Are deflationist theories of truth an alternative to correspondence theories or an explanation of them?

Prologue

The argument of this essay is that there is no alternative to the theory of truth as correspondence of statements to realities, even though what that means ultimately cannot be made clear.  This epistemic and semantic correspondence is a form of what more broadly is the paradigm of representation, which names a now largely discredited model, if not in semantics and epistemology, in aesthetics and perhaps also the thinking of the political.  This problem, much addressed in recent Continental philosophy, is external to the more technical considerations here, though in structuring the paper as a commentary on a discussion of the problem in a book by French analytical philosopher Pascal Engel (brief quotes from which I have left in the original French, with my English translation in footnotes), I hope to have elucidated a certain exhaustion.  To which are added, at the end, some brief remarks on the extension of these concerns to assertions of matters of value such as that something should or ought to be or be done, or that something is desirable in itself or is good or beautiful (what do such judgments mean?).  

It seems to me that several areas of reply are open, one of which is to use the lack of alternatives in a call for return to order, as in Margaret Thatcher’s defense of capitalism.  Two others are to distinguish truth and knowledge, as Heidegger does, and Alain Badiou with a mathematical idea of truth based on a Lacanian approach to set theory resting in turn on a post-Kantian Parmenidean faith in the identity of what exists with what can be thought.  Another is to follow Nietzsche in rejecting the very idea of truth.  That does not spell the end of philosophy if its concern is at one with its method as that of thinking, whatever philosophy decides thinking to be.  Perhaps what defines the idea of truth is ultimately simply an idea of authority, and if thinking is anarchistic that might be because it is in some way autotelic.  Perhaps a third answer is Aristotle’s, which Heideggerian phenomenological hermeneutics appropriated: thinking, if not truth, is making sense of experience. 

Since this essay appears on a site devoted primarily to discussion of film and thought about it (including in such related fields as philosophy of art), I will close this preface by noting that the statement with which Aristotle begins the Metaphysics is an excellent point of departure for understanding all of the arts of the senses including cinema.  My translation freely modifies, with no care for accuracy of correspondence to the Greek original, the standard English one by Jonathan Barnes:

“Everyone naturally desires to make sense of their experience, and the surest evidence of this is the pleasure we take in the objects of our senses.”

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Are deflationist theories of truth an alternative to correspondence
theories or an explanation of them?

A commentary on Pascal Engel, La Verité

(c) William Heidbreder 2011

 “Le point où nous sommes parvenus semble être le suivant. . . . C’est pourquoi on appelle parfois la théorie en question la théorie de vérité comme redondance, ou théorie déflationniste, parce qu’elle opère une véritable déflation de nos tentatives inflationnistes pour voir dans la vérité une propriété substantielle.”[1]

Introduction

This extract, from Pascal Engel’s short survey of theories of truth La vérité, forms part of a discussion of the question, what constitutes truth?  This question can take at least two different forms: what is it that renders a statement, proposition, or belief true; and what is meant by the “truth” of statements, propositions, and beliefs?   The theme of this passage is “deflationist” theories of truth, sometimes called “minimalist” theories, [2] which equate the meaning of a statement that a proposition is true with the meaning of the proposition. The thesis is that truth can be understood as a sort of linguistic function in lieu of a “relation substantielle” such as the relation a proposition has to a reality in the world, as in correspondence theories.   The stakes include the following: Is there a viable alternative to correspondence theories of truth, and if not, how can the relation of correspondence be understood?  What are the necessary features of the property, relation, or function of being true?  And if to assert that a proposition is true is just to assert it, what, if any, are the necessary features of assertion that must be understood to be implied in its use?  Does the theory of truth we adopt have implications for what kinds of statements can be true, and in particular, how can we understand moral and aesthetic truth claims? 

The various classical theories to which deflationism is an alternative are all theories of what makes a statement, belief, or proposition true.   Deflationist theories present themselves as an alternative answer to this question that is free of all metaphysical baggage and perhaps of the difficulties presented by the other theories.  But are they are an answer to the same question of what makes a proposition true, or do they only explain what it means to hold a proposition to be true, and leave the question of truth-making unanswered?  If so, what is it they succeed in explaining?   If it is true that to assert the truth of p is just to assert p, what can be concluded from this?  And in what sense can truth be a logical function, and in just what might this function consist? 

