- Robust Theories and Deflationary Theories
- Losing the Issues
- The Flight from Robust Theories
- Sentences to the Rescue
- Back to Propositions?
- The Liar
1. ROBUST THEORIES AND DEFLATIONARY THEORIES
- Philosophy deals in abstractions. It is concerned with highly general categories, such as mind, matter, consciousness, causation1, time, values, and so on. The limit of abstraction is reached with categories that apply equally to everything. The paradigm is existence, which applies to everything, of whichever kind, that exists. Truth, by contrast, characterizes only some of the things we might say or believe, for to every truth about how things are, there corresponds the falsehood asserting that they are otherwise. Suppose we call the things we might say or believe, propositions (there are some choices about that, but for the moment we ignore them). Then truth is similarly abstract in that it can apply to propositions of any kind, on any subject matter. We can talk of mind, matter, numbers, time, or of what was, or will be, or might have been, and we can talk of mundane things like snow and penguins. And on all these matters, we can say things that are true, or, of course, things that are not true. So what is truth, if propositions from any sphere of interest can equally share it? What do all true propositions share, that is lacked by all false ones?
- It might seem easy enough to give an answer. Aristotle said ‘To say of what is that it is, or of what is not that it is not, is true2.' This is perhaps the first expression of the correspondence theory of truth: True propositions tell it like it is, or in other words for a proposition to be true is for it to correspond with the facts. It is important to realize that this is a platitude that nobody denies. But the difficulties start when we try to flesh out the notions involved. What kind of ‘thing' is a fact: for example, are there general facts, negative facts, hypothetical facts and if so, what are they made of? Then, what kind of correspondence is in question? If we think, for instance, of the correspondence between a portrait and a subject we have to imagine that true propositions correctly ‘picture' the world. This is not easy to understand, except metaphorically. And for that matter what kind of thing is a proposition? Some have taken propositions to be creatures of the mind, for only thinkers think things that are true or false. But what then is this complex in the mind that represents facts outside it? Others take propositions to be abstract structures, but then we would need to know both how the structure corresponds with facts, and also how the mind gets into a judgemental relationship to the complex. Still others hope to dispense with propositions in favour of sentences, and that will occupy us later.
- Many of the philosophers represented in this collection are pessimistic about our ability to answer these questions. They think that the answers traditionally given generate insuperable problems. Some think that people trying to describe a correspondence relation make a category mistake, by turning facts into complexes of things, which they are not. We describe this issue in more detail later. Some think that the theory requires a separation between the mind, as the domain of propositions and judgements, and the world, as the domain of facts. And they think this separation generates an intolerable gulf, eventually leading to scepticism about our ability to know true things about the world. Again, we say a little about this later. Such philosophers turn their pessimism in one of two directions. Either they try to find something else than correspondence with the facts to discover what truth is. This was the direction taken by the earliest philosophers represented here, who suggest notions such as membership in some favoured coherent set of propositions (Bradley, Joachim, giving rise to the coherence theory of truth) or even utility (James, giving rise to the pragmatic theory of truth). Or, they reject the question, denying that there is in fact any real project of discovering what truth is. This is a far more popular move among the later opponents of correspondence theory. We start by saying a little about the second deflationary approach.
- We talked of truth along with existence as reaching the heights of abstraction. When we approach these heights, the air becomes very thin indeed. Perhaps it becomes too thin to support philosophical reflection at all. If we asked ‘what is existence, in general?' many philosophers might suppose that we have gone too far, so that while we might reasonably address the question of what the world must be like for stones or minds or penguins to exist, no entirely general question about ‘what it is to exist' can be posed or addressed. At best, we might say something about the utility of an entirely general word, ‘exists', ready to combine with particular noun phrases and perhaps other terms, so that we can frame intelligible thoughts about particular propositions: tame tigers exist, Santa Claus does not exist. And if this seems the right way to go here, it might also commend itself in the case of truth. Perhaps there is nothing in general to say about truth in general, although there will be things to say about particular truths, such as that they are important, or trivial, or interesting, or boring, or that some are more basic than others, or that they do or do not depend upon particular features of the world.
- This deflationary view denies that there is an issue of ‘the nature of truth in general'. After that, the rejection of any entirely abstract questions about the nature of truth can be phrased in different ways. It has been expressed by saying that truth is not a ‘real' property, or a ‘robust' or metaphysically interesting property, or even that ‘is true' is not a predicate at all3. At their most flamboyant, deflationists have maintained that the concept of truth is ‘redundant', or that talk in terms of truth is purely ‘formal', so that the forms of words in which we say that something is true merely represent ‘devices' with various logical purposes. The details of how to formulate a general deflationism matter, and some of the papers collected here take issue with others over just such details. But all such views agree that a general inquiry into the nature of truth as an abstract property is wrongheaded.
- This collection is designed to take the reader into an appreciation of the problem of truth by looking mainly at the strengths, and weaknesses, of deflationism. The issue is amongst the most baffling and the most important in contemporary philosophy. For deflationism is both disconcerting and surprising. It is disconcerting, because if truth disappears as a general topic, then too much else may seem to disappear with it. Our awareness of the world is at least largely an awareness that various things are true: that we are in a room of some shape and size, surrounded by people like ourselves and so on. An awareness of our situation is just an awareness that various things are so, and that others are not. It is in these judgements of what is true that our minds meet the world. So if there is nothing to say about truth in general, this may seem to imply that there is nothing to say about the relationship between mind and world in general. And if that topic is denied to us, then much of philosophy seems to disappear with it. Can we really hope to say nothing about how it is that we represent the world to ourselves, or how it was that we became creatures capable of judgement and belief? Conversely, if these topics are indeed vivid and real, why should they not be described as inquiries that, by throwing light on the nature of our representation of reality, thereby throw light on the nature of truth?
2. LOSING THE ISSUES
- The disconcerting effects of deflationism can also be illustrated if we consider what might at first sight look like an ascending ladder of things to say about a statement. Suppose we take a mathematical or moral judgement p, that virtually everyone will wish to assert, for example, that two plus two equals four, or that genocide is always wicked. The ladder takes us from p, to ‘it is true that p', to ‘it is a fact that it is true that p', to ‘it is really a fact that it is true that p', and, if we like, to such flourishes as ‘it corresponds to the eternal mathematical (or normative) order governing the universe that p'. Deflationism is then the claim that the view from the top of this ladder, or from any point on it, is just the same as the view from the bottom. The substantive content of what is said remains just the same: p (a deflationist can admit that rhetorical force is added or subtracted as we go up and down the ladder, but that is all). Other people may be inclined to ascend this ladder believing that by the end they are making substantial claims about the original proposition. The last, for instance, might be thought to be a deep, philosophical, Platonic, remark about the status of the original claim. But for the deflationist it is at best a flowery way of asserting that two plus two equals four, or that genocide is always wicked, which is where we started4 . So we lose the metatheoretical standpoint, or place from which debates about the status of the original assertion might have been conducted. This is certainly surprising, and it may be regarded as a fatal loss. Or, instead it may be taken as a desirable liberation from old ghosts and metaphors. In this way the issue of deflationism is intimately connected with the question of whether we can achieve a standpoint from which to mount substantive metatheoretical claims. Indeed, in Chapter XVIII, Rorty argues that by dismantling any substantive conception of truth we enable ourselves to transcend almost the entire western philosophical tradition. If we become pessimistic about our chances of achieving such a standpoint, perhaps thinking of them as stepping outside our own skins, or standing on our own shoulders, then a deflationist approach to truth will be a natural ally.
- Philosophically, it is an extremely powerful ally. Rorty is certainly correct that many debates in different areas are typically framed in terms of truth. Consider the example of ethics. People ask whether ethical commitments are capable of truth, or really true, or literally true, or true in the same sense as other commitments. These questions seem important. They are motivated by the sense that ethical ‘facts' are especially elusive, or difficult to place in the order of nature. Some philosophers want to deny that there are such facts at all, preferring to see ethics as having a non-descriptive, non-representational function. Deflationism may threaten to undermine such positions, since they seem to require a substantial, robust, conception of truth in some areas by contrast with which ethics is supposed to be different5.
