Truth: An Elevation
I present deflationism as commending a flattening of the correspondence conception of truth: the putative relation between language and world which constitutes truth is collapsed such that the content of the truth predicate is exhausted by the contents to which it applies. I seek to show that, independent of any other virtues it might possess, this flat characterisation of truth appears unable to account for the content of truth predications to sentences/propositions the speaker does not understand. I describe such uses of true as cognitively opaque. Much the greater part of the paper will be devoted to showing that cognitive opacity is problematic for all species of deflationism; that, far form being marginal, it is ubiquitous; and that the extant deflationary proposals for dealing with the phenomenon either confuse it with a quite separate problem or are otherwise inadequate. I draw the conclusion that we have good reason for thinking that truth is not flat. In consequence, I suggest that we can view truth as elevated via a metarepresentational role that, while going beyond disquotation, does not resuscitate a correspondence conception.
Deflationism is a slippery doctrine; at its core, however, is the thought that an adequate account of the concept of truth will show it to be flat with the contents to which it applies. Thus, in its most familiar form, the doctrine says that an adequate theory of truth will consist of each instance of the disquotational schema, or some generalisation thereof:
(DS) True(P) iff P,
where ‘True(P)’ stands for a predication of is true to a quotation-name of a sentence or a propositional nominal (e.g., The proposition that P), and 'P' on the right flank is the result of extirpating ‘P’ from either of its respective contexts on the left flank. It is claimed that the logical equivalence of DS marks the truth predicate as a disquotational device: is true cancels the quotation to move ‘P’ from nominal to sentential position, from mention to use (mutatis mutandis for propositional truth bearers. Apart from the misleading nomenclature, the situation is not fundamentally different for propositions (see below).) Truth is thus a circumlocution, but an indispensable one. The predicate allows us indirectly to assert any number of sentences picked out by its subject (e.g., infinitely many logical truths picked out by Every instance of excluded middle…).
Deflationism is often presented in opposition to - a deflation of - a correspondence conception of truth. This conception is elevated, we might say, in that truth is explicated in terms of a uniform relation whose relata are truth bearers (sentences, propositions, etc.) and/or their parts and elements of the world - facts, objects and properties. In simple terms, an explication of truth involves the mentioning of that which bears truth. On this conception, to understand truth is to see one’s language or thoughts side by side with the world, as it were, with truth holding just if the two relata match or correspond. This perspective is flattened by deflationism: if there is no more to truth than the instances of DS, then, it seems, to attribute truth to a sentence is not to place it in a relation with the world, but to say something about the world - truth is flat with the contents to which it is attributed, its content is exhausted by the contents to which it applies. This thought perhaps goes back to §1 of Tarski’s (1956), but has been most forcefully stated by Quine (1970/86) and, thereafter, Leeds (1978), Soames (1984, 1999), Horwich (1990), and Field (1986, 1994a). Opposition to deflationism tends to arise either from the idea that a correspondence notion of truth has an explanatory role which deflationism cannot accommodate (e.g., Devitt (1984), Field (1986)), or from the idea that the content of truth is in some sense richer than is demanded by DS without being as robust as the correspondence conception, i.e., there is an appropriate space to occupy between deflationism and correspondence (e.g., Davidson (1990, 1996), Gupta (1993), Wright (1992)). The arguments I shall present in this paper take up strands of both of these challenges. My claim is that a certain class of truth predications are not assimilable into DS, a fortiori, they are not explained by the function of disquotation or compendious assertion. My problem is not one of grammar or logic or property metaphysics, but of cognition; that is, I shall argue that thoughts of truth are available to us when the contents to which we are attributing truth are not. In simple terms: we can attribute truth to that we don’t understand. Thus, our conception of truth is not in general characterisable as being flat with the contents over which we employ our concept. Much the greater part of my time will be taken up arguing for this claim and against some potential ripostes. This accentuation of the negative is worthwhile, for while the cases I consider have been discussed in the deflationist literature, especially by Field (1994a), they are commonly seen as being marginal or easily accommodated by DS. I hope to show that both of these judgments are wide of the mark and that the problem cases go to the heart of deflationism. On the positive side, though, I shall suggest a natural approach towards the cases made available by a minor but still significant departure from DS. This involves properly acknowledging the intuitive pull of an elevated notion of truth via the thought that truth is primarily a metarepresentational concept, and only secondly a disquotational one: metarepresentation is disquotational only when we have independent access to the content represented, but such access is in no sense constitutive of possessing the concept of truth. I here readily concede that this positive account will be sketched rather than fully elaborated, although I think that it follows naturally from the arguments that precede it and marks a genuine departure from the deflationism vs. correspondence dichotomy.
Our colloquial concept of truth is governed by what is commonly referred to as the correspondence intuition.
(CT) The truth of a sentence s is a function of two factors: (i) what s says (s's meaning) and (ii) how the world is. If the world is as s says, then s is true; otherwise false.
A traditional way to unpack this intuition is to analyse truth as a complex property that relates meanings to facts. For a rough approximation, ACT will suffice:
(ACT) ("x)[True(x) v (åp)(x = ‘p’ & ‘p’ means that p & it is a fact that p)]
Thus, instantiating and simplifying:
(1) ‘Snow is white’ is true iff ‘Snow is white’ means that snow is white & it is a fact that
snow is white.
Consider first the second conjunct of the right flank. It is a fact that P appears to say no more than P. We can, of course, use declarative P for interrogative ends and certain background scenarios could make sense of its being used for opative or imperative ends. Still, as a declarative, It is a fact that P is to P as double negation is to its sentential argument. That is: It is a fact that P iff P. We can thus simplify further and drop the redundant appeal to facts to leave the complement of the nominal fact:
(2) ‘Snow is white’ is true iff ‘Snow is white’ means that snow is white & snow is white.
(The verb of the second conjunct may be stressed to emphasise that we are saying something about the state of snow, unlike the complement of the first conjunct where we are merely articulating what a sentence means independent of the actual state of snow.) Consider now the first conjunct of the right flank. We know, for all P, that ‘P’ means P, and we now have P ( = ‘Snow is white’) in sentential position as the second conjunct. We can thus delete the first conjunct, which leaves us with an instance of DS:
(3) 'Snow is white' is true iff snow is white.
An immediate consequence of this deflation is that CT, contrary to expectation, does not commit us to a uniform property that underlies each truth. The truth of ‘Snow is white’ consists in snow’s being white; the truth of ‘Grass is green’ consists in grass’s being green, and so on ad infinitum. This deflation is targeted at a rough notion of correspondence. Still, deflationism can be seen as a program: rather than seeking substance behind truth, the deflationary conception challenges the correspondence conception to find a role for language-world relations in the explication of truth. The force of the challenge is provided by an account of how (CT) may be fully captured by the flattened DS and how such a deflated notion of truth may be useful, indispensable in fact, without recourse to correspondence (see Field (1986) for this methodology and Horwich (1990) for an attempt to follow it through).
The subsumption of (CT) under DS is effected by the relationship between meaning and truth:
(TM) If s means that p, then s is true iff p.
In essence, (TM) tells us that the disquotational effect of the truth predicate is governed by a constraint that instances of DS realise a translation relation, i.e., that the subject of is true means the same as the sentence on the right of the biconditional. The idea is that the necessary and sufficient conditions under which a sentence would be true are provided by the content of the sentence. To determine the content of truth over a range of sentences G, therefore, it is necessary and sufficient to fix the contents of G (here I avoid problematic issues of truth gaps, and other cases of factual defectiveness and pathology, which are a problem for everyone (see Field (1994b).) Truth, we may say, brings no more content with it than is already present in the content of that to which it applies.
A natural question to ask of deflationism is what is the good of a truth concept so thinly characterised. Quine’s (1970/86, Chp.1) celebrated answer, adopted by many, is semantic ascent. If we have a single sentence in mind, by DS, its truth claim is an “indirection”; for given the disquotational transparency of the predicate, we can assert the sentence, and so directly talk about the world rather than the sentence. However, if we have an infinite number of sentences in mind (e.g., every instance of a tautological schema) or simply an unspecified sentence, assertion is not an option. Moreover, if we stay with objectual quantification, under which all bound variables must be in singular term position, the truth predicate is not eliminable. For example:
(4) a. Every instance of excluded middle is true.
b. *("x)[EM(x) t x]
c. Something Bill said is true
d. *($x)[Bill said(x) t x]
Truth provides the service of a predicate for the stranded variables in 4b., d. by which we may indirectly assert the set of sentences that satisfy the predicates of their antecedents. This service, though, does not extend the content of truth beyond DS; it provides the same content indirectly. For knowing that a sentence p satisfies the predicate of the antecedent allows one to detach the consequence, then by DS, one can assert the sentence. For example:
(5) (i) ("x)(F(x) t True(x)) (by assumption)
(ii) F(p) (by assumption)
(iii) F(p) t True(p) (by UI(i))
(iv) True(p) (by MPP(ii), (iii))
(v) p (by DS).