The extract moves from a problem common to classical theories that turn on the explanation of correspondence to an introduction of deflationism, which holds “truth” to be semantically superfluous, to a brief discussion of the possibility that truth is a logical function of propositions or statements rather than a substantive relationship they have to something else.   In the first paragraph, Engel argues that coherence, pragmatist, and verificationist theories of truth cannot escape the intuition that truth involves the correspondence of a statement or proposition with some kind of reality, while at the same time it seems impossible to explicate the notion of correspondence except, circularly, with reference to the notion of truth.   In the second paragraph, Engel introduces the idea, central to deflationist theories, of an equivalence between “il est vrai que p” and “p”.  This can be explained as giving the necessary and sufficient conditions for p being true: “il est vrai que p si et seulement si p.” One can, then, understand a deflationist theory in at least two ways: as explaining what we are saying when we say that a statement or proposition is true, and as explaining what makes a statement or proposition true or false.   In the third paragraph, Engel briefly explores the intriguing but not fully explicated suggestion that, consistent with the supposed fact that “dire que ‘p’ est vrai, c’est simplement asserter que p,” truth can be considered as a simple logical function of statements or propositions, in contrast to the “substantial” relations of correspondence, coherence, utility, or verifiability.  Instead of indicating a property such as corresponding with an objective reality, which is “substantive” at least in the sense that that reality has an extra-linguistic “substance,” the predicate “is true” could be understood as merely a function of statements or propositions, a function susceptible of a purely formal and syntactic characterization, following the analogy of negation, conjunction, and disjunction in logic.  

I

At the beginning of the chapter on the four “théories canoniques de la vérité” (correspondence, coherence, pragmatism, and verificationism), Engel indicates that there are at least two questions concerning the nature of truth: “Quelle est la signification du mot ‘vrai’?” and “par quel criterès [est-ce que] nous recconnaissons la vérité”? The classical theories of truth are responses to the second question; we will see that deflationist theories essentially respond to the first question but sometimes present themselves as responding to the second, with problematic consequences.

Correspondence theories understand truth as a relationship between what is said or thought on the one hand and what is on the other; this is the definition of Aristotle.   This existence to which what is said refers is often understood as an arrangement of things, as is indicated by the expression “adequatio rei et intellectus.” That is to say, “there must be a thing that makes each truth true. ”[3] For example, in the logical atomism of Russell and the Wittgenstein of the Tractatus,, “un fait est un ensemble structuré d’entités de la réalité, un complexe d’individus et de leurs propriétés ou relations.” (19).   There are several problems that result from the effort to identify the arrangements of things that correspond to those of words in phrases.  These include the question of facts which correspond to negative propositions (are there negative facts, or do two propositions, one true and one false, correspond to a single positive fact which obtains in the one case and does not obtain in the other?); relational facts (“Le fait que Naples est au sud de Rome est-il independent du fait que Rome est au nord de Naples”?); and facts that correspond to distinct propositions that describe the same situation in different ways (e.g., “Le chat est sur le tapis” and “La minotte est sur la carpette”).   In these three types of situation, one could well suppose “qu’il a autant de faits que de manières équivalents de décrire des objets” (22), and that seems absurd.    Yet, otherwise, it seems difficult to maintain that all true propositions correspond to a fact, which the correspondence theory seems to require.

Perhaps the solution is to observe that our propositions are part of a web of interrelated beliefs and that certain terms and propositions belong with other terms and propositions in such a way that together they refer to the same situation in the world.  These relationships include belonging to and synonymy: as examples of the latter, minotte is another name for chat and carpette another name for tapis.  Similarly, the grammar of “to the north of” and “to the south of” on the one hand and affirmation and negation on the other ought to tells us that in each case two or more propositions are rendered true or false by the same situation.   The function of representing that correlates a statement with the precise fact that appears to be named by it, understood in terms of the expressions used, is by itself too poor to fully determine what can be said to exist.   We must also take account of our grammar and the complex categories we use to divide up the world and say what is part of, dependent on, or otherwise connected to what.

But there is a more fundamental problem with correspondence theories that is underlined by Frege, and which applies also to coherence theories and every other theory that purports to explain what renders a proposition true: if one supposes that a proposition is true if it corresponds to a fact (or is coherent with others, or meets some other criteria), one can always ask if it is true that it does. And so, says Frege, every attempt to define truth collapses[4] because with every definition of truth in terms of something else, we can still ask if it is true that this holds.   And so we are caught in a circle that always returns to an apparently unanalyzable, inexplicable concept of truth.  As Frege says,

. . . in a definition [of truth] certain characteristics would have to be stated.  And in application to any particular case the question would always arise whether it were true that the characteristics were present.  So one goes round in a circle. Consequently, it is probable that the content of the word ‘true’ is unique and indefinable.[5]

Perhaps at most what we are entitled to say is not that correspondence with a fact or circumstance is what makes a statement true but that it is part of what we mean when we say that a statement is true.   Frege says truth is indefinable ¾ we cannot say what it means ¾ but what he shows is that we cannot say what it consists of that explains it.   We will see that deflationist theories have the virtue, and perhaps the vice, of really only explaining what being true means.  They do this by providing something like a semantic equivalent to correspondence in which what is correlated is not propositions and states of affairs but named propositions said to be true and the same propositions functioning as descriptions of states of affairs.  Because what is said to be true is just an iteration of the description, deflationist theories are immune to the Fregean criticism, since Frege's question, “But is that true?” when applied to the definiens becomes merely an iteration of the question implicit in the definiendum, so there is no additional question that is being begged.  I will return to this.  