- Again, people ask whether to accept a scientific theory and to assert its theses falls short of accepting or asserting them as true6. Some philosophers think scientists accept theories only as instruments for prediction, not as literal truths about the contents or structures of nature. But if we cannot defend a robust or substantive notion of truth, this contrast as well begins to disappear. There would be little or no contrast between putting forward a theory, and putting it forward as true. So the space for instrumentalism seems to become squeezed out. If the deflationist thinks there remains an issue here, then he will need to frame it in some quite different way.
- Given deflationism, then, there is no question, for instance, whether ethical commitments are strictly or literally true, or true in the same sense as empirical judgements. The word ‘true' has the same, deflated, use in every area, so ethical commitments will be true in just the same sense as any others. Similarly in the scientific case there seems to remain no gap between asserting p and asserting p to be true.
- Another metaphysical inquiry that is threatened is that of looking for the ‘truth-makers' for different categories of proposition. The idea is that there must be something in virtue of which various propositions are true, and the metaphysician can search for what it is. Some of this may survive deflationism, but the theory strongly suggests a trivial answer: the truth-maker for the judgement that p is, trivially, that p. According to the deflationist, it will be characteristic of bad old correspondence views to want a more substantial answer than that, dissecting the fact that p into ‘components', for example. The point is that if we want philosophical debates, we can no longer look to truth to help us to frame them.
- Deflationism also threatens to rub the bloom off another flower. Truth is a grand notion, an ideal. It is important. It is the target or aim of our investigations. It forms a ‘norm' for assertion and belief, as is argued by Wright in Chapter7 XIII. Deflationism seems to sweep all that away. That can be alarming. Does it leave us with no conception of a difference between truth and falsehood at all? This sounds like postmodernism, or scepticism about whether there is any real distinction between the true and the false. But here, at least, deflationists can defend themselves. They do not have to be sceptics or postmodernists, for they can and should give their own account of what it is to think of truth as a goal, target, or norm. To say that truth is an ideal or a norm merely means this: you tell me about some claim in question, p, and I will tell you under what circumstances it would be right to believe it or assert it. It will be right to believe or assert p if, and only if, p. The point here is that this is a ‘schema' which will fill out differently for different propositions. It is good or right to believe that cows fly if and only if cows fly; good to believe that cows swim if and only if cows swim. So, says the deflationist, there is no single norm or ideal in play. There is just a piecemeal construction of when it is right to assert or believe the individual things, one by one, that we might be interested in (this kind of deflationist reasoning is resisted by Wright in Chapter XIII).
- But why sympathize with deflationism in the first place? It might seem to be quite easy to say substantive, interesting things about truth in general. Although the air is thin, we can just about breathe in it. True propositions correspond with the facts. As we have said, everyone will agree to this. And it sounds to be a robust proposal, enabling us to see truth as a relational property. Truth takes its place amongst other such two-term relations: the correspondence of the image in the mirror with the scene in front of the mirror, or the correspondence between a map and a landscape. The correspondence theory associates truth in belief or assertion with such things as a true likeness. Common sense surely applauds such a proposal, so what can be wrong with it?
3. THE FLIGHT FROM ROBUST THEORIES
- Everyone can agree that a statement is true if it corresponds with the facts. For ‘corresponds with the facts' may be just an elaborate synonym for true. The question is whether it unpacks the notion, giving us a genuine account of it as a relation between elements of two different categories: propositions on the one hand, facts on the other. We have already met one reason for doubt. Thinking this way, it may appear, involves thinking of two distinct standpoints. There is the standpoint we occupy when we judge that p. Then in addition there is the standpoint we occupy when we step back, and judge that the judgement that p indeed bears the right relation to the fact that p. But then it is reasonable to urge that there are not two distinct standpoints here, but only one (see, especially, Frege in Chapter V). There are indeed mental processes that we can call ‘standing back': becoming cautious about p, checking one more time whether p, and so on. But these are all processes of reflecting and checking whether p. None of them introduce a separate topic, and yet the correspondence theory seems to demand that there is both a separate topic and a separate standpoint from which it can be judged. It is here that we see the illusory nature of the idea that we can step outside our own skins or stand on our own shoulders. Another way of putting the point is that in examples like the mirror and the map we have access both to the original and the image, so there can be a genuine empirical investigation of their correspondence or fit. In the case of judgement, we apparently do not. To ‘come upon the facts' is already to judge that things are thus-and-so.
- It may seem natural to retort that nothing very extraordinary is called for here. Surely there is the everyday process of taking a judgement, say, that there are cows in the garden, and checking whether it corresponds with the facts—that is, verifying it. Indeed there is, but, insists the deflationist, this is just the process of verifying whether there are cows in the garden, best done by looking round the garden for cows. There is again only one standpoint, that of the investigator of the garden. There is not a distinct standpoint of having both the judgement and the fact before one, and essaying a comparison of them. Apprehending a fact is just the same things is judging that something is so. Facts are not things (not even bunches of things such as aggregates or structures) that can be seen to be present even if we do not know what to make of them. In the present volume this is stressed in different ways by Bradley, Ramsey, Strawson, and Wright. A good way to see this is to think of logically complex facts. It may be a fact that if you had touched the plug you would have got a shock, or a fact that Bishop Stubbs did not die on the scaffold, or a fact that either there were more than eighteen or fewer than seven people in the room. Facts have logical complexity: not surprisingly, they have exactly as much complexity as the propositions we choose to assert. And the real world—the world of dated, particular, events and things in specific spatial and temporal orderings just does not seem able to contain anything of this kind of complexity: negative, or disjunctive, or counterfactual situations, for example8.
- The difficulty, then, lies not in just saying that a judgement is true if it corresponds with the facts, for that is harmless. It consists in trying to pump the platitude up into a substantial theory involving a real two-place relation between judgements and facts. To many philosophers this is a hopeless enterprise, requiring that we treat both propositions and facts as ‘things', which they are not.
- Dissatisfaction with the correspondence view became orthodox both amongst philosophers influenced by Kant and Hegel, and by American pragmatists, around the beginning of the twentieth century. But their dissatisfaction typically took the form of offering different substantial theories, rather than deflationism. We start the collection with selections from this period, in which substantive alternative proposals about truth are made, by Joachim, Bradley, and James, and we include an example of a rebuttal of one such proposal (that of James), by Russell.
- Russell rightly notices that James intertwines what is supposed to be a relatively pure proposal about the nature of truth, with rather more diffuse, but attractive, remarks about scientific method, empiricism, and so on. And one highly significant feature of this literature is the way in which the theory of truth is entangled with the theory of the proposition, or the theory of judgement, or in other words, of what it is to have a belief in the first place. So, in Chapter I, H. H. Joachim illustrates one way in which the idea of judgement has itself been thought problematical. Joachim was what later became known as a holist. He believed that individual propositions or judgements are logicians' abstractions from a much larger organized ‘significant whole'. So to approach the problem of truth by concentrating upon the individual judgement is to begin in the wrong place. The ‘proposition' is already a heavily theoretical notion. Joachim insists that there is no such thing as understanding or knowing one proposition in isolation from others. Rather, we have to start with a systematic structure, a science, or what Joachim calls a system ‘not of truths but of truth'.
- Joachim's idea anticipates a later doctrine of Quine, who wrote that ‘the Unit of empirical significance is the whole of science9' . It can be appreciated if we reflect that there could be no state of understanding and knowing just one proposition of natural science (say ‘electrons have negative charge') or one proposition from history ('Napoleon was an emperor'). To come to understand these things requires an education in a great deal of physics or a great deal of history. It requires coming to appreciate the inferences that would support them, and the consequences that they have (this is at least one of the things Bradley means by saying that ‘much of given fact is inferential10'). It requires coming to see the world in different terms. Such an education is not the brick-by-brick accumulation of individual self-standing pieces of knowledge, a thing which Joachim calls ‘a mutilated shred torn from the living whole in which alone it possessed its significance11'. In such increases of understanding, as Wittgenstein put it, ‘light dawns gradually over the whole12'.