Field (1986, p.58) and Horwich (1990, pp.26-7) have suggested that this function of compendious assertion exhausts the utility of our concept of truth. In effect, we have a truth predicate as a proxy for a substitutional quantifier. With such quantification we could do away with the truth predicate:
(6)a. (Pp)[‘p’ is an instance of EM t p]
b. (åp)[Bill said ‘p’ t p]
But we do have a truth predicate, not because it expresses a substantive property indispensable to our thoughts about realism, scepticism, relativism, linguistic understanding, etc., but just so that we can assert infinite conjunctions and disjunctions. Thus, 4a. & c. are equivalent to 7a. and b respectively:
(7)a. If ‘S1’ is an instance of EM, then S1; and if ‘S2’ is an instance of EM, then S2; ...
b. Either Bill said ‘S1’ and S1; or Bill said ‘S2’ and S2;…
Deflationism is very much a mixed bag and some positions would resist various aspects of the above characterisation. The core notion, however, that deflationism flattens truth so that the content of the truth predicate is exhausted by the contents it covers rather than being caught by a relation between language and the world is, I think, fundamental and it is this notion which is the root of the problems I shall discuss. Some of the differences within deflationism will be looked at in detail, although not exhaustively. I here assume that those aspects neglected do not challenge or even substantially complicate the broad picture I shall present.
3: Truth and Content
An account of truth should do at least two things: tell us what it is for something to be true and detail the content of truth claims, i.e., what conceptual contribution ‘is true’ makes to the meaning of our sentences, the contents we thereby express. On the first issue, deflationism appears to be pretty clear. In opposition to traditional analyses, deflationism offers no general answer to the general question, What is truth? What it is for ‘Snow is white’ to be true is something quite distinct from what it is for ‘Grass is green’ to be true. Any common factor there is to what constitutes the truth of two or more sentences will merely be a reflection of the co-occurrence of the same lexical items in the sentences. This flatness - that the truth of a sentence is not explained by the sentence or its parts being in uniform relation to other elements (facts or objects) - has led some to read deflationism as spurning the notion of a property of truth (e.g., Boghossian (1990) and Wright (1992)). Such flatness is central to what Field (1986) has called pure disquotationism, but the nihilistic reading is typically rejected (e.g., Horwich (1990, 1999), Field (1994a) and Soames (1999)). It is, for sure, open to a deflationist to say that there is no property of truth, that the truth predicate is redundant save for pragmatic effect or the avoidance of plagiarism; insofar as they may be regarded as deflationists, such is often taken to be the position of Ramsey (1927), Ayer (1936), Wittgenstein (1953), Strawson (1950) and Williams (1976), although disagreements may be had here (Field (1986) regards Ramsey as a correspondence theorist and Ayer as departing from pure disquotationism.) Deflationists, however, certainly do not need to take the truth predicate to be empty, and that it does not give way under explicit analysis - that What is truth? is not answered with a corresponding abstract noun - need not be taken to be a mark against its status as expressing a property. If we count properties off non-redundant predicates, then so much gives us a property of truth, albeit a thin one. Characteristically, deflationists stipulate truth to be that property expressed by the predicate which gives the DS instances their a priori status and plays the consequent disquotational role in our language. It bears emphasis that, since deflationism eschews uniform analysis in favour of a flat characcterisation, it can not say much more about the property of truth. That is the very point of the thesis! For the purposes of this paper, I shall happily let deflationism have its property of truth; indeed, I should say that I find little reason to think that there is or could be any uniform account of what would constitute propertyhood such that the deflationary reading may be impugned. Perhaps, however, the interest in whether or not there is a property of truth is due to a conflation with the second issue raised above to do with the content of truth. This question is of much greater interest and will be the focus of the sequel.
What are we saying when we claim that P is true? By DS, it would seem that the answer is P. But if this is the official answer, then we seem to return to nihilism: truth offers a mere linguistic slap on the back. It seems to be often thought that such nihilism may be side-stepped: the quantificational contexts which motivate the semantic ascent explanation of truth show that, in general, the nihilistic synonymy claim does not hold (e.g., Horwich (1990, 1999) and Soames (1999)). This is indeed the case, if we assume that the appropriate synonymy relation would require the grammatical eliminability of ‘is true’ in all contexts. Yet this is far too strict a construal of sameness of meaning. The real import of our question is what content the truth predicate contributes to P is true that is not already articulated by P. If the answer is ‘None at all’, then while we may tarry over the locution ‘synonymous with’, the content of the truth predicate would be wholly exhausted by the content of that to which it applies. If, on the other hand, truth does introduce an independent contribution to the content of its hosts, then what on earth is it? It does not show up on the right flanks of DS instances, for they are mere articulations of the contents of the sentences claimed to be true. Nor is it contained in the provision of compendious assertion, for that utility is innocent precisely because it extends DS only logically, not semantically. The deflationist seems to be in a corner. He must, on the one hand, concede that the truth predicate has no independent content, i.e., the content of P is true is wholly inherited from, or exhausted by, P. On the other hand, he must steer clear of concluding that truth is a mere linguistic slap on the back, for that would presage nihilism.
There are two basic ways to manoeuvre here. First, one can simply accept that the content of P is true is indeed wholly provided by P, but then show that this has none of the supposed inimical consequences. Second, one can attempt to forge a difference of content on the basis of providing an account of the content of truth in terms of the schematic properties of DS independent of any particular sentences to which it applies. One might thus say that the content of truth in general is such and such without identifying its content in each particular case with the contents of disquoted sentences. Now I think that neither of these approaches can account for the apparent content of many truth constructions. Indeed, we shall see that they fail precisely on the cases which are supposed to save truth from nihilism, i.e., truth generalisations. I shall explain the relevant features of the constructions in the next section, then show how they are not accommodated by DS in §5.
4: Cognitive Opacity
We have arrived at the idea that deflationism is cornered into the thesis that the content of truth is wholly inherited from, or exhausted by, the content of that to which it applies. Let us assume that the issue of synonymy is otiose. The question is: What is the content of P is true? Can we avoid simply answering ‘P’? Well, why should we so much as attempt to avoid that answer? Gupta (1993) has provided a lovely reason. On grounds similar to those presented above, Gupta takes deflationism to be necessarily committed to truth’s exhaustion by the content over which it has application. Let the ideology of an account of concept C be those concepts to which the account essentially appeals in its explication of C. If we are to possess C, the account says that we must possess its ideology. Turning to deflationism, as characterised, we find that the apparent ideology of truth is that set of concepts expressed in the contents over which the predicate applies, i.e., every concept that may be expressed on the right flank of an instance of DS. But this is absurd. Our English predicate ‘is true’ applies to every declarative sentence of any language (we may exclude ‘factually defective’ sentences, but the kicker remains.) Yet, as a simple matter of fact, no-one understands every concept that may be expressed in a declarative sentence. Thus, either no-one possesses the concept of truth or we each have different concepts of truth which wax and wane with our conceptual competence. The first limb is ridiculous, not to say self-defeating. The second limb seems to be equally absurd; does the student’s concept of truth change after her forgetting what a Taylor series is, but is then as it was after she revises for Analysis 101? Surely not. More simply, if there is no univocal concept of truth, then the set of DS instances do not fix its content, for there is no one concept whose content might be fixed. Again, deflationary truth appears to be empty, contentless.
Gupta’s dilemma is quite beautiful and, to my mind, has not been satisfactorily recognised, still less resolved. I shall not, however, develop the quandary. The problem I have in mind is certainly of the same species as Gupta’s but is its converse. The problem with deflationism, for Gupta, is that it demands that we understand more than we do. My problem with deflationism is that it appears to demand that we understand less than we do. These two sides obviously fit together, but they are independent. Even if deflationism could settle comfortably on either horn of Gupta’s dilemma, the problem I have in mind would remain (we shall consider in §5 a deflationary suggestion from Field that truth is idiolect-relative). The problem is simply that we understand truth where we have relinquished any access to the content to which truth is predicated. What is required of deflationism here, I should say, is an analysis of the relevant kinds of context, for they constitute data on our judgments about truth, they are not a reflection of any particular philosophical or otherwise theoretical account of truth that might be refuted in the abstract. If no such successful analysis is forthcoming, we arrive at the idea that the content of truth cannot be fixed merely by the content of what it covers. To skip ahead, somewhat, this naturally leads to the thought that truth is not flat after all: truth involves some constitutive recognition of a relation between language and world. That is to come. Let us look at how deflationism gives us less than we have.