The problem with the other classical theories of truth is that they are not able to replace but at best to supplement a theory of correspondence by providing either additional conditions that must be met for a proposition to be true or conditions whose presence would suggest that the relationship of correspondence is satisfied.   Engel shows that this is the case for coherence theories.    Counter-examples can be provided which appear to show that beliefs or propositions can be found to satisfy the criteria of coherence that we would clearly regard as false.   

Coherence theories give as the condition for truth a relationship of propositions, statements, or beliefs, to other propositions, statements, or beliefs.   As Engel formulates the principle of coherence, “une proposition, un jugement ou une croyance p est vrai si et seulement si p appartient à un ensemble cohérent de propositions, jugements, ou croyances” (25).  It is perhaps easier to make sense of this as a necessary but not sufficient criterion of truth if we observe that a proposition which is inconsistent with other propositions which we believe would normally be rejected, particularly since by the law of non-contradiction the only alternative is to reject all of the other beliefs which are negated by the proposition in question.  Indeed, the law of non-contradiction is a principle of coherence, and it is a necessary but not sufficient criterion of the truth of propositions, which cannot tell us that a proposition is true but can tell us that it is necessarily false.   Thus, in at least this minimal, logical, sense, a certain coherence is indeed one of the criteria of a proposition’s being true. 

However, it seems coherence cannot be a sufficient criterion of truth because a proposition could cohere with other propositions that we hold for true and yet be clearly false.  Russell gives as an example, cited by Engel: “bien que les très respectable évêque Stubbs soit mort dans son lit, la proposition ‘Mgr Stubbs fut pendu pour meutre’ peut être conjointe à tout un ensemble d’autre propositions, de manière à passer le test de cohérence, et par conséquent devenir vrai” (26-27). The peculiarity here is that a given empirical proposition is about some situation in the world (say, the death of Mgr. Stubbs), but its truth is said to be determined entirely independently of that relationship, and as long as we understand the proposition to give us information about the world, it seems strange to say that its correctness can be entirely a function of its relationship to an ensemble of other propositions (which may or may not have anything to do with Mgr. Stubbs or his death), and so it is at least unclear how they can suffice to render it true, although as the example of non-contradiction shows they might well rend it false.   Engel notes that an ensemble of fictional statements could be held to be true, which points to the need to at least supplement the criterion of coherence with one of “seriousness” à la Frege (see below). The example of Bishop Stubbs can also be generalized to yield a formula for generating false propositions by virtue of their coherence with true ones: pour tout ensemble E de croyances varies, il est possible d’ajouter à E un ensemble C de croyances fausses, mais cohérentes avec E. (E + C) sera néanmoins faux . . . “ (27).

The coherentist could respond to these objections, Engel explains, by attaching certain criteria to the other propositions coherence with which can make a proposition true.  For example, “On peut . . . soutenir que le test de cohérence réside dans la possession d’une méthode de justification fiable” (27).  But as Engel points out this still would not immunize the proposition against the possible pertinence of Russell’s objection.   The only way of doing that seems to be reintroduce correspondence, because the statement that Bishop Stubbs was hanged for murder can be rendered false by information about the world, viz., the possession of information presenting some incompatible circumstance such as that he died in his bed.  The addition of a reliable method of justification does not prevent one from being mistaken.    These considerations lead Engel to conclude that it is difficult to maintain a theory of pure coherence:

Comment alors éviter de réintroduire en sous-main la définition de la vérité comme corréspondance ou adéquation? Le cohérentiste peut le supposer implicitement, auquel cas sa théorie sera circulaire, ou bien il peut l’admettre franchement, et soutenir un théorie duale, selon laquelle la vérité est à la fois cohérence et corréspondance (28).  

Much the same thing is true of pragmatism: either it reposes on correspondantist claims to which it also holds in what is at best a dual theory, or its claims are defeated by our intuition that although a proposition meets the tests of truth on pragmatist grounds it is nonetheless false because it fails to correspond to the facts.   