- What has this to do with truth? It suggests that the virtue of an individual proposition, of being true, cannot be understood except derivatively, from the virtue of a whole system or organized body of knowledge. For Joachim, as for the later Wittgenstein, it also suggests that it is wrong to consider even the whole system outside the context of the changing human practices that issue in its expression. But what is the virtue of whole systems, if it is not to consist in their containing numbers of individual truths? This is one problem facing the main historical competitor to the correspondence theory, namely the ‘coherence' theory of truth. According to this a statement is true if it is a member of some suitable coherent set of statements. But the question is, which set13? Joachim, like Bradley, is far from clear. He talks of a ‘self-fulfilling' process, as if there were some kind of internal motor ensuring that our increasingly coherent sets of beliefs are somehow on a progressive curve. This suggests uncomfortable overtones of Absolute Idealism, in which Thought progresses in accordance with a complex score underwritten by Reason, and few philosophers can sympathize much with that.
- Bradley indeed writes as if he thinks that an ideal system does not so much cohere together, as somehow become identical with the world14. The idea is this. The correspondence view gives us a picture of propositions or judgements on the one hand and facts on the other, entering into some mysterious relationship. Truth is ‘seriously dyadic15'.But this implies an impassable gulf between mind, the domain of propositions, and the world, the domain of facts. The way to avoid this gulf, for Bradley, is to see the mind as itself containing facts. There is not a question of bringing mental entities into some favoured relation with worldly entities, and then comparing them. To avoid this we must make the mind and the world literally identical. Again, it is very unclear what this identity theory can mean, although some recent philosophers express sympathy with it16.
- The writings of this period remind us that it is living, active, subjects that have thoughts and beliefs and are capable of judgement at all. To present the issue by starting with static mind contemplating static propositions, abstracted away from all the context of surrounding practices and judgements necessary to give them any sense in the first place, is certainly to court the danger of missing the main course. So these thoughts of Joachim and Bradley are designed to make us uneasy with a simplistic conception of ‘the proposition' and ‘the fact' as two elements that, as of right, exist—and that then may or may not correspond with each other. Each writer suggests that some highly complex abstraction is responsible for us being happy with talk of ‘the proposition (judgement, etc.) that p'. And it is the very abstraction that is responsible for us being happy with correlated talk of the fact that p. The correspondence theory seems inevitable only because, in Strawson's words, ‘What could fit more perfectly the fact that it is raining than the statement that it is raining? Of course statements and facts fit. They were made for each other17'. Bradley and Joachim could have said the same, only using it to motivate either coherence or identity theories, not deflationism, as Strawson intends.
- For Russell as well the major problem with truth was first understanding the nature of judgement. Russell, at the time he was writing the essay collected here (1908), thought that the principal problem was one of saying what the mind was related to, when it made a judgement. We cannot simply say that the mind is related to a fact, for then we would have no theory of false judgement, where there is no fact in question (this remains a problem for modern versions of an identity theory). Russell instead related us to a complex of ingredients together making up whichever proposition we believe. These ingredients would include the things about which we make judgements, and the relations or properties attributed to them. But he was unable to explain how the ingredients united to make a distinctive judgement. Famously, unless there is some principle uniting them, we would be unable to distinguish between two subjects, each related to the complex (.John, loves, Mary) but one of whom judges that John loves Mary, and the other of whom judges that Mary loves John18.
- The problem of understanding judgement continues. In Chapter XVII, one of the most recent papers collected here, Davidson suggests that there is a family of connected concepts, including belief, desire, cause, action, and truth, which illuminate one another—but that it is folly to expect a definition of any one of them. It is a significant feature of Davidson's chapter that we are led back to the idea that deflationism itself is to be rejected principally because it gives us no wider philosophy of judgement and belief. This is also the concern aired in Chapter XV by Dummett, and it is approached from a different direction by Wright.
4. SENTENCES TO THE RESCUE?
- By contrast, there has been a persistent tradition in the philosophy of language that turned its back on any problem about the nature of belief or judgement, and satisfied itself with the sentence or sometimes the utterance, as the bearer of truth. Compared with judgements or propositions, sentences and utterances might seem to be reassuringly solid: concrete, datable, manageable empirical items. For writers starting here, at least one side of the equation is under control, and then attention switches to the ether side—the facts or situations or states of affairs that serve to make sentences true (or, if we are deflationists, attention switches to explaining why we need not worry about the other side). It will be for the reader to judge whether this is an improvement or a retrogression. It is, for example, a major part of Strawson's objection to Austin that the latter had simply mistaken the grammar of ascriptions of truth, by attaching them to utterances rather than statements.
- The preference for sentences is, however, reinforced by at least two developments in recent philosophy. One is Tarski's influential work on truth. Tarski sought ‘a materially adequate and formally correct definition of the term "true sentence19"'. We say more about Tarski's definition later. From the outset, Tarski described his project in terms of sentences. The definition that Tarski constructed was limited to the sentences of formalized languages—in Tarski's view, if we bring formal methods to bear on natural languages, contradictions associated with the Liar paradox inevitably arise. Nevertheless philosophers have applied Tarski's methods and ideas to natural languages, preserving for sentences the role of truth-bearer. The other development is the general mistrust of any notion of a proposition or judgement, most famously voiced by Quine.
- If propositions are deemed disreputable, and good work seems mostly to proceed by embracing sentences, then concerns about the nature of judgement may seem to drop away. Dispensing with propositions Quine championed 'disquotationalism', a prominent contemporary form of deflationism that takes sentences to be the primary truth-bearers. According to Quine, saying
is just an indirect way of saying something about the world—namely, that snow is white. So why employ ‘true' at all, if instead we can talk directly about the world? The disquotationalist answer is that we do not always attach ‘true' to a quote-name of a sentence. We may, for example, combine ‘true' with a definite description ('What Claire said yesterday was true'), or a quantifier ('Every sentence of the form "p or not p" is true'). In the first case, our use of ‘true' allows us to affirm something Claire said even if we cannot supply a quote-name of her utterance. What we say is equivalent to an infinite disjunction20:
What Claire said ='aardvarks amble' and aardvarks amble or what Claire said = ‘antelopes graze' and antelopes graze or....
In the second case, by predicating ‘true' of all sentences of a certain form, we affirm an infinite conjunction:
Tom is mortal or Tom is not mortal,
and snow is white or snow is not white,
So it is not just that the truth predicate is ‘a device of disquotation21'; it is also a device for expressing infinite conjunctions and disjunctions22. And these infinite conjunctions and disjunctions23 are about the world—about aardvarks, antelopes, Tom, and snow, among other things. Whether we mention sentences via quote-names, definite descriptions, or quantification, the truth predicate serves ‘to point through the sentences to the reality24'.
- If an important logical role of ‘true' is to express infinite disjunctions25 and conjunctions, then the following disquotational definition of truth appears natural:
DisquT: x is true iff (x=‘s1' & s1) or (x=‘s2' & s2) or …,
where ‘s1', ‘s2', ... abbreviate sentences26. We may notice that Tarski's T-sentences
are easy logical consequences of DisquT, given a suitable infinitary logic27. So, given such a logic, the definition satisfies Tarski's condition of material adequacy on a definition of truth28. Here is one way to present disquotationalism, in terms of a disquotational definition of truth. Alternatively, we might present disquotationalism as an axiomatic theory, where the axioms are the T-sentences. Either way, disquotationalism is an infinitary account of truth: it is expressed either in terms of an infinitary definition or in terms of infinitely many axioms. And this may give us pause.
‘s1' is true iff s1
‘s2 is true iff s2
- We might instead turn to this finitely stated schematic definition:
x is a true sentence29 iff [There Exists] p(x=‘p' & p).