A salient feature of our concept of truth is what I shall refer to as cognitive opacity: we can understand a sentence, thought or other representation to be true without understanding the representation itself, its content is opaque to our minds. This kind of opacity which attaches to truth is only distantly related to the familiar referential opacity induced by cognitive attitudes, such as belief, desire, etc. If Jones utters ‘P’, and Smith consequently believes what Jones said, then Smith understands whatever Jones said; Smith’s belief content - that P - is not about what Jones said, Smith shares a content with Jones. On the other hand, Smith might think what Jones said is true without understanding his words at all. Here, Smith’s content is surely about ‘P’ - what Jones said - for it cannot be the same content as is entertained by Jones: ex hypothesi, Smith lacks access to that content. Jones’s reliability might be unimpeachable in Smith’s eyes; so, if Jones says ‘P’, then Smith thinks ‘P’ is true. The commonality with referential opacity is that perhaps both notions are best expressed via quotation, although cognitive opacity does not depend upon quotation. It makes no difference how Smith picks out Jones’s utterance - singular description, quantification, name, pointing, whatever. The point is that he can still think that it is true without understanding it. On reflection, it is obvious that we might have all kinds of reasons or not much reason at all for thinking, believing, hoping,… that ‘P’ is true, without understanding that P. One may trust one’s interlocutor; one may know that the sentence has been proved; one may recognise that the sentence is a tautology; one may infer a claim from general grounds (e.g., its written in the Bible); one may hypothesise or conjecture truth with a view to future understanding; one may hope that a colleague’s abstruse results are true; and so on and on.
The issue of cognitive opacity is certainly not a central feature of the deflationist literature; the prevailing view, insofar as one is discernible, appears to be that the issue is trivial. This view is perhaps engendered by the thought that the opacity effects are restricted to heterophonic truth claims, those expressed by the truth predicate of one language being ascribed to a sentence of a foreign language. The discussion of such claims has focused on their formal peculiarity: their DS instances can only be formed at the cost of creating a jumble of languages such as (8):
(8) 'Der Schnee ist weiss' is true iff der Schnee ist weiss.
Note that (8) is neither an English nor German sentence. This, though, is not the source of the problem. The trouble for deflationism is that while a monolingual English speaker can entertain the left-flank of (8), the content of his thought is clearly not equivalent, for the speaker, to the right flank. In short, the content of P is true just cannot here be inherited from ‘P’ because one can understand the first sentence without understanding the second. Prima facie, the content of truth cannot be fixed by the content to which it applies, because we can possess the first without the second. There is more to truth, it seems, than disquotation provides.
One option of escape, canvassed to me by more than one philosopher, is to claim that an English monolinguist, say, does not in fact understand “‘Der Schnee ist weiss’ is true” because he does not understand the subject sentence. Russell’s invidious contrast between theft and honest toil springs to mind. It is difficult to see what possible grounds there can be for disclaiming such a speaker’s apparent understanding, and I have seen none whatsoever offered. It might be that the speaker’s understanding is in some sense etiolated (see below), but it strikes me as simply absurd to think that the speaker is uttering gibberish, that his mind is blank. In a similar vein, it has been suggested to me that the relevant concepts are all ‘terms of art’, and cognitive opacity is just not in the rubric of a deflationary understanding of truth and content. Well, this might be so, but are we not concerned with our concept of truth? Terms of art are there to explicate our concepts, not to substitute them.
It might be thought that cognitively opaque truth claims are really quite marginal, or perhaps in some sense degenerate, to be looked at askance. I shall look later at a version of this complaint which says that opacity arises due to quotation and sentences; if one favours propositions, the problem evaporates. For the moment let us stay with sentences, for many do favour the sentential version of DS anyhow.
Firstly, there is indeed something about cognitive opacity which encourages mistrust, but feelings do not lead to conclusions. The kind of scenarios intimated above certainly seem coherent, and, without an independent proposal as to what might be amiss with them, it would be question begging to insist that something must be amiss on no basis other than that the truth claims are not caught by DS. In the absence of an alternative diagnosis, perhaps their oddness is due to their departure from the norm that we should be responsible for our truth claims; we have no right to be going about claiming such and such is true without knowing what such and such amounts to. Cognitive opacity obliges us to borrow the grounds for our claims, for we cannot assess the claims ourselves. But such deference, I should say, is perhaps not that uncommon and has certainly been accepted by many in the not unrelated area of natural kind reference (see Putnam (1975)). Moreover, we are still responsible for our claims to the extent that we should have some grounds for trusting the source of the claims. Either way, for one’s reasons to be vicarious is no sign of conceptual incoherence (see §5). Further, marginal data sometimes hold the key to our understanding of the wider phenomenon. Whatever its epistemological status might be, cognitive opacity cannot be dismissed by the deflationist as marginalia precisely because it is prima facie data against any flat characterisation of truth.
Secondly, the above points are somewhat academic, for cognitive opacity arises in the very contexts which are meant to buttress the idea that our grasp of truth is exhausted by our grasp of the contents to which it applies. Recall that, since truth applied to a given sentence is an indirection - the equivalence of DS allows us to disquote and drop the predicate - the raison d’ être of the truth predicate is said to be its provision of the means for compendious assertion, its being proxy for a substitutional quantifier. Consider again the cases discussed above, here exemplified in GT:
(GT) (i) Everything Gödel said is true
If Gödel said ‘S1’, then S1; or if Gödel said ‘S2’, then S2; etc.
(ii) Every instance of excluded middle is true.
If ‘S1’ is an instance of EM, then S1; or if ‘S2’ is an instance of EM, then S1, etc.
(iii) Goldbach’s conjecture is true.
If ‘S1’ is GC, then S1; or if ‘S2’ is GC, then S2; etc.
The point of these readings is that they do not go beyond the aegis of DS. For example, for any sentence p, if we know that Gödel said p, then that licenses us to say p, just as if we had predicated truth of p. Disquotation is still operative, but rather than explicitly being given a sentence, we are given a condition, as expressed in the restriction on the quantifier, whose satisfaction by a sentence allows us to disquote. In effect, then, the contents of the generalisations are exhausted by the contents of the sentences covered. Such, after all, is the intention behind the notion that truth is merely a device of utility; if the contents of truth predications were not caught by the contents to which they apply, then fixing the set of DS instances would not capture the content of truth. If, then, cognitive opacity restricts the DS-characterisation of the content of individual truth claims, we should expect it do likewise where an indefinite number of sentences are at issue. The same reasoning applies going the other way: we are appealing to a general condition, as expressed in the restriction on the quantifier, to license individual truth claims, but no such condition determines that any speaker will understand the sentences that satisfy it. The extent to which the sentences are understood will be a function of individual speakers’ conceptual wherewithal, not the intrinsic semantic competence called upon to understand the generalisations. It follows that while truth claims will be licensed, their disquotations will not be.
This problem does not affect the standard deflationary reasons given for our recourse to the truth predicate (pragmatics aside): (i) that what we want to claim to be true is a number of sentences too numerous to assert - everything Gödel said, every instance of excluded middle, etc. - and (ii) that we are ignorant of the sentence(s) in question - perhaps Goldbach’s conjecture. Both of these reasons bear on our performance not conceptual competence; that is, it is assumed that we understand the sentences that fall under the restriction on the quantifier; otherwise, we would not understand the disjuncts which are supposed to determine the content of the generalisations. But of course, we do not understand all the sentences at issue.
Clearly, understanding the sentence, ‘Everything Gödel said is true’, does not involve understanding the sentence ‘Every z-consistent finite extension of Peano arithmetic contains an unprovable formula that is satisfied in the intuitive model of the arithmetic’. Likewise, understanding ‘Every instance of excluded middle is true’ does not involve our understanding each instance. This point is unfortunately missed by many because of a use-mention confusion. If we believe that everything Gödel said is true, then, it seems, we should assent to
(9) If Gödel said ‘Every z-consistent finite extension of Peano arithmetic contains an
unprovable formula that is satisfied in the intuitive model of the arithmetic’, then every
z-consistent finite extension of Peano arithmetic contains an unprovable formula that is
satisfied in the intuitive model of the arithmetic
But while the generalisation clearly obliges us to think that (9) is true - if we denied it, we would contradict ourselves - (9) itself can express an aspect of the content of our belief in Gödel’s invariable veridicality only if we understand what z-consistency is, what finite extensions are, what Peano arithmetic is, etc. For by conditional detachment - left-right across the DS instance - we should be able to assert, not merely assent to, what Gödel said. As it is, most people are quite happy not to have the foggiest idea what any of these terms mean, but they are not ipso facto semantically confused when they declare that everything Gödel said is true. It is, for sure, a complex issue what is involved in being able to express some content P, but merely assenting to ‘P’ on general grounds - because Gödel said it - does not constitute understanding by anyone’s lights. By DS and (9), a speaker who lacks the appropriate concepts is able to do nothing other than dumbly assent to a sentence about matters beyond his conceptual reach. For example, the constituent concepts make no contribution to other contents the speaker possesses; the speaker accepts no content governed inferences from or to the sentence; the speaker is constitutively unable to recognise grounds which would confirm or refute the sentence. In sum, the content of the sentence would be unstructured for the speaker, precluded from playing any role in the speaker’s mind, either in relation to other contents or to external conditions. But content is not like that. (See Author 3 for a detailed discussion of the content of quantification.)