            In the simplest form of pragmatism, le “critère [de vérité] est l’utilité ou succès” (29).   Russell points out with respect to pragmatist theories that they too seem clearly false when they contradict intuitions about correspondence:

si savoir que p est vrai c’est savoir qu’il est utile de croire p, alors il devrait s’ensuivre que quand, par exemple, nous voulons savoir s’il est vrai que la neige est blanche, nous voulons savoir s’il est utile de croire cette proposition; ce qui n’est évidemment pas le sens de la question initiale.[6]

The two questions may be linked in certain contexts, but in others the question of the truth of a belief and that of its utility are clearly separate questions, and they remain separate questions even if we say that the utility of a belief gives its validity, a notion that seems closer to truth than utility itself.   For one could hold that there are false beliefs that are valid, justified, and worth believing.    It seems very hard to pry the concept of truth loose from notions of reference.   That is why it is easy to imagine circumstances where a proposition that it is useful to believe is clearly false.  As Engel puts it, “Il y a de nombreuses choses qu’il est utile de croire, mais qui sont fausses, et vice versa” (29), and while truths are beliefs that it is often useful to have, this is in many cases at least because it is their truth that makes them useful to believe.  Indeed, in this simple form the notion seems absurd and hardly worth entertaining, though it does seem to capture an important feature of the role that truths play in our lives and why they are important to us, and if linked instead to such things as the success of scientific predictions, where the utility of a theory clearly has a constitutive relationship to its truth, the notion does not seem quite so naïve and improbable. 

Pierce has a sophisticated notion of epistemic or cognitive utility that links the truth of statements to the successful use of methods of scientific inquiry.   He believe, in Engel’s formulation, that “une croyance est vraie si et seulement si elle résultait, dans des conditions idéales, de la méthod approprié de l’enquête, et si elle était cohérente avec la totalité des données disponibles dans ces conditions idéales” (31).  This is an epistemic notion of truth, like coherentism, whose criteria it partly adopts: truth is a function of our knowledge and the justifications for our beliefs.   But the scientific method produces only tentative results and scientific knowledge is corrigible; thus, this theory seems to entail, which Pierce also maintains, that “nos croyances communes, comme nos croyances scientifiques, sont révisables, et que nos ensembles de croyances doivent être modifies à la lumière de l’expérience” (31).  This can mean one of two things: either our method of inquiry has improved or the ensemble of other beliefs with which a newly discovered proposition must be coherent has changed, on the one hand, or our method of inquiry has simply enabled us to discover something new on the other.   In the former case, what enables us to tell that our method of inquiry or the ensemble of available beliefs has improved from an epistemic standpoint if not that we have discovered something new?  As Engel puts it,

si nos croyances doivent être révisées à la lumière de l’expérience cela ne signifie-t-il pas que la réalité que l’expérience, y compris à son terme idéal hyperbolique, est supposées nous fournir, est indépendante de cette expérience et des ensembles de croyances que nos méthodes fiables d’enquête sont supposées produire ?  (32). 

Thus, no more than coherentism can pragmatism, in either its simplistic or Piercean versions, provide an alternative to correspondence except by either presupposing or at best supplementing it.     

Verificationism fares no better in providing an alternative to correspondence.

Verificationism is the theory that the truth of propositions lies in “la possibilité de leur vérification par expérience possible” (33); it can be formulated as “x is true iff x is provable, or verifiable in ideal conditions.”[7]   Pragmatists frequently have a verificationist theory of signification.  Thus, for (Pierce) “la signification d’une proposition est sa conformité avec l’expérience possible” (32-33): here it is a question of correspondence with external reality, only it is the possibility rather than the actuality of this correspondence which counts, which is why the criteria can be epistemic, internal to our cognition   This is the case with “warranted assertability” (the term is Dewey’s) if it is taken to mean verifiability.   In any case, we should want to know what constitutes a suitable warrant for an empirical proposition if it is not the knowledge of the certainty or likelihood of the existence of a state of affairs. 

Like the other classical theories, verification thus has difficulty keeping a pure conception of truth that doesn’t involve elements of correspondence, and indeed that is not ultimately explained in terms of correspondence, if only a prospective or possible correspondence.   Additionally, if verification means confirmation by experience, there is the problem that theories can be underdetermined by evidence and that therefore rival theories that are incompatible with one another might be equally confirmed, and thus, as Popper notes, in an objection similar to Russell’s to coherence theories, any theory might be seen to be confirmed with suitable modifications: “toutes nos croyances ou théories, moyennant des ajustements appropriés, pourraient être rendues cohérentes avec l’experience” (34), which is absurd (it violates Popper’s principle that a theory to be possibly true must be falsifiable).