Obvious problems arise if we interpret the quantifier objectually30. But the alternative move to a substitutional reading has its difficulties, because there is a threat of circularity. Substitutional quantification is typically characterized in terms of truth (more specifically, in terms of true substitution instances31). A disquotationalist might abandon a direct definition of truth in favour of a recursive account, according to which ‘true' is defined Tarski-style in terms of the more basic notions of reference and satisfaction. Given a language with a finite stock of names and predicates, reference may be disquotationally defined by a finite list of sentences of the form '"a" refers to a', and satisfaction by a finite list of sentences of the form ‘x satisfies "F" iff x is F'. In this way, reference and satisfaction are finitely defined—and so truth is finitely defined too. But such a recursive disquotationalist is restricted to languages whose sentences have the appropriate kind of logical form. And there is an array of truths that are notoriously hard to fit into the Tarskian mould: belief attributions, counterfactuals, modal32 assertions, statements of probability, and so on33.
- In short, there is a question about the very statement of the disquotational theory. There is also a question about its scope. According to the disquotational definition of truth, the sentence ‘Penguins waddle' is true, given that penguins waddle. And on the axiomatic presentation, given the T-sentence ' "Penguins waddle" is true iff penguins waddle' and given that penguins do waddle, we may infer that the sentence ‘Penguins waddle' is true. But ‘Penguins waddle' may be a false sentence of some language other than English. This is one reason for supposing that the disquotational theory must be restricted in scope, restricted perhaps to the sentences of a single language. And there is reason to think that even this restriction is not enough. The sentences within the scope of the definition are used (as well as mentioned) in the definiens; and in the axiomatic T-sentences, every sentence to which ‘true' applies is used (as well as mentioned). If we are to understand the definiens, or understand all of the axiomatic T-sentences, we must understand each of these sentences. And even if the sentences are restricted to a single language, say English, such an understanding would require ‘massive conceptual resources', to use Gupta's phrase (Chapter XVI, 297). If the scope of the definition goes beyond the English sentences that we understand, then our understanding of the definiens and the T-sentences, and hence our understanding of ‘true', appears to be compromised.
- Some disquotationalists favour a restriction to the idiolect of the speaker34. For example, according to Field's characterization of ‘pure disquotational truth', a person can meaningfully apply ‘true' only to utterances she understands. Field suggests, as a heuristic, that when I say a sentence is true (in the pure disquotational sense) I am saying that it is true-as-I-understand-it. And Field goes on to characterize pure disquotational truth in terms of a strong equivalence: my claim that utterance u is true (that is, true-as-I-understand-it) is cognitively equivalent to u (as I understand it). So the T-sentence:
(T) ‘Aardvarks amble' is true iff aardvarks amble
expresses a cognitive equivalence—according to Field, a T-sentence holds ‘of conceptual necessity', and enjoys an ‘axiomatic status' (Chapter XIX, 362, 372). In general, we should expect the disquotationalist to confer some kind of necessity on the T-sentences, given that the T-sentences are either the axioms of the theory or logical consequences of a definition along the lines of DisquT.
- But we may feel a strong pull in the other direction: surely the T-sentences are contingent, not necessary. At first sight, rather than serve as an axiom or a partial definition of truth, (T) serves to say something contingent about a particular English inscription or type of inscription. It is, after all, a contingent matter that ‘aardvarks amble' means what it does, or is used the way in which we use it. Consider a possible world w in which aardvarks amble, and the sentence ‘aardvarks amble' is used to mean what we mean by ‘pigs fly'. (T) is false in w: the left-hand side is false because in world w the sentence ‘aardvarks amble' is not true, but the right-hand side of (T) is true, because aardvarks amble in w. So while (T) is true in the actual world, it is only contingently true. Or to put it another way: the sentence ‘aardvarks amble' might not have had the truth conditions that aardvarks amble; it might have had the truth conditions that pigs fly.
- At what point should the disquotationalist resist this reasoning? Note that while the used sentence on the right side of (T) is taken to be a sentence of actual English (which truly describes how things are in w), the mentioned sentence on the left is taken to have the meaning it has in w, and is evaluated according to this meaning and how things are in w. In reasoning to the contingency of (T), we apply ‘true' to an interpreted sentence that does not belong to our idiolect. So it is here, presumably, that Field for one will balk: pure disquotational truth cannot be applied in this way. When I say that a sentence is true (in the pure disquotational sense), I am saying that it is true-as-I-actually-understand-it, not true-as-I-might-have-understood-it. The mentioned sentence on the left of (T) must be the same sentence as the used sentence on the right—the same sentence of my idiolect.
- It is sometimes claimed35 that disquotationalists can guarantee the necessity of the T-sentences by the restriction to idiolect only if the sentences in my idiolect are necessarily in my idiolect. The argument runs as follows. Let ‘true-in-M' abbreviate ‘true in my idiolect'. Consider the T-sentence:
(T') ‘Aardvarks amble' is true-in-M iff aardvarks amble.
Suppose there's a possible world in which aardvarks amble and in which I speak the same idiolect M, but ‘aardvarks amble' is not in M. Then (T') is false in this possible world. And so the disquotationalist cannot allow a sentence to belong only contingently to my idiolect. As a consequence there can be no changes within my idiolect: if I learn a new sentence or forget an old one, I speak a new idiolect. To most philosophers this would be a counter-intuitive result.
- This may be a powerful argument against some forms of disquotationalism, but against Field's version it seems to have little force. In the possible world we envisaged, it is false that ‘aardvarks amble' is true-in-M. So it is assumed that the predicate ‘true-in-M' can fail to apply to a sentence which is actually a true sentence of my idiolect (supposing of course that aardvarks amble). But then the predicate ‘true-in-M' cannot capture ‘true' in Field's pure disquotational sense. For, on our understanding of this sense of ‘true', to say of a sentence that it is true is to say that it is true-as-I-actually-understand-it. There is no possible world in which ‘true' fails to apply to a sentence which is actually in my idiolect and is actually true. Compare this remark of Field's:
‘So even if ‘snow is white' had been used in English pretty much the way that ‘grass is red' is actually used, ‘snow is white' would still have been true in the purely disquotational sense36.'
'True' in the purely disquotational sense cannot apply to true sentences outside my idiolect—but it also cannot fail to apply to sentences actually within my idiolect, even if those sentences belong only contingently to my idiolect.
- These restrictions on pure disquotational truth are very strong. They secure my understanding of the definiens of DisquT and the axiomatic T-sentences; and they secure a strong necessity for the T-sentences. But one may feel that we are a long way from our commonsensical notion of truth. After all, we do want to say that we might have used our words in such a way that ‘snow is white' would not have been true. And we do apply ‘true' to sentences beyond those of our actual idiolect. We do this when we express our modal37 intuition that ‘aardvarks amble' might have had the truth conditions that pigs fly. We do it when we say ‘Most of what Socrates said was true', even though we have little or no understanding of ancient Greek. And we are perfectly willing to admit that there are true sentences of our language (English) that we do not understand.
- The broad concern here is that disquotationalism makes a subject's conception of truth too much dependent upon the question of which language she understands, and how much of a language she understands. A speaker ignorant of aardvarks will not know what would make the sentence ‘aardvarks amble' true. This is what her lack of zoological knowledge consists in. But it seems strange to think that her notion of truth is itself impoverished. Similarly, if I expand my understanding, bringing new sentences into my repertoire, it is strange to say that I thereby expand my conception of truth. And if two people speak entirely distinct languages, then nothing will be in common between the list of T-sentences we construct for one and that which we construct for the other, yet we would not want to infer that their conceptions of truth are therefore entirely distinct.
5. BACK TO PROPOSITIONS?
.6. THE LIAR
- According to Field, we should be methodological deflationists (Chapter XIX, 367-8), taking pure disquotational truth to be the fundamental truth concept as long as this adequately serves our practical and theoretical purposes. The present worry is that pure disquotational truth is just too restricted to serve these purposes. Perhaps, then, we would do better to abandon sentences, and return once more to the idea that judgements, beliefs, or propositions are the fundamental truth-bearers. Instead of working in terms of (T), we work in terms of
(P) The proposition that aardvarks amble is true if and only if aardvarks amble.