As it stands, then, any version of the inheritance thesis appears to be belied by the very constructions which are meant to define the utility of a deflationary truth predicate. Before moving to how deflationism might revise this appearance, we should deal swiftly with a concern raised to me on a number of occasions (the thought also seems present, though not explicit, in Grover et al. (1975), Horwich (1990) and Soames (1999).)
So far, cognitive opacity has been discussed with reference to sentential DS and, consequently, generalisations have been treated as featuring quantification over sentences. Now it might be thought that cognitive opacity is a symptom of this choice of sentences as primary truth bearers with subjects of the truth predicate being quotations of sentences. However, if propositions are understood to be primary, then cognitive opacity seems not to arise. Consider (10):
(10) The proposition that snow is white is true.
It is not possible to understand (10) without understanding the restrictive relative clause in the subject (Recanati (2000) dubs this transparency feature of ‘that-clause’ reports iconicity.) But that clause is just what is claimed to be true. Consequently, anyone who understands (10) will, all else being equal, understand (11):
(11) The proposition that snow is white is true iff snow is white.
If we take this form of DS as default, the deflationary inheritance thesis appears to go through, because the content over which truth is defined is articulated in the left flanks of DS and so must be accessible to anyone who understands the truth claim. In sum, a truth predicate of propositions is essentially disquotational.
This reasoning is flawless, but it deflects not a jot the problem of cognitive opacity. First off, as data, speakers understand the predication of truth to sentences they don’t understand, sentences which express propositions they can not entertain. It is really beside the point to find a construction by which such a truth claim cannot be expressed, for such claims can be expressed otherwise and we still lack an account of their content by deflationary strictures. So, a move from sentential DS to propositional DS might have various benefits, but resolving cognitive opacity is not one of them. More significantly, propositional DS offers no help for the inheritance thesis regarding generalisations. Consider Horwich’s (1990, pp.3-4/32-3) suggestion for the form of generalisations with propositional truth bearers, where ‘<p>’ is a propositional nominal place holder:
(PG) ("x)[x = <p> & F(x) t true(x)]
This offers no advantage whatsoever, for, again, Horwich reads it as giving way to (12) and so as implying that an understanding of the generalisation involves an understanding of every expressible proposition. This conclusion falls foul of cognitive opacity rather than resolves it.
(12) If the proposition that S1 is F, then S1; and if the proposition that S2 is F, then S2,
The same reasoning applies to the prosentential analysis of Grover et al. (1975). Grover (1992) does admit a sentential truth predicate taking quotations as subjects, but understands that use to be marginal and explicable by the official story, under which, e.g., ‘Everything Gödel said is true’ is analysed as (13)
(13) For all p, if Gödel said it is true, then it is true.
Here, it is true is a variable of sentential position bound by the prefixed quantifier; for each instantiating value of ‘p’, the prosentences inherit its content. Thus, an instance of (13) is not (14), but is (15):
(14) If Gödel said ’CH is satisfied in a model for ZFC’ is true, then ’CH is satisfied in a
model for ZFC’ is true
(15) If Gödel said ‘CH is satisfied in a model for ZFC’, then CH is satisfied in a
model for ZFC.
Such is the very point of prosentences: they allow quantification over sentences via variables in sentential position, rather than variables in singular term position whose values are not sentences themselves but their names. But this just means that the values of the variables will be in assertoric position, i.e., the sentences will be clauses of the speech-act verb, which implies that a speaker who understands the generalisation will also understand every sentence which may occur in the position. Again, cognitive opacity is not explained.
5: Some Suggestions
As explained at the foot of §3, there appear to be just two options for the deflationist. First, he can accept the inheritance thesis in the strong version that P is true has the same content as P and then seek to explain the above data in line with the thesis. Second, he can defend a weaker version of the inheritance thesis under which P is true has a distinct content from P, and then seek to show that the data adumbrated is quite consistent with deflationism. Both of these approaches have been pursued. I shall first look at Field’s following of the first one, then Horwich’s and Soames’s following of the second one.
Field (1994a, 1994b) defends what he calls pure disquotationism (the position was first advertised in Field (1986) although not endorsed):
(PD) (i) The content of the truth predicate, as understood by speaker S, is restricted to the
sentences S understands.
(ii) For each speaker S, P is true is cognitively equivalent to P
The first thesis is a restriction of truth to idiolects. Here Field happily settles on the second horn of Gupta’s dilemma: the content of truth is indeed different for different speakers. This thesis might seem an easy victim to the absurdities raised in the above discussion of the dilemma. Indeed it might. But the position must be understood in light of Field’s wider commitments. For instance, Field (1986, p.58) deserves the greatest credit for properly recognising that a disquotational truth predicate can only be defined for sentences understood. If we don’t understand a sentence P, then it just “makes no sense to wonder whether [P] is true in the disquotational sense”, for to do so would be to wonder whether P. Field’s methodological point, then, is that if one is a deflationist, (i) is something one has to learn to live with. More significantly, Field’s (1994a, 2001a) general account of content is based on individual conceptual/computational role, under which content attributions are made on the basis of a similarity with one’s own case. Thus, Field is not proposing that we all necessarily talk past each other, but that our mutual understanding is a function of mutual simulation of conceptual role. Thus, we can perfectly well understand the truth-thoughts of another speaker, but in doing so we are using our own thought of the other’s content as the disquotation of his truth claim; we are not thinking of the other’s content as a relatum in a mind-world relation, i.e., truth is still defined on our own content and so remains disquotational. This position is motivated by Field’s long standing Quinean suspicions over inter-linguistic synonymy. We may profitably skip over the details of Field’s general understanding of content, yet the extent to which his account does not work for truth may be read as proportionally militating against the account in general. Our chief concern is with Field’s second thesis.
. Field appears to intend the claim of cognitive equivalence to be somewhat impressionistic whose details are to be provided once we have some working inferential/computational role account of content. Still, let (CE) fix what Field has in mind:
(CE) ("S)("C)[P is cognitively equivalent to P* for speaker S iff
(i) S holds P under cognitive attitude C iff S holds P* under C &
(ii) there is no Q such that if S holds Q under C, then S holds P under C but not P*, or
P* under C, but not P]
The first condition tells us that if a speaker believes, doubts, rejects,… P, then he will believe, doubt, reject,…P*, vice versa; and the second condition says that this coincidence is impervious to anything else the speaker might believe, doubt, reject, etc.
Unlike Field’s first thesis, this second one, or at least its import, has been commended by numerous others. The prosentential theory (Grover, et al. (1975) and Grover (1992)) appears to entail something approaching a cognitive equivalence: by the theory, True(P) inherits its content from 'P', and, so anaphora-like, has the same meaning as 'P'. I am circumspect about attributing the thesis to Grover, for in at least one place she considers a metalinguistic use of ‘true’ that would resist a straightforward explanation in terms of cognitive equivalence, although it is presumed that it would still be explainable in terms of anaphoric discursive connections (see Grover 1992, Chp.6, esp. §4.1). However, the official line is that “a token of a sentence like…’”Snow is white” is true’, has as its propositional content - in a given context - the content of its antecedent [viz., ‘Snow is white’]” (Grover, 1992, p.180). In general, all those who would claim that is true expresses no property, such as Ramsey (1927) and Strawson (1950), are also committed to some form of cognitive equivalence, notwithstanding the pragmatic dimension to ‘is true’. To keep things finite, we may presume that if Field’s theses fail for principled reasons, then so do those of Grover and the others. I shall not argue that here, although it will be clear how the arguments transplant.
Now the coherency of cognitive opacity amounts to a prima facie confutation of Field’s first thesis: we appear to understand truth where we don’t understand what is true - our concept of truth stretches beyond our idiolects. Consequently, the second thesis also falls: if P is outside of my idiolect, I can believe that P is true, but can not believe P itself. What is the deflationary defense?
Although Field (1994a) presents his discussion in terms of "applying "true" to sentences in other languages", he is explicit that cognitive opacity, not just heterophonicity, is the real issue. Still, as we shall see, he runs the two issues together. Field’s (1994a, p. 274) favorite encapsulated formulation of his pure disquotationism is: “a sentence is disquotationally true iff it is true-as-I-understand-it”, where the right flank is explicated via (PD). Thus, if the problem were simply one of foreign languages, then it would have no purchase on Field’s account, but the problem directly concerns idiolects.
