddish foil there is a “natural joint,” visible perhaps to God but not to us, and that though our usage does not track this joint exactly, owing to the joint's naturalness a kind of “magnetism” attracts our word “red” to it, so that without any help from us the meaning of the word aligns perfectly with the joint, thereby making chip #500 count as red or count as nonred, depending on which side of the joint it lies on. This view may seem fantastic, but that does not distinguish it from many other views in the vagueness literature.

  Disqualification. Another defense would be to claim that though the sentences “You have stopped” and “Chip #500 is red” are neither true nor false, which is to say, neither express true propositions nor express false propositions, that is not because they express propositions that are neither true nor false, but simply because they do not express propositions at all. That would disqualify them as counterexamples to bivalence or for that matter any other thesis about propositions.

  Now some sentences indeed do not express propositions. Interrogatives and imperatives are uncontroversial examples. Even sententialists who avoid the notion of proposition need something like a distinction between proposition-expressing sentences and others, and have introduced a bit of jargon, “truth-apt,” to mark this distinction. The defense against the threat to the equivalence principle being contemplated is the easy one of just claiming that the problem sentences are like interrogatives and imperatives in not being proposition-expressing or truth-apt. This line is very often taken, independently of any concern about debates over the nature of truth, with failed presuppositions, and is sometimes taken with borderline cases as well. However, it faces a serious objection.

  It is widely held that people's actions are to be explained in terms of their beliefs (and their desires), and also widely held that what one believes when one believes is a proposition. Given these widely held views, if someone when asked “Why did you act as you did?” replies with evident sincerity, “Because things were thus and so, or so I believed,” then there is a presumption that the person did believe that things were thus and so, and that there is a proposition to the effect that things are thus and so for the person to believe. Citation in explanation of action thus provides a presumptive sufficient condition for the existence of a proposition, and our examples seem to pass this test. Asked why he put the unconscious mouse under the bell jar to revive it, an eighteenth-century chemist might well have answered, “Because I was assured the air under it had been dephlogisticated.” Asked why she staked her money on red in the color-chips game, a player might well say, “Because there'd been a run of red, and I had a hunch this one would turn out to be red, too.”

  Deviance. Another defense would be to concede that there are counterexamples to bivalence, but deny that these give counterexamples to the equivalence principle. Since the principle of bivalence follows from the equivalence principle given classical logic, to take this line one would have to reject classical logic. Some deviant logic would then presumably be needed, but a number of them have been worked out in the literature on indeterminacy.

  A proposal called the Kleene strong trivalent logic was developed to deal with cases of presupposition failure. This logic tells how the status of a compound as true or false or neither is supposed to be determined systematically by the status of its components. For example, it counts a disjunction as true iff either disjunct is true, and false iff both disjuncts are false, and neither true nor false (a status variously called neuter or indeterminate or gappy) in all other cases. This logic of truth-value gaps has a mirror-image logic of truth-value gluts.

  To deal with vagueness, some have proposed fuzzy logics, according to which, contrary to all the theories of truth considered in this book, there are infinitely many truth values or degrees of truth, from zero or pure falsehood to one or pure truth, through every real (or surreal) number between; “Chip #500 is red” would presumably be a half-truth.

  A different proposal called the Van Fraassen supervaluation logic was also developed to deal with vagueness. The thought behind it is that the very circumstance that there is nothing to make “red” the right thing to call the problem chip is enough to make “orange” a right thing to call it, and vice versa. One needn't adopt the attitude that everything not obligatory is forbidden. There may be no natural line between red and orange, but there are several places where it would be permissible to draw an artificial line, and “precisify” the concept of red. Paradigm chips among others are determinately red, or red for every permissible precisification, while foil chips among others are determinately nonred, or nonred for every permissible precisification, but Chip #500 and others like it are neither determinately red nor determinately nonred. Something is counted supervaluationally true (or false) iff it is true (respectively false) for any permissible precisification. Thus “Such-and-such a chip is red” is true (or false) iff the chip in question is determinately red (or determinately nonred), but is neither true nor false in borderline cases, which count as red on some precisfications and nonred on others.

  Before the reader becomes too enthusiastic about nonclassical logics, it must be noted that the logics we have been discussing were not originally motivated by a desire to save the equivalence principle, and whatever their other merits, as originally designed they fail to save the equivalence principle simply because as originally designed they do not say anything at all about sentences involving the truth predicate. But we will meet some of these logics again when we turn later to consideration of “solutions” to the alethic paradoxes.

  4.4 DOUBLESPEAK, DEPENDENCY, DEFEATISM

  Doublespeak. Another defense might begin by positing that the word “not” has, besides its ordinary meaning in expressing logical negation, another, special meaning expressing rejection of the saying of something rather than negation of the thing said. It could then
be claimed that though one is tempted to say of such an example as “You have stopped” or “Chip #500 is red” that it is not true and also not false, perhaps the two occurrences of “not” here are expressing the special meaning and not the ordinary one. In that case, by saying the examples are “not” true and “not” false, one is not really contradicting the principle of bivalence, which would require one to say “not true and not false” in the ordinary, not the special sense.

  This suggestion looks like a clear violation of the methodological maxim known as Occam's Eraser (“Senses are not to be multiplied beyond necessity”), an analogue of the better-known Occam's Razor (“Entities are not to be multiplied beyond necessity”). Positing an ambiguity in the word “not” looks like proposing a linguistic thesis merely to get out of a philosophical difficulty.

  But it turns out that linguists have, for their own purely linguistic reasons, been moved to posit a “metalinguistic” negation distinct from ordinary negation, whose use indeed only commits us to its being in some way inappropriate to say something, and not to the logical negation of the thing said. The distinction is supposed to be illustrated by such pairs as the following:

  (2a) In that country, they don't eat tomatoes, they suspect they are poisonous.

  (2b) In this country, we don't eat tomahtoes, we eat tomaytoes.

  (3a) He's not intelligent, his I.Q. is 80.

  (3b) She's not intelligent, she's a world-class genius.