According to Horwich, the basic truth concept is propositional-truth, not utterance-truth or sentence-truth. And in its application to propositions, the truth predicate is unrestricted: ‘true' applies to all propositions. To accommodate propositions that are not yet expressible, Horwich supposes that every proposition is expressed by a sentence in some possible language. He also assumes that whatever can be expressed in some possible language can be said in some possible extension of English. So in order to encompass all propositions we need only consider possible extensions of English38. The axioms of Horwich's minimal theory are all the instances of the schema:
The proposition that p is true iff p,
and there is an axiom for each proposition, whether or not that proposition is actually expressible. Acceptable substituends for the occurrences of ‘p‘ are sentences of English, actual and possible. So Horwich's minimal theory is composed of infinitely many axioms, infinitely many of which we cannot formulate or understand. We could hardly be further removed from speakers' idiolects.
- Clearly, understanding 'true' cannot be a matter of understanding all the axioms of the minimal theory. According to Horwich, our understanding of 'true'—our knowledge of its meaning—consists in our disposition to accept a priori those axioms that we can formulate39. This disposition provides the best explanation of our overall use of the term ‘true'. So, by appeal to the view that meaning is given by use, Horwich maintains that the meaning of ‘true' is constituted by this disposition. This provides the Truth predicate with a fixed meaning, even when it is applied to propositions that we cannot formulate or understand.
- We can now see how Horwich will address the issues that confronted the disquotationalist. For Horwich, understanding ‘true' is not a matter of understanding all the axioms of the truth theory, and so an understanding of ‘true' does not require massive conceptual resources. Foreign languages present no special problem, because 'true' applies to all propositions, and in particular to all those expressed in foreign languages. And there seems less room for controversy about the modal40 status of:
(P) The proposition that aardvarks amble is true iff aardvarks amble.
(P) makes no reference to any apparently contingent fact about English, and it is interlinguistic rather than intralinguistic. We can maintain that (P) is a priori, for everyone is in a position to know that (P), whether they speak English or not just as the speakers of a foreign language know that 2+2=4, even if they don't recognize this sentence as an expression of what they know. So (P) cannot be criticized as presenting a contingent fact about English as part of the definition of truth.
- The problem instead is whether the notion of a proposition is as innocent of involvement with truth as deflationism requires. Let us take a closer look at Horwich's minimalist schema:
(M) The proposition that p is true iff p.
Instances of this schematic generalization are obtained by replacing the two occurrences of ‘p' by tokens of an English sentence. For example, putting a token of ‘aardvarks amble' for each occurrence of ‘p', we get (P). We may feel some discomfort here: the tokens of ‘aardvarks amble' are placed in two quite different contexts. The first token forms part of a referring term, the term ‘the proposition that p'. The second constitutes the right-hand side of the biconditional. With Davidson, we may wonder how these two appearances of ‘aardvarks amble' are connected (Chapter XVII, 318). At any rate, it is clear that certain conditions must be placed on such an instantiation. We can list four (see Horwich, Chapter XIV, 244-5):
(i) each ‘p' is replaced with tokens of an (actual or possible) English sentence,
(ii) these tokens are given the same interpretation,
(iii) under that interpretation they express a proposition, and
(iv) the terms ‘that' and ‘proposition' are given their English meanings.
- So the very statement of Horwich's minimal theory is shot through with semantical concepts and talk of sentences. This may raise two concerns. First, since talk of sentence-tokens is unavoidable anyway, might it not be advisable to work with sentences (or token utterances) all along? Why not be more economical and adopt the schema
constrained by conditions (i) and (ii)? This avoids the overt appeal to propositions, which will come as a relief to anyone, like Quine, who finds them suspect or mysterious. The thought is encouraged by Horwich's own claim that the minimal theory of truth for propositions is easily inter-derivable with a minimal theory of truth for utterances41.
- The second concern is prompted by the observation that when we specify the axioms of the minimal theory we must employ a number of semantical concepts: the notion of a language (specifically, English), the notion of an interpretation, the relation of expressing, and, of course, the notion of a proposition. Since the minimal theory of truth itself depends on these notions, the concept of truth cannot be used to explain them. So for the minimalist, the challenge is this: explain these fundamental semantical concepts, but do not appeal to the notion of truth anywhere in your explanations. Indeed both Horwich and Field suggest that deflationism about truth goes hand in hand with deflationism about reference, and if this is right there can be no appeal to reference either42.
- According to Horwich, a use theory of meaning will do the job43. (For example, Horwich assumes that a use-theoretic account can be given of ‘u and v express the same proposition44'.) So a use theory of meaning does a lot of work for the minimalist, supplying a meaning for ‘true' and for the semantical terms needed to state the minimal theory. And it does all this in terms that make no reference to truth. Many philosophers would doubt whether this can be done, and this is the central issue between Davidson and Horwich in the Chapters XVII and XIV respectively. Strawson anticipated the difficulty: ‘And it is, indeed, very strange that people have so often proceeded by saying "Well, we're pretty clear what a statement is, aren’t we? Now let us settle the further question, namely what it is for a statement to be true45"'.
- Strawson's point is also visible in Ramsey's paper (Chapter VI). Having made deflationary noises about the concept of truth, Ramsey immediately goes on to raise worries about the notion of belief. So, for example, Ramsey would dismiss any problem about what it is for a judgement to be true. Just make the judgement, as either (T) or (P) instructs. But he thinks there is a big question over what is involved in making any judgement in the first place. His own approach is, in effect, behaviouristic. In particular cases, he thinks belief can indeed be identified without any reference to truth, or to situations or states of affairs, or to the worldly side of things. He thinks a belief in, say, the probability of a horse winning a race can be identified by means of the use such judgements have, for instance in voicing commitments to particular betting rates on events, at least under idealized conditions. Ramsey's work therefore provides an instance of the kind of thing Horwich thinks we must be able to do in general, which is to provide an account of meaning in terms that are entirely free of semantic notions such as reference and truth. Another hopeful example would be an expressive theory of ethical judgement, which explains what we are doing entirely without reference to ethical facts or situations.
- Sooner or later, any truth theorist—deflationist or not—must confront the notorious Liar paradox. It is perhaps surprising how little deflationists have to say about the Liar. Field and Horwich recognize that certain restrictions and exceptions must be made because of the semantic paradoxes47, but there the matter is allowed to rest. According to Horwich,
There is no reason to suppose that the minimalist answers that are advanced in this essay could be undermined by any particular constructive solution to the paradoxes—so we can temporarily set those problems aside48. But it remains to be seen whether deflationism is compatible with positive attempts to resolve the liar.
- Consider a Liar sentence like or It we instantiate the disquotational definition DisquT to (1) or (2), a contradiction is easily reached, assuming classical logic and semantics. And since the T-sentences for (1) and (2) are contradictory, they cannot serve as axioms of a consistent disquotational theory. Principled restrictions are needed.
- One way to avoid liars and truth-tellers is to define truth for a language in which ‘true' does not appear. But this restriction is surely too severe. Deflationists are after an account of truth for natural languages or for speakers' idiolects, and ‘true' is certainly a term of English and a term of my idiolect. And a perfectly ordinary utterance involving ‘true' can turn out to be paradoxical. Suppose I write on the board:
(3) The sentence written on the board in room 101 is not true.
If a false sentence is written on the board in room 101, (3) is straightforwardly true. If I am in room 101, and I don't realize that I am, then I have unwittingly produced a Liar sentence. In this case, (3) is paradoxical not in virtue of its intrinsic syntactic or semantic form, but in virtue of the empirical facts49. If the disquotationalist throws out paradoxical utterances on the grounds that they belong to a language beyond the scope of the theory, then she will also need to throw out utterances of the same type that are within the intended scope of the theory. The deflationist must find some other approach to semantic paradox.