For the purposes of this discussion, let us again appeal to a monolingual English speaker - Bill - who has ground for thinking that
(16) ’Der Schnee ist weiss' is true
(or, if one prefers, ‘The proposition expressed by the sentence ‘Der Schnee ist weiss’ is true’). Now what Field wants to show is that the truth predicate in (16) may still fall under PD, even though Bill does not understand the quoted sentence. Field presents three approaches. The first is regarded as "the least satisfactory", the remaining two as equally viable, though suitable for distinct purposes (Field (1994a, p.272)). I shall argue that none of the three treatments offer a satisfactory account of cognitive opacity.
Field's (op cit, p.272) first proposal is "extended disquotational truth". Here (16) would give way to (17):
(17) 'Der Schnee ist weiss' is synonymous with a sentence of mine
that is true in the purely disquotational sense.
Field appears to be reasoning as follows: 'The problem (16) poses for disquotationism is that 'Der Schnee ist weiss' is not in the speaker’s idiolect, and so he cannot disquote. There is no getting around this. But what (17) offers is a sentence the monolinguist does understand that means the same as 'Der Schnee ist weiss', and this sentence may be taken to be true-as-Bill-understands-it. This sentence of Bill’s idiolect may then express the content of what his interlocutor is saying and thus act as the quasi-disquotation of (16).'
Field commends that this proposal be avoided if possible. It is a clear departure from pure disquotationism in that the truth of a sentence is explicated in relation to another sentence, and so any DS instance on the model of (16) would lose its flatness, i.e., the content of truth would not be directly inherited from the content covered but by a relation between sentences. It also pivots on an inexplicated notion of inter-linguistic synonymy which Field is leery of for familiar Quinean reasons (see Field (1986, 1994a, 1994b).) Field (1994b, p.223, n.3) considers inter-linguistic synonymy to be an evaluative rather than factual notion, cognate with good translation, which is fine on its own terms but would introduce profound vagaries into one’s account of truth. Nor, of course, may synonymy be unpacked in terms of sameness of truth conditions, for that would obviously be illicit for a deflationist: the concept of truth would be employed in the explication of a ...means the same as... relation, and so would not be merely disquotational. Field (1994a, p. 272) suggests that the deflationist might find “an unobvious way” in which to “admit a useful and well-behaved notion of extended disquotational truth”. Still, such a way would perhaps be redundant, for any virtues of the present proposal can be otherwise caught by Field’s further proposals.
It bears emphasis, though, that even if some notion of synonymy were fit to play an explanatory role in (17), cognitive opacity would remain unexplained. We can rephrase (17) by turning the putative synonymy relation into a condition on an acceptable DS instance. Thus:
(18) (åp)[If Bill knows that ‘p’ (in his idiolect) is synonymous with ‘Der Schnee ist weiss’,
then Bill holds that ‘Der Schnee ist weiss’ is true iff p]
Now (18) is patently true, but that there is a sentence ‘p’ synonymous with ‘Der Schnee ist weiss’ in Bill’s idiolect does not mean that Bill knows that it is such. But we are assuming that Bill knows no German, which amounts (more or less) to Bill’s not knowing, for all p in his idiolect, which German sentence p* is synonymous with p. (18), then, does not characterise what Bill understands; it simply specifies a condition under which Bill would know a DS instance for ‘Der Schnee ist weiss’, but cognitive opacity arises precisely where the antecedent is not met. If (18) were to resolve the problem of cognitive opacity in general, then it would account for the cases where we lack the concepts expressed in sentences we claim to be true (set theoretical concepts, say); but this is does not do. Here the problem is not only that we don’t know that p is synonymous with the sentence claimed to be true, but that we also lack p tout court. I shall return to this issue presently.
Field's second approach is to accept language jumbles, and let foreign sentences form the right-hand side of DS instances. Thus, (16) is accounted for as if it were homophonic, giving rise to the earlier encountered (8):
(8) 'Der Schnee ist weiss' is true iff der Schnee ist weiss.
Field (1994a, p.274) is right to say that (8) is "perfectly well understood despite its not conforming to the grammatical rules of any standard language". So long as a sentence is understood, a speaker is free to use it in conjunction with any other understood lexical items, grammar permitting. But here's the rub! (8) simply does not express a cognitive equivalence for Bill, for the truth claim is cognitively opaque to him; disquotation is thus precluded. Field is well aware of this. Even so, a deflationist would be justly loath to eschew (8). It is optimally simple as a disquotational account of heterophonic truth claims: it appeals to no notion of synonymy or its cognates and it provides a uniform account for any sentence a speaker understands, whatever the language in question may be. Still, it offers no amelioration to the problem of cognitively opaque truth claims. Or so it seems; Field has since changed his mind on this, as we shall see.
Field's tactic is to offer a third option that complements rather than competes with the language jumble approach. The putative virtue of this third option is that it can "be used even for those sentences we don't understand" (Field (1994a, p.274).) So, the virtues of the jumble approach can be enjoyed without foregoing an account of cognitive opacity. This dual strategy, of course, means that a uniformly flat disquotationism is forsaken. Even so, if non-uniformity is the only price paid for a fully general account of truth claims, perhaps it is worth paying. Uniformity preserves simplicity and elegance, but such virtues ought to be compromised if the alternative is a partial theory.
The central problem for the first approach is its ineliminable appeal to synonymy. Field's third suggestion is to rid himself of this troublesome concept, and in its stead appeal to a notion of "truth relative to a correlation". On this approach, (16) is analysed as (19):
(19) "Der Schnee ist weiss" is true relative to a correlation with a sentence
of mine which is true in a purely disquotational sense.
Now "correlation" is not merely another term for synonymy. If it were, no advance would be made on the first option. Still, the correlates cannot be arbitrarily chosen: they must, in some sense, share the same meaning (equivalent conceptual role, say). The notion of correlation caters for those who flinch at an objective synonymy relation; it is neutral between disputes of meaning or content. So, those who follow Quine, and reject any objectivity claims in the realm of meaning, may still appeal to the notion of a correlation and cash it for the "context-sensitive and interest-relative" notion of a good translation (Field (1994a, p. 273)). The correlation approach, therefore, is more flexible, and thus more useful than the first approach.
Like the extended approach, the correlational account furnishes an instance of DS for the subject who understands the named sentence (whether foreign or not) of a given truth claim. But such a service is now provided by language jumbles. The motivating claim, rather, for the correlational approach is that it accounts for cognitively opaque truth claims. If it does so, then so does the extended approach, setting aside any qualms about synonymy; for both accounts give conditions for a mapping onto a truth claim of a sentence that (in some favoured sense) means the same as the named sentence of the truth claim but may also be true-as-the-speaker-understands-it. But this does not entail, of course, that the subject knows any sentence that meets the conditions. An account of truth is not, as such, an account of meaning. In essence, then, Field's correlational account specifies the conditions under which cognitive equivalence would hold between an opaque truth claim and a sentence in a given subject's idiolect. Perhaps not much hangs on precisely how we are meant to understand extensions of disquotation, yet, not only does the truth predicate not act as a formal device of disquotation, but there is also no specification of a sentence that is cognitively equivalent to the truth claim. Field, however, appears to assume that the account enables a specification of a correlated sentence equivalent to the named sentence.
Field (1994a, p. 274) writes, in support of the correlation account,
in trying to come to understand a foreign sentence we may try out several different correlations to our own sentences to see which makes most sense.
If our view of cognitive opacity is restricted to foreign sentences, then Field's assumption appears correct. We may assume that all natural languages are more or less equally expressive. Granting this, it follows that Bill knows that there is some sentence of his idiolect that correctly correlates with the German sentence 'Der Schnee ist weiss', and, as Field says, we can imagine Bill conjecturing upon various sentences of his idiolect that would provide him with some understanding of his German interlocutor; upon settling on one, that sentence may then act as the disquotation of the truth predication to the German sentence. Note that while the truth claim would indeed give way to a sentence whose truth is disquotationally true for Bill, the truth claim itself would not admit disquotation. This, in itself, is quite coherent, but there is a crucial difference between this account and the standard homophonic story. There, a subject's understanding of a truth claim just is its disquotation, such is the whole point of PD. In the cognitively opaque case, however, a speaker need not have any sentence in mind, whether conjectured or not, to understand the truth claim. This follows from the fact that Bill can understand a truth claim antecedent to the trying out of different correlations. After all, it makes perfect sense to think of Bill as simply accepting the truth of a German utterance on trust, and not being concerned with any correlation. Field's suggestion, therefore, is somewhat besides the point: correlations are potentially available, yes, but they do not constitute what it is to understand a truth claim opaquely. And so, with the jumble approach in place, the correlational approach appears otiose.