- A familiar approach to the liar adopts a non-classical semantics that allows truth-value gaps. On such an approach, Liar sentences are neither true nor false. Now the correspondence account seems to have a natural enough way with gaps. If we characterize the correspondence theory as follows:
A sentence is true iff it corresponds to a state of affairs that obtains,
we can say that a sentence is false if it corresponds to a state of affairs that does not obtain, and neither true nor false if it fails to correspond to any state of affairs. Truth-value gaps do not seem to compromise the correspondence intuition.
- Are gaps available to the disquotationalist? It is far from clear that they are. The natural disquotational definition of falsity is this:
DisquF: x is false iff (x=‘s1' & -s1) or (x=‘s2' & -s2) or….,
where ‘s1', 's2', abbreviate sentences. Suppose we assume that some sentence 'sk' is neither true nor false. Then, using an infinitary logic which is otherwise classical, we obtain a contradiction: -sk follows from DisquT and --sk follows from DisquF50.
- In the face of this reasoning, the disquotationalist might place gappy sentences beyond the scope of the disquotational account. Or she might try to block the reasoning by adopting a non-classical logic (to be articulated in terms that cannot include truth, falsity, or gaps). Either way, the disquotationalist must supply a positive account of gaps if they are to play an explanatory role, and it is not obvious how that is to be done.
- But suppose for a moment that a disquotational account of gaps is forthcoming. Then the disquotationalist might hope to avoid restrictions on DisquT and the T-schema. Consider for example the T-sentence associated with (1):
‘(1) is false' is true iff (1) is false.
It might be proposed that this biconditional is true, because both sides are gappy. In general, suppose that ‘p' is a Liar sentence. The idea is that
may be counted true if both sides are gappy. So no contradiction follows if we instantiate DisquT to ‘p', or take the T-sentence for ‘p' as an axiom. Instead ‘true' and ‘false' will be ineliminable terms—DisquT will be a circular definition, and some T-sentences will contain ineliminable uses of ‘true' and ‘false' on their right-hand sides. In the spirit of the ‘revision' theory of truth, we might accept each T-biconditional as a partial definition of truth for all sentences—liars included—and accept the consequence that truth is a circular notion51. Such an approach may well tempt the disquotationalist: even the truth of Liar sentences is a matter of disquotation.
- However, it seems that the disquotationalist cannot take this tack. Consider again the T-sentence for the Liarlike sentence ‘p'. We are taking 'p' to be gappy. So the right-hand side of the T-sentence is gappy. But the left-hand side is false: it is false that ‘p' is true52. So the T-sentence is not true.This is an instance of a more general problem: given a gappy sentence (whether a Liar sentence or not), the corresponding T-sentence appears to be untrue. In order to maintain the truth of such a T-sentence, we might introduce a weak notion of truth53, where '"p" is true' always has the same semantic status as ‘p' (In particular, if ‘p' is gappy, so is '"p" is true'.) The revision theory is a theory of this weak notion54. But it would seem that the disquotationalist cannot ignore the strong notion of truth, where if we say of a gappy sentence that it is true, we have said something false. Presumably the deflationist wants to deflate all truth, weak and strong.
- The strong notion of truth is related to strengthened reasoning about the Liar. Versions of strengthened reasoning have provided the primary motivation for contextual views of truth55. For example, given the Liar sentence:
we may go on to declare (L) gappy. But then it follows that
But given (P) and given what (L) says, it seems that we may infer
On a contextual analysis, the reasoning is valid. (L) is pathological in its context of utterance. But then we can stand back from its context of utterance, and assess (L) on the basis both of its pathologicality and what it says. Since it is pathological and so not true, and since it says it isn't true, (L) can be assessed as true in the subsequent, reflective context of ®. On some but not all contextual views, the shift from the context of (L) to the reflective context of (P) and ® is a shift in a Tarskian hierarchy from a lower to a higher level of language56.
- It is not easy to square such contextual accounts with disquotationalism. If (L) really is semantically pathological, then it is so because it attributes lack of truth to itself: ‘true' in (L) is ineliminable, and cannot be disquoted away. And if (L) really is true (when assessed from a reflective context, or from a higher level of language) then the disquotationalist must admit truths from which ‘true' cannot be disquoted. And this compromises the disquotational conception of truth.
- Strengthened reasoning also presents problems for the prosentential theory of truth. According to the prosentential theory, ‘true' is used in forming prosentences. In the discourse:
Mary: Chicago is large
John: If that is true, it probably has a large airport
the expression ‘that is true' is a prosentence, which shares its content with its antecedent, namely ‘Chicago is large'. In a parallel fashion, the Liar sentence ‘this is false' relies on its antecedent for its content, but, in the words of Grover, ‘it is, unfortunately, its own antecedent and, as such, fails as an antecedent supplier of content57'. According to the prosentential account, Liar sentences fail to have content.
- Consider, however, the strengthened reasoning, and (P) in particular. In discussion of strengthened reasoning Grover remarks that ‘if "true" is prosentential' then (P) ‘fails to express a proposition58'. The conditional does seem true: according to the prosentential treatment (P) relies for its content on that of its antecedent (L)—but (L) has no content. Yet it is surely highly counter-intuitive that (P) is without content. Further, if we accept reflective evaluations like ®, then the prosentential account is closed off to us. If Liar sentences are true or false (on reflection), then they cannot be without content.
- In contrast, the correspondence intuition remains intact, or so it might be argued. According to the correspondence conception, (L) is true if and only if it corresponds to a state of affairs that obtains. And (L) does. The state of affairs here is a semantic state, that of (L)'s being untrue in its context of utterance. And this state obtains, because (L) is semantically pathological in its context of utterance. According to the correspondence conception, (L) is indeed true. On this correspondence line, (L)'s truth is grounded in a semantic state of affairs, and not a non-semantic state of the world. We cannot represent this fact or state of affairs in non-semantic terms. Perhaps—the correspondence theorist might conclude—this is why the disquotationalist finds strengthened reasoning so intractable.
- It seems, then, that the disquotationalist will find little comfort in any of the resolutions of the Liar we have mentioned, whether gap approaches, the revision theory, contextual accounts, or certain hierarchical views. And the difficulties seem not to be confined to the disquotationalist—it is not clear that Horwich's minimalist is any better off. As Horwich himself notes, the move to propositions seems to close off any appeal to gaps59. And there is a further issue for the minimalist.
- Consider again the Liar sentence
Consider the associated instance of the minimalist truth schema (M):
(m) The proposition that (L) is not true is true iff (L) is not true.
What should we make of (m)? What is the proposition referred to on the left-hand side? If, for example, we adopt a contextual theory, then we might say that (L) expresses a true proposition. And if we take the right-hand side to be true as well, (m) is true. So (m) is not contradictory at all. We are in danger of losing sight of the Liar. To avoid that, we must bear in mind that (m)'s truth was established by a prior contextual theory of truth. Another theory may identify another proposition, or none, as the subject of the left-hand side, and a different truth-value for (m). The problem lies with the schematic expression ‘the proposition60 that p'. Given a Liar sentence, it is a highly non-trivial question as to what proposition, if any, it expresses. It takes a positive account of semantic paradox to determine the reference of ‘the proposition that p' when we put a liar sentence for ‘p'. We can make sense of (m) only if we're already in possession of a theory of truth. But then it seems that we cannot in general regard instances of Horwich's schema as axioms of a theory of truth, for there may be instances whose truth is established by a prior theory61.
- These last reflections on the Liar paradox lend support to the contention that we cannot take the phrase ‘the proposition that p' for granted, when we reflect upon truth. Deflationists pride themselves on avoiding any engagement with the disputed notion of a fact. But it is much harder for them to avoid engagement with the notion of a proposition, or that of a judgement or idiolect or language, at least while retaining any title to doing philosophy at all. And these notions seem to prove as difficult—and, if we may say so, as robust—as that of truth itself. Gaining an understanding of the nature of the truth-bearers is a common problem faced by deflationists as much as by philosophers on the robust side, and for that matter by contemporary writers just as much as by the older tradition.
- Such considerations suggest that the prospects for robust semantic notions, truth included, are by no means as poor as some writers suppose. Perhaps indeed the idea that truth is seriously dyadic is too natural for it ever to disappear from the philosophical scene. It seems that in this area, at least, and in spite of a century of formidable achievements, philosophy is in little danger of talking itself out of a job.
Footnote 2: Metaphysics, Gamma 7.27, trans. Christopher Kirwan (Oxford, 1993).
Footnote 3: 'Truth, to coin a phrase, isn't a real predicate': D. Grover, J. Camp, and N. Belnap, ‘A Prosentential Theory of Truth', Philosophical Studies, 27 (1975), 97. See also the papers collected in D. Grover, A Prosentential Theory of Truth (Princeton, 1992). We return to prosententialism briefly below, p. 276.
Footnote 4: Blackburn calls this ‘Ramsey's ladder', and registers warnings about philosophies that take advantage of the horizontal nature of Ramsey's ladder to climb it, but then announce a better view from the top. One way in which the theory of truth makes contact with more general, 'postmodernist', scepticism about ‘truth' in the humanities in general is visible here: scepticism whether we get anywhere by climbing Ramsey's ladder can easily turn itself into scepticism about truth in general. See S. Blackburn, Ruling Passions (Oxford, 1998), 78.
Footnote 5: The debates about the correct way to frame 'expressivist' approaches to ethics are pursued in A. Gibbard, Wise Choices, Apt Feelings: A Theory of Normative Judgment (Cambridge, Mass., I X1)0); S. Blackburn, Essays In Quasi-Realism (New York, 1993); and M. Smith, ‘Why Expressivists about Value should love Minimalism about Truth', Analysis, 54 (1994) 1-12.
Footnote 6: See B. C. Van Fraassen, The Scientific Image (Oxford, 1980) for the best-known recent suggestion that in science acceptance does and should fall short of belief in the truth of what is accepted.
Footnote 7: Another norm is that our assertions and beliefs should be justified, and that is different from being true. But we aim at truth, by obeying constraints of justification. An assertion is justified, in this sense, when it is reasonably supposed to be true. An act of assertion may be subject to still more norms, such as those of being appropriate or polite, but these are not our concern.
Footnote 8: Conversely, if a place for facts can be found in the world, then they cannot be as complex as propositions. But this compromises the correspondence relation: how do fine-grained propositions correspond to coarse-grained facts? For recent work on the correspondence theory that bears on the present issue, see D. M. Armstrong, A World of States of Affairs (Cambridge, 1997); J. Barwise and J. Perry, Situations and Attitudes (Cambridge, Mass., 1983); B. Taylor, ‘States of Affairs', in G. Evans and J. McDowell, (eds.), Truth and Meaning: Essays in Semantics (Oxford, 1976), 263-84, also Modes of Occurrence (Oxford, 1985), ch. 2; M. Pendlebury, ‘Facts as Truthmakers', Monist, 69 (1986), 177-88; and G. Forbes, ‘Truth, Correspondence and Redundancy', in G. McDonald and C. Wright (eds.), Fact, Science and Morality: Essays on A. J. Ayer's Language, Truth and Logic (Oxford, 1986), 27-54.
Footnote 9: ‘Two Dogmas of Empiricism', Philosophical Review, 60 (1951), 20-43, repr. in From a Logical Point of View (Cambridge, Mass., 1953), 42.
Footnote 10: p.32 in this vol.
Footnote 11: p. 48 in this vol.
Footnote 12: On Certainty (Oxford, 1969), §141.
Footnote 13: See Wright, Ch. XIII in this vol.; see also R. Walker, The Coherence Theory of Truth: Anti-Realism, Idealism (London: Routledge, 1989).
Footnote 14: For a convincing case that Bradley, at least, identified truth and the world, see S. Candlish, ‘The Truth about E H Bradley', Mind, 98 (1989), 331-48.
Footnote 15: The phrase is Crispin Wright's, Truth and Objectivity (Cambridge, Mass., 1992), 83.
Footnote 16: It is present in J. McDowell, Mind and World (Cambridge, Mass., 1994) and J. Hornsby, ‘Truth: the Identity Theory', Proceedings of the Aristotelian Society, 97 (1997), 1-24.
Footnote 17: p. 168 in this vol.
Footnote 18: This problem is not avoided by reminding ourselves that the sequence is an ordered triple. For there is no guarantee that anyone contemplating the ordered triple takes the first element to be the subject that does the loving. There are other ways of mapping elements of the triple onto a judgement or a fact. This echoes the difficulty of seeing facts as combinations of things. Frege had earlier made a contribution to this problem by comparing predicates to functions, introducing ‘unsaturated' elements into the proposition.
Footnote 19: Tarski, ‘The Concept of Truth in a Formalized Language', in Logic, Semantics, Metamathematics (2nd edn.), trans. J. H. Woodger, ed. J. Corcoran (Indianapolis, 1983), 152. There is disagreement about Tarski's motivations: e.g. according to some,Tarski was after a physicalistic reduction of semantic concepts (see e.g. H. Field, ‘Tarski's Theory of Truth', Journal of Philosophy, 69 (1972) ), while according to others, Tarski was after an eliminative definition that would guarantee that a language for which ‘true' could be defined was not subject to paradox and contradiction (see J. Etchemendy, ‘Tarski on Truth and Logical Consequence', Journal of Symbolic Logic, 53 (1988); support for this reading can be found in Tarski (Ch. IX in this volume, 127).
Footnote 21: W. V. O. Quine, Philosophy of Logic (Englewood Cliffs, 1970), 12.
Footnote 22: See S. Leeds, ‘Theories of Reference and Truth', Erkenntnis, 13 (1978), 111-29; H. Field, The Deflationary Conception of Truth', in MacDonald and Wright (eds.), Fact, Science and Morality, 85-117; Field, Ch. XIX in this vol.; Gupta, Ch. XVI in this vol.
Footnote 24: Quine, Philosophy of Logic, 11.
Suppose that for x we put ‘What Claire said yesterday'. Then among the infinitely many quote names 's1', 's2', ... that occur in the definiens, there will be one, and only one, that is the quote name of what Claire said. Suppose this quote name is 'sk'. Then the disjunct ‘what Claire said yesterday=‘sk' & sk‘ is the only true disjunct in the definiens—all the others will contain false identity statements. If we drop these false disjuncts, we obtain:
What Claire said yesterday is true iff what Claire said yesterday = ‘sk' & sk. So the truth of what Claire said is just a matter of the disquotation of its quote name. This is just the result we would expect from a disquotational definition of truth. Such a definition is suggested by remarks in Leeds, ‘Theories of Reference and Truth', 121-1 and n. 10; and versions of it are presented explicitly in Field, 'Deflationary Conception of Truth', 58; M. Resnik, 'Immanent Truth', Mind, 99 (1990), 412; and M. David, Correspondence and Disquotation 11 Oxford: 1994), ch. 4 and p. 107. Footnote 27:
e.g. put ‘snow is white' for x. We will obtain just one true disjunct on the right. If we eliminate the false disjuncts, the definition yields:
‘snow is white' is true iff ‘snow is white' = 'snow is white' and snow is white.(Compare the reasoning in n. 22, above.) Dropping the trivial identity conjunct on the right-hand side, we obtain the T-sentence:
‘snow is white' is true iff snow is white. For a discussion that bears on DisquT and infinitary logic, see David, Correspondence and Disquotation, 100-4. Footnote 28: This condition, that all the T-sentences follow from the definition, is stated on p. 120 of this vol. Elsewhere Tarski endorses a definition of truth just like DisquT, but limited to languages that contain only a finite number of sentences that can be enumerated. See A. Tarski, ‘The Concept of Truth in Formalized Languages', in Logic, Semantics, Metamathematics (2nd edn.) trans. and ed. John Corcoran (Indianapolis, 1983), 152-278, esp. 188). Even in the general case, where a language may contain infinitely many sentences, Tarski considers each T-sentence to be a ‘partial definition of truth', and goes on to say: ‘The general definition has to be, in a certain sense, a logical conjunction of all these partial definitions' (p. 120 in this vol.). As he immediately notes, since the number of partial definitions may be infinite, we will have to explain what is meant by a 'logical conjunction of infinitely many sentences'. Tarski himself deals with the complication by adopting the recursive method (see below).