This line of criticism might be objected to on the grounds that what is necessary to understand cognitively opaque truth claims is the capacity to form correlations, not the actual hypothesising of given correlations. After all, the subject is said to know that some sentence correlates, not any specific sentence. It is clear, however, that there is no guarantee that, for every truth claim a subject understands, there is some sentence of his idiolect that correlates with the quoted sentences of those truth claims.
As mentioned above, there is the impression that a subject can always have some correlate in mind, but this is because Field's discussion only concerns truth ascriptions to foreign sentences. We assume that English and German, say, are equally expressive languages; consequently, for any German sentence, an English speaker can find an appropriate correlate sentence in his own language. But this happy coincidence does not hold generally. Trivially, not every speaker understands the same set of sentences. The issue of cognitive opacity pertains to what individual speakers understand (their idiolects), not to what can be said in particular designated natural languages. Cognitively opaque truth claims, therefore, need not involve foreign sentences. A truth claim is opaque because the subject does not understand the object-sentence, not because the object-sentence is foreign.
Andrew Wiles's proof of Fermat's last theorem was widely covered in the media. The key to the proof consisted of a sub-proof of the Taniyama-Shimuru conjecture: Every semi-stable elliptical curve is a modular form. Newspapers featured the sentence (or its equivalents)
(20) 'Every semi-stable elliptical curve is a modular form' is true.
Now, we may presume, the journalists in question know nothing of topology, and nor do they expect the readers of their copy to be appraised of the subtleties of the complex plane. Still, the journalists are entitled to the truth claim and so are their readers. Indeed, all parties concerned know (20) (assuming that the report is true). They know (i) that proof implies truth, (ii) the statement of the conjecture, and (iii) that Wiles's proved the conjecture. This is all quite familiar, but it does not involve a subject knowing that every semi-stable elliptical curve is a modular form. He knows that the conjecture has been proved, and that is sufficient entitlement to know that (20). For a mere follower of the above reasoning, then, (20) is not cognitively equivalent to its disquotation. And what would be an appropriate correlate for the subject-sentence of (20)? For the untrained nothing would spring to mind. If the concepts are lacking, so is a correlation.
The same point, of course, holds for any sentence which expresses concepts absent from the repertoire of a given subject. Consider the sentence: "Kleptomaniacs are mendacious". Many English speakers, if not most, do not know what kleptomaniacs are, nor what it is to be mendacious. Nevertheless, many would readily recognise that the sentence is an English declarative, cued, perhaps, by the occurrence of an apparently plural subject in agreement with the third-person plural form of be. Still, mere recognition that the sentence is grammatical is no reason to think that it is true. But now consider the sentence
(21) If kleptomaniacs are mendacious, then kleptomaniacs are mendacious.
Here grammatical form is a reason to think that the sentence is true, notwithstanding the fact that a subject might not know what is being said, what it means. All the subject need recognise is that any sentence which says that if such-a-things are so, then such-a-things are so is true. The subject, then, has a sound reason for claiming that (21) is true. But precisely because the subject does not know what it is for such-a-things to be so, the truth claim is not equivalent, for her, to its disquotation. Obviously this result generalises to all grammatical constructions which imply truth.
A subject, for sure, has the capacity to develop the concepts to be able to express an inexhaustible range of judgments, including, it goes without saying, those used in the above examples. But the correlated sentences Field imagines are clearly those a subject does understand, not those he would understand were he to garner the right knowledge. This being so, the correlational approach advances an account of cognitive opacity only for those truth claims whose subject sentences have a translation that is understood by the speaker. The account does not touch the cases where the sentence is simply not understood, where the concepts expressed are unavailable to the subject.
Field (2001b), in a postscript to his (1994a), suggests that while a correlated sentence might well not be available for each truth claim opaque to a given speaker, such unavailability just means that these claims would possess an indeterminate content for the speaker in step with the indeterminacy of the subjects of the predicate (for the speaker). In effect, this thought amounts to the thesis that only the second potentially optimal jumble account need be endorsed. That is, the truth predicate enables us to incorporate ‘new’ sentences into our idiolects. The extent to which these sentences may enjoy an independent inferential life, as it were, in our thoughts is the extent to which we understand the predication of truth to them. Thus, the real issue for Field is not to understand how we can ascribe truth to sentences we don’t understand, but how we can understand our not being able to do so. I can see no reason, however, for such a counter-intuitive move. As we have seen, a speaker is perfectly able to express coherent thoughts with opaque truth claims, something he is not able to do with their subjects. Moreover, the determinacy or otherwise of our generalised truth thoughts appears to be wholly independent of the determinacy of our understanding of the contents covered, for the first type of thought does not provide access to the contents covered - nothing is given to be incorporated. Thus, the idea of incorporation is here inapplicable, but cognitive opacity still obtains. Perhaps some notion of grades of determinacy can be elaborated, but without such a notion, the thought that an opaque truth claim and its sentential subject must march in step as far as the speaker is concerned appears to be a mere reflection of a commitment to the cognitive equivalence thesis, a thesis which is called into doubt by the very phenomenon of cognitive opacity.
It should be noted that the above problems do not ride on the back of any particular view of meaning or content. They are carried along by nothing more than data about our judgments on truth and their confrontation with Field’s suggestions. I do not, therefore, contend that my stance against the inheritance thesis is apodeictic. Yet the confounding data are so apparently recalcitrant that I think it reasonable to conclude that something is grievously amiss with the very idea that one can give a flat interpretation of truth. Where this conclusion should lead us will be discussed in the following section. Before that I shall look at the weaker version of the inheritance thesis which abjures cognitive equivalence while still holding that the content of truth is wholly provided by, via DS, the contents it covers.
The kind of position I have in mind is that offered by Soames (1999) and Horwich (1999). There are, for sure, differences between the two, but their attitude towards cognitive opacity is quite similar: all there is to truth is recorded in the instances of DS, and this gives truth a constant feature which applies independently of whether an individual speaker understands the contents to which truth is applied. The immediate problem here is that deflationism says that there is no uniform, constant content to truth claims: truth is flat with the contents it covers. How, then, can a speaker extract a content from DS which can apply to P independently of whether the content of P is available? Horwich (1999) simply asserts that there is a constant meaning to truth which a speaker can have in mind when he attributes truth to a claim made by an interlocutor he takes to be reliable, even though he does not understand what he said. Horwich appears to have in mind the notion that a speaker is disposed to accept a priori each instance of DS (In Horwich (1998), such a disposition is taken to constitute the ‘meaning’ of truth). Similarly, Soames takes speakers’ a priori acceptance of DS instances to be explanatory basic, constitutive of possessing the concept of truth. But these claims appear to be non sequiturs as far as cognitive opacity is concerned.
Competent speakers might well be disposed to accept DS instances, but how, precisely, does this help us? When Bill trusts Karl and claims after him that ‘Der Schnee ist weiss’ is true, Bill is precisely not disposed to accept the relevant propositional DS instance, for he knows no German. He might accept the DS language jumble for the sentence, but if he does, it would be because of its morphological properties rather than its content, and this would reintroduce cognitive opacity. The point is simple. An appeal to what a speaker is disposed to accept does not identify the speaker’s underlying reasons. In the non-opaque case, a speaker is disposed to accept a DS instance for ‘Snow is white’ because, presumably, he thinks that the whiteness of snow is a necessary and sufficient condition for the truth of the sentence. Such, after all, is what the DS instance says. In the opaque situation the scenario is quite different. A speaker would accept a jumble DS instance, not because of what it says, but on the basis of a reflection upon its form. But this means that the speaker would accept the DS instance because he thought it was true independent of what it says, just as one would accept every instance of a tautological schema. This is just a recapitulation of the problem with which we began: cognitive opacity suggests that truth is not flat with content. As an explanation of cognitive opacity, an appeal to a speaker’s dispositions appears to be circular.
It bears emphasis that I am not here suggesting that there are two notions of truth, one for opaque use, another for transparent use. No-one, I take it, favours such an egregious position. It might seem, then, that if there is just the one notion, and that is (in whatever sense) captured by instances of (DS), then opaque usage may be explicated via a counterfactual supported by the transparent case. Thus, Soames (personal correspondence) has suggested that if Bill were to understand a given German sentence, then he would take its truth to consist in no more than the appropriate DS instance. As far as it goes, I think this is correct, but it is the difference between the cases that is important. In the cognitive opaque case, Bill can only accept a DS instance on the basis of its schematic features. The thought he entertains, therefore, is not expressed by any DS instance with the target truth claim on the left flank simply because he knows no disquotation; his thought, rather, must be about the form of a DS instance. And this thought can only be that the instance is true, for only such a thought will motivate rational assent without understanding. Cognitive opacity again!
Similarly, pace Horwich’s apparent claim, a brute acceptance disposition towards the DS instances is not sufficient to constitute possession of the concept of truth. To tackle properly the putative role of dispositions is obviously beyond my present scope, although their explanatory status is, I should say, dubious at the very best (see Author 1, 2). Speakers no more find themselves salivating at the sounds of particular words (hence the comedy of Homer Simpson’s inhumanity upon his hearing ‘doughnut’ and the like), than they find themselves saying ‘Yes’ at particular sentential enunciations. Indeed, it is, I think, not hyperbolic - I think, in fact, it’s trivial - to say that appeal to dispositions has made no serious contribution to our understanding of any aspect of human linguistic and conceptual competence. Horwich’s (1998) appeal compounds this judgment (see Author 2).
The situation we have arrived at is that a flat characterisation of truth appears unworkable for cognitively opaque truth claims. This was to be expected: if the content of that said to be true is unavailable, then the content of the truth predication as a whole cannot be understood in terms of it. We have looked at a range of options to alter this appearance, but all stumble on the simple point because all take the content of truth to be wholly inherited or otherwise fixed by the content to which it applies. Perhaps it would not be unreasonable, then, to reject this thesis about truth. Perhaps the two factor intuition of CT has to be respected without collapsing the meaning-world relation onto the content of that claimed to be true. This I shall propose.
The purpose of this paper so far has not been to refute deflationism. The thesis has too many disparate strands for anything so final. All I hope to have shown is that cognitive opacity is not a marginal feature of truth and that the extant deflationisms are unable to accommodate it on principled grounds: the opacity shows that truth claims in general are not flat with the contents said to be true. From the methodological optic of Field (1994a), it might seem that cognitive opacity should simply be placed on the in-tray of deflationism along with much else. I have no argument against non-existent proposals, but I think the above reasoning suggests a different approach.
Let us assume for argument that where a speaker does understand a sentence claimed to be true, then the speaker finds the DS instance a priori acceptable and may even treat the flanks as cognitively equivalent. This breaks down in the cognitively opaque case. If we further assume that there is a univocal concept of truth, then this would indicate that there is a feature of our concept of truth that, while invariant between transparent and opaque uses, nevertheless reflects the difference between the two in that the former uses are not explainable in terms of any DS instance. I am not sure if any thesis worth calling deflationism can accept such an invariant feature, for it is inconsistent with both the cognitive equivalence thesis and the general thought that DS instances are explanatorily sufficient. That said, the feature which I think fits the bill is not a great departure from DS; the feature I have in mind is metarepresentation.
By 'metarepresentation' I mean the representation of a representation as a representation, where by 'representation' I mean something that bears content, whether this be a sentence, a mental state, or something else. So, for a representation to be a metarepresentation it is not sufficient for it merely to embed another representation; rather, it must do so in such a way that the representation-represented relation is available to the possessor of the content. The concept of truth is metarepresentational in this respect: it enables us to think that the represented (the world) is as the representation (the subject of is true) says. On this understanding, to think that p is true is to be in a position to think about p as a representation, over and above taking in p as a fragment of the world. We can model this situation as follows:
(R) 'Snow is white' Þ [snow is white]
(MR) '"Snow is white" is true' Þ 'Snow is white' Þ [snow is white]
In (R) the sentence represents (as indicated by the arrow) that snow is white, where, just as with DS, the content doubles as both meaning and world. (MR) splits the two: it says that snow is white (the italics indicate assertoric force), but as the content of the sentence ‘Snow is white’, i.e., it represents ‘Snow is white’ as representing that snow is white. ‘But does it not then follow that we need some notion of correct/accurate/reliable representation, which would force us back to a correspondence conception?’ I think not.
Firstly, (MR) does not require a notion of ‘true-representation’ in order to be read as entailing that snow is in fact white, for the relationship is here depicted as transparent, that is, the representational relation in (R) is metarepresented by the truth claim in (MR) such that, by disquotation, the content of the truth claim can be articulated in the same terms as that of 'Snow is white', i.e., we can think about snow and its colour. In other words, if we understand 'p' in '"p" is true', then we can see through the truth predicate to the way the world is independent of our choice of representational vehicle. Metarepresentation, therefore, is not inconsistent with a flat interpretation of truth in the present case.
Secondly, no general answer is provided for the question What is truth?: the property of truth is as thin as the deflationist one. Nor have facts been reintroduced as neutral worldly fragments as relata for sentences. Truth is a property of representations and it obtains only if the world conspires with representations' contents. So much I take to be wholly untendentiously expressed by (CT). What I am suggesting is that the concept of truth allows us to think about our thoughts in relation to the way the world is, we are not simply taking in the world when we think a thought to be true, we are assessing a representation-represented relation. This is certainly a large part of what the correspondence conception seeks to capture. Yet, on the present view, the property of truth - what it is for a representation to be true - can be perfectly specified by DS without explicit mention of the representing relation, for that is implicit in our access to the contents themselves. In other words, the extension of is true is fixed against the background of a stable representational access to the world as depicted in the move from language to world in DS. This is the sense in which the initial deflation of the correspondence theory is fundamentally correct (see §2). But to employ a concept of truth in the evaluation of one's thoughts, judgments, beliefs and so on requires acknowledgment of this background, for possession of a truth concept involves an understanding that one’s thoughts about the world can go right or wrong independently of their internal layout. One must, as it were, picture one’s thoughts and the world side by side to see if the latter is as the former says. To possess the concept of truth is to be able to represent one’s self in a representational relationship with the world.
What I have said can happily be read into the first chapters of both Quine (1960) and (1970/86): truth enables us to ascend to thoughts about our relation to the world via our truth vehicles. What deflationism takes from Quine, as I have been understanding the thesis, is that there is no principled bar to our being able to descend - truth can always be flattened. So, if the metarepresentational role of the truth predicate were to be in line with deflationism in general, then one would always be able to move from representation to represented, i.e., always be able to flatten content onto world and so forget about the representation-represented relation. The deflationist, for sure, holds that such elimination is not always possible as a matter of syntax - that’s why we have a truth predicate! But it is assumed that the metarepresentational feature of the truth predicate is always transparent, i.e., one can always see through the predicate to retrieve the content of that claimed to be true; the restoration of objective reference, as Quine puts it. Thus, we have the claim that truth predications to quantifier NPs are equivalent to infinite disjunctions/conjunctions, which implies that we understand each sentence covered. We also saw this claim with Field’s suggestions for tackling cognitive opacity, all of which have behind them the thought that a speaker can always recover the content claimed to be true. But what cognitive opacity shows is that such transparency is not always the case. This is especially so with generalisations themselves. When we think that, say, something Bill said is true, we need not have any claim of Bill’s in mind, although we might; still less are we compendiously asserting anything. Surely, our thought is ineliminably general: we are expressing a thought about something - whatever it was - that Bill said, namely, that it is true. This thought is perfectly coherent even if what Bill said is in fact beyond our ken and so we are not in a position to assert it, even if we would assent to it just because Bill said it. Likewise, if we think that everything Gödel said is true, our thought is about what Gödel said; we do not necessarily take ourselves to be in a position to make assertions about the incompleteness of arithmetic or the consistency of the continuum hypothesis with ZFC. In this sense, generalisation over truth vehicles is a common species of opaque metarepresentation, for to generalise often involves relinquishing understanding: our claim is about what’s true independent of whether or not we understand it..
What emerges, then, from the issue of cognitive opacity, I think, is that is true is firstly metarepresentational, and only secondly disquotational. The latter feature holds just if a subject understands the sentence to which truth is predicated. The former feature holds whatever understanding the subject possesses. Metarepresentation, in other words, is not essentially transparent. In terms of our simple case, we can depict this situation as (MR*):
(MR*) '"Der Schnee ist weiss" is true' Þ 'Der Schnee ist weiss' Þ [...]
Here, 'Der Schnee ist weiss' is represented as a representation, as expressive of a thought, yet what it represents is unavailable to the speaker. As it stands, then, (MR*) does not describe a complete thought, for the thought does not have a bearing on the world: the 'thought' is neither true nor false. Whither the missing worldly part?
If Bill, our English monolinguist, were to understand 'Der Schnee ist weiss', then he would know what Karl, as it may be, is committed to - snow’s being white. That is, from
(R*) 'Der Schnee ist weiss' Þ [snow is white]
he could instantiate the embedded representation relation of (MR*). As it is, Bill does not understand German, nevertheless his understanding of is true, as captured in CT, commits him to the world being a certain way, for (MR*) does represent the German sentence as a representation. Now cognitive opacity arises where we entertain the truth of some representation we do not understand; obviously, then, we cannot be the source of the representation: it must be generated outside of our minds and in such a way for us to consider it truth apt. As earlier emphasised, this second condition is quite lax; the fact that a given individual (a cult leader, say) uttered something might be sufficient. Cognitive opacity, we may say, is vicarious: we get to entertain a thought via the thought of someone else. So, in making his truth claim, Bill is committed to the world being as Karl says it is. Thus:
(MR**) '"Der Schnee ist weiss" is true' Þ 'Der Schnee ist weiss' Þ [what Karl says]
Likewise, our subject scratching her head over the Taniyama-Shimuru conjecture can still claim that 'Every semi-stable elliptical curve is a modular form' is true. She is committed to the world being as Wiles proved it to be. And so on. In general, what completes the thought expressed by a cognitively opaque truth claim is a description of the content of the subject of is true in terms of the thought of another. This description establishes the subject sentence as meaningful, and so gives the whole claim a definite content. And the availability of some such description is guaranteed via the conditions (externally constituted) which led the subject to think the sentence truth apt.