Footnote 29: Following Tarski, ‘Concept of Truth in Formalized Languages', 159.
Footnote 30: There is the problem of quantification into quotes. And the string 'x= "p" & p' is grammatically ill-formed, since the variable 'p', taken as an objectual variable, cannot serve as a conjunct.
Footnote 31: See David, Correspondence and Disquotation, 78-93; P. Horwich, Truth (Oxford, 1990, 26-8); Davidson, Ch. XVII. In this vol., 317-18. Field has suggested that we explain substitutional quantification in terms of infinite conjunctions and disjunctions, leading us back to the infinitary DisquT (see Field, ‘The Deflationary Conception of Truth', 57-9, and David, Correspondence and Disquotation, 98 ff.).
Footnote 33: See Field, Ch. XIX in this vol., 374; Horwich, Ch. XIV in this vol., 253-4; David, Correspondence and Disquotation, 117-19.
Footnote 34: See Field, Ch. XIV in this vol.; Resnik, ‘Immanent Truth'.
Footnote 35: See e.g. David, Correspondence and Disquotation, 134-5.
Footnote 36: p. 381 in this vol.
Footnote 38: Horwich, Truth, 20 n. 4
Footnote 39: Horwich, Ch. XIV in this vol., and Truth, 36.
Footnote 41: Horwich, Truth, 103-8.
Footnote 42: See Horwich, Ch. XIV, 248, and Field, Ch. XIX, 365. It is not entirely clear that a deflationist theory of truth implies a deflationist theory of reference. Philosophers such as Strawson deny the substantiality of ‘facts' without denying the existence of robust word to world reference links. Elements of a sentence can pick out elements of the world, without the sentence as a whole corresponding to anything such as a ‘complex' of such elements.
Footnote 43: Field also advocates a ‘truth-free' account, but one in which conceptual role is one ingredient of meaning and ‘indication relations' are another. See Ch. XIX, 356-9.
Footnote 44: p. 249 in this vol.
Footnote 45: p. 171 in this vol.
Footnote 46: Field for one is aware of this danger. There is always the possibility that when the deflationist's explanations are done ‘he will have reconstructed the inflationist's relation "S has the truth conditions p", in fact if not in name' (p. 367 in this vol.; see also p. 356).
Footnote 47: See e.g. Field, Ch. XIX in this vol., 353, n. 1; Horwich, Ch. XIV in this vol., and Truth, 41-2.
Footnote 48: Truth, 42.
Footnote 49: As Kripke has pointed out, there is a riskiness to our ordinary uses of ‘true': under suitably unfavourable circumstances, virtually any use of ‘true', however innocent it may look, leads to paradox. See S. Kripke, ‘Outline of a Theory of Truth', Journal of Philosophy, 72 (1975), 690-716.
Footnote 50: Here is a derivation of the contradiction.
Replacing x in DisquT by 'sk', we obtain:
‘sk' is true iff (‘sk'=‘s1' & s1) or (‘sk'=‘s2' & s2) or … (‘sk'='sk' & sk) or … . Only one of the disjuncts on the right-hand side is true (all the others contain false identity statements). Eliminating the false disjuncts, we obtain:
(a) 'sk' is true iff 'sk'='sk' & sk. Eliminating the trivial identity conjunct on the right-hand side, we arrive at the T-sentence for 'sk': Since 'sk' is neither true nor false, 'sk' is not true, and so, given (b), we obtain Next replace ‘x' in DisquF by 'sk'. We obtain
‘sk' is false iff (‘sk'=‘s1' & -s1) or ('sk'='s2' & -s2) or … (‘sk'='sk' & -sk) or …. Eliminating the false disjuncts on the right-hand side, we obtain
(d) ‘sk' is false iff 'sk' = ‘sk' & -sk. Eliminating the true conjunct on the right-hand side, we obtain
(e) 'sk' is false iff -sk. Since 'sk' is neither true nor false, 'sk' is not false, and so, given (e), we obtain And we have a contradiction at lines (c) and (f). Footnote 51:
Footnote 52: Compare an argument of Dummett's (see M. Dummett, ‘Truth', Proceedings of the Aristotelian Society, 59 (1959), 141-62) which arises in the course of examining Frege's claim that ‘It is true that p‘ has the same sense as p: ‘Suppose that p contains a singular term which has sense but no reference: then, according to Frege, p expresses a proposition which has no truth value. This proposition is therefore not true, and hence the statement "It is true that p" will be false. p will therefore not have the same sense as "It is true that p", since the latter is false, while the former is not.' (p. 145).
- We should emphasize that the revision theory itself does not appeal to gaps. The revision theory of truth was first developed in A. Gupta, ‘Truth and Paradox', Journal of Philosophical Logic, 11 (1982) as a response to the Liar paradox. See also A. Gupta and N. Belnap, The Revision Theory of Truth (Cambridge, Mass., 1993). At the heart of the revision theory is the idea that all the instances of the T-schema together give a complete and correct definition of the concept of truth. Since no restriction is placed on the T-schema, there will be instantiations to sentences that essentially refer to truth (e.g. Liar sentences). Consequently, this definition is circular.
- According to Gupta and Belnap, the revision theory of truth ‘is a consequence of combining a general theory of definitions and Tarski's suggestion that the biconditionals be viewed as partial definitions. Tarski's suggestion brings out clearly the circularity in the notion of truth…' (Revision Theory of Truth, 142).
- The circularity in the concept of truth gives rise to a revision process—for certain sentences, their truth or falsity is not a stable feature. (Consider for example the Liar sentence 'This sentence is false'. If we ascribe truth to it, we must revise that ascription, declaring it false, and then in turn revise that ascription, and so on indefinitely.) According to the revision theory: '… the objects of the world are not neatly divided into those that have the property of truth and those that lack it. but rather they stand in a hypothetical relation to this property: if an object were to have (or lack) the property of truth, would it maintain that status?' (A. Yaqub, The Liar speaks the truth: A Defense of the Revision Theory of Truth (Oxford, 1993) 5.
Footnote 53: Gupta and Belnap present this distinction in Revision Theory of Truth, 22, citing S. Yablo, 'Truth and Reflection', Journal of Philosophical Logic, 14 (1985), 297-349.
Footnote 54: See Gupta, and Belnap, Revision Theory of Truth, 22, 29 and n. 52.
Footnote 55: See C. Parsons, ‘The Liar Paradox', Journal of Philosophical Logic, 3 (1974), 381-4; T. Burge, 'Semantical Paradox', Journal of Philosophy, 76 (1979), 169-98; J. Barwise and Etchemendy, The Liar (Oxford, 1987); H. Gaifman, ‘Pointers to Truth', Journal of Philosophy 89 (1992), 223-61 and K. Simmons, Universality and The Liar: An Essay on Truth and the Diagonal Argument (Cambridge, 1993).
Footnote 56: See Burge, ‘Semantical Paradox' and Barwise and Etchemendy, The Liar for contextual accounts that are hierarchical; the contextual account in Simmons, Universality and the Liar, rejects the hierarchy in favour of a ‘singularity' account.
Footnote 57: Prosentential Theory of Truth, 124.
Footnote 58: Ibid. 203.
Footnote 59: Truth, 80.
Footnote 60: This is also a general concern of Davidson, Ch. XVII in this vol., 318.
Footnote 61: For more on deflationism and the liar, see K. Simmons, ‘Deflationary Truth and the Liar', Journal of Philosophical Logic (forthcoming).
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