I am not here claiming that, say, Karl's claim commits him to snow’s being white while Bill is only committed to Karl's believing something or other. Both parties will be wrong if snow is not white. The difference is that Karl understands the status of his claim as ultimately bearing on the colour of snow. For him, his truth claim gives him a transparent cognitive access to the world. Bill's thought, on the other hand, is indirectly (vicariously) related to the world; it is contingent upon Karl's thought. He can think that 'Der Schnee ist weiss' is true only via a speaker for whom 'Der Schnee ist weiss' alone may express a thought. But this vicariousness does not affect the truth conditions of the two claims, they are the same, it is only that Bill does not know this; we in the know are free to state them as either (A) or (B):
(A) 'Der Schnee ist weiss' is true iff der Schnee ist weiss
(B) 'Der Schnee ist weiss' is true iff snow is white.
Here we see that the bare idea that the extension of ‘is true’ is to be stated disquotationally remains intact, for how we state the equivalence is not extensionally important. After all, it is not up to us to determine the conditions under which our thoughts are true.
Cognitive opacity, then, does not mark either a metaphysical or logical break from the kind of account we would give of standard truth claims. Truth is univocal; there is no need for any "extended" or "relativization to a correlation" notion of truth. The difference lies in the route to the ground that determines the truth of the claims for the respective parities. If a subject understands a sentence claimed to be true, then he can disquote; if he does not, he can not. But the understanding of is true is uniform across the difference. Such, after all, is as it should be. Cognitive opacity concerns the idiosyncrasies of what subjects understand, their particular conceptual wherewithal. We should not be obliged to re-jig our account of truth because of individual peculiarities. My modest metarepresentational account suffers from no such obligations.
 Field (1986) elaborates a deflationary conception of truth but does not endorse it; he does later in (1994a, 1994b).
 A clear respect in which ACT is rough is that it takes a correspondence theory to be primarily concerned with sentences and facts, whereas the kind of theories proposed by (e.g.) Davidson (1969), Field (1972), and Devitt (1984) take the truth of sentences to be determined by ‘correspondence’ relations between subsentential elements and objects/properties. This difference will not affect the arguments of the sequel, for the crux is that the deflationist says that DS is sufficient; an account of reference or satisfaction is essentially separate from a theory of truth (see Grover and Belnap (1973), Horwich (1990, Chp.7) and Field (1994a)).
 Williams’s (1976) position appears to be that while ‘is true’ is not redundant, it is still not a ‘real predicate’: its sole purpose is to turn NPs such as ‘What Bill said’ into well-formed sentences by which we can indirectly assert whatever Bill said; and because the NP is not a name, there is nothing referred to which ‘is true’ may be true of. Williams is trivially correct about the NP’s not being a name, but that is irrelevant to whether truth is a property or not. We can smoothly treat what as operating like a quantifier, just as other determiners do. Thus: (What x: Bill said x)[true(x)]. Here, ‘is true’ is a real predicate, however that misbegotten phrase might be employed. A much more simple worry for Williams is that we can easily predicate truth to names of sentences. Call the previous sentence ‘Harry’. There can be little doubt that Harry is true.
 For a deflationary response to Boghossian (1990), see Soames (1999, Chp.8).
 What I am referring to as cognitive opacity is equivalent to what Recanati (2000) would call non-iconicity (a representation R is iconic iff it embeds a representation R’ such that entertaining R entails that one entertains R’).
 The cognitive opacity induced by quotation does not depend upon any particular account of quotation. It is obviously flush with the Tarski/Quine hieroglyph theory, under which the flanked material is semantically inert as ‘let’ is in ‘letter’. Equally patent, it is flush with demonstrative-parataxis theories. It is also perfectly consistent with the idea that quotation is a punctuational element signaling that we using the flanked material to refer to itself (see, e.g., McDowell (1980) and Washington (1992)).
 See Quine (1953, p.135; 1966/76, pp.195-6), Grover et al. (1975, pp.99-101), Davidson (1984, passim; 1990, p.285), Field (1986; 1992; 1994a), Gupta and Belnap (1993, pp.27-8), David (1994, pp.135-9) and Chomsky (2000, p.204, fn. 10).
 Such language jumbles were first considered by Quine (1953, p. 135) and dismissed as “meaningless”.
 It might be claimed that we have a plurality of concepts of truth, each apt for a different discourse (e.g., Wright (1999)). The suggestion is of no help in the present situation, even if otherwise commendable. Cognitive opacity is not restricted to certain discourses: the issue bears on what individual speakers understand, not on the subject matter or ‘grammar’ of areas of language. Besides which, deflationism is presented as explanatorily sufficient. Thus, following Wright’s lead would, at the very least, complicate the deflationist line, as Wright himself is at pains to point out.
 Grover, et al. (1975, pp. 99-101) also beg the question against cognitive opacity in their discussion of ‘”Der Schnee ist weiss” is true’. They assume that one’s quoting sentences would be due to pragmatic reasons alone, and conjecture that quotation might be analysed as a ‘Consider’ prefix, which is presented as operating somewhat like Frege’s horizontal stroke. Thus: ‘Consider: Der Schnee ist weiss. That is true’, where the second sentence inherits its content from the considered sentence. Grover, et al. suggest that this analysis has not been entertained because of the spurious thought that one can only mention, not use, foreign sentences. But the issue of cognitive opacity is quite independent of whether or not we can use foreign sentences. If one does not know German, then quoting a German sentence could not possibly be the consideration of a content; consequently, there would be no content available to be inherited by the second sentence. I think this is sufficient to show that there is something amiss with the analysis of quotation, but even if the analysis were accepted, cognitive opacity would remain untouched. Simply as data, we can talk about sentences we don’t understand in all manner of ways - quotation, description, name, quantification, etc. - and attribute various properties to them, including truth. This is where cognitive opacity arises; it does not arise from a spurious restriction, which Grover et al. rightly dismiss, on what sentences we can use (see n.4). Field, as we shall see (§5), is perhaps guilty of the same error.
 Field’s current simulation position was first advertised in Field (1986) via Gordon (1986), although not endorsed. The general idea that meaning attributions are essentially simulative goes back to Quine (1960) and Sellars (1963). A formal presentation of meaning attributions close to Field’s (2001a) Sellars-like account is also to be found in Lehrer (2000).
 For purposes of exposition, I have swapped around Field’s options: the current option is Field’s third, and my third is his second. This difference of order, suffice it to say, does not distort Field’s line of argument.
 The notion of metarepresentation is current in a number of diverse fields (see Sperber (2000)). The formulation and understanding of the notion I am employing is influenced by Pylyshyn (1978) and Perner (1991), although I do not here commit myself to their wider claims.
 It is not clear if Quine’s position is that one should always be able to descend. That one can appears to be central to Quine’s account (e.g., 1970/86, Chp.1; 1987, pp.212-6; 1990/92, pp.79-82); he does say, for example, that “’True’ is transparent” (1990/92, p.82). But Quine also tends, in opposition to Horwich and Field, to distinguish DS from semantic ascent such that truth has a genuine meta-linguistic role that is not reducible to the formation of infinite conjunctions/disjunctions. This seems to me to be an echo of Tarski’s attitude (see especially Tarski (1944, §16; 1969, pp.111-2).) Grover (1992, Chp.9) also sees this difference, although for the reasons given throughout this paper, I think that her differentiation of prosententialism from all other deflationisms in terms of their attitude to metarepresentation is inaccurate.
 Recanati’s (2000) key thesis is that metarepresentation is transparent (iconic, in his jargon). Recanati’s notion of metarepresentation, however, is restricted to direct reporting and, more generally, clausal subordination, i.e., where the reprseneted representation is displayed in the representing representation. I am using ‘metarepresentation’ more broadly; for me, ‘Everything Gödel says is true’ is metarepresentational qua a quantification over Gödel’s representations: the sentence says something about what Gödel said. For Recanati, this sentence is patently non-iconic. Indeed, I understand Recanati to be in perfect agreement with me about the non-iconicity (= cognitive opacity) of the central indirect cases - quotation, quantification, naming, etc. - to which I have appealed to motivate cognitive opacity. Modulo these cases, my disagreement with Recanati is terminological, not substantive.
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