II

Engel presents deflationist theories as a solution to the difficulties of defining and giving conditions for truth.   From the foregoing discussion, we may conclude that a criterion for the success of a deflationist theory is that it either provides a suitable alternative to correspondence theories, which none of the other classical theories seem able to provide, or that it provides an account of the correspondence relation, or at least, of what we mean when we seem to invoke that relation.  

Again, it is possible to distinguish explaining what it means to say that a proposition or statement is true from explaining what kind of circumstance can make it true.  That is, there are two related but distinct ideas here: (1) to assert that p is true is the same thing as to assert p (here Engel cites Frege, who says this exactly (35)),[8] and (2) the assertion of p explains, and gives the reason for, the assertion that p is true.   In the second case, it is tempting to read the relationship as a unidirectional one, although the biconditional, since it operates in both directions, must be understood as equally entailing that the assertion that p is true “explains” the assertion that p: for they are equivalent. Arguably, there is and must be such a unilateral relationship that provides this explanation, and it can only be, ultimately, the relationship of the proposition to an extra-linguistic reality.   A semantic theory can at best tell us how to talk about that relationship.

One version of deflationism, the decitational theory, depends on the notion that what can be true or false are statements, and it is for this reason the most problematic version.   Decitationalism understands truth in terms of the “decitational schema”: “’p’ is true iff (if and only if) p.”  The principal problem is that if truth is said to characterize statements rather than the propositions that they assert, a statement could be considered true in deflationist terms without the need to believe it or even understand what it means, whereas Moore’s paradox ¾ the apparently contradictory character of statements like “Il pleut, mais je crois qu’il ne pleut pas” ¾ appears to show that to assert a proposition we must believe it. [9] As Engel puts it, “. . . affirmer qu’il pleut, c’est impliquer qu’on croit qu’il pleut; par consequent, les deux affirmations semble se contredire” (48).

The decitational theory seems to allow anything that can be uttered to be “true,” and this goes against our ordinary intuition that only certain kinds of utterances can be true or false.   Engel notes, “Si ‘vrai’ n’est qu’un prédicat d’assertion [by which he means the assertion of a statement], alors il semble pouvoir s’appliquer à n’importe quelle phrase ‘p’, que nous en connaissions le sens ou non, et que nous sachions ou non pour quelles raisons elle est asserté.”   This is a consequence of holding that to assert is simply to say.   Just as one can say something without the intention of being understood seriously (which Frege will make a criterion of truth), one can say something that is nonsense: e.g.,  “Les snarks sont des boojums.” Engel comments: “Mais on ne pourrait, semble-t-il, en inférer qu’il a asserté que les snarks sont des boojums que si l’on connait le sens de la proposition que cette phrase exprime” (37).   Another problem is that if we are to avoid the paradoxical conclusion that there are meaningless truths, truth becomes relative to a language: the cited phrase must be part of the language of the person citing or translatable into it, so that he or she knows what proposition is being expressed.   So we can include in our understanding of “assert” that to make an assertion is, among other things, to say something meaningful and understandable, which suggests that the candidates for truth in a suitable deflationist theory must be propositions or thoughts and not merely utterances. 

Redundance theories of truth aren’t subject to these problems, because they take propositions rather than statements to be what are true or false, and propositions, as what statements assert, by definition have a meaningful content   Redundance theories explain truth in terms of the “schema of equivalence: “The proposition that p is true iff p.” Frege is the ancestor of redundance theories.   Frege holds that when we assert that a proposition is true we make the same assertion as when we simply assert the proposition.  “. . . the sentence, ‘I smell the scent of violets’ has just the same content as the sentence ‘it is true that I smell the scent of violets’.  So it seems, then, that nothing is added to the thought by my ascribing to it the property of truth”[10]

Frege’s idea is perhaps best understood not as the notion that to say that a proposition is true is merely to assert it (unless, circularly, we define “assertion” to include “claiming to be true”), but that when we assert a proposition (when we utter it “seriously”), we mean the same thing as when we say that it is true, and vice-versa.  This seems to point to a kind of non-vicious circularity; it is non-vicious because the two expressions really are synonymous, and it is circular because the biconditional indicates that each term of the equivalence schema can serve as an explanation of the other.  Thus Horwich notes that “the minimalist account .  .  . does not enable us to specify in non-circular terms the content of attributions of truth.”[11] That truth implies assertion because assertion implies truth would not entail that there is a relation of correspondence but, although Frege himself rejects that possibility, would not exclude it either.  Thus Quine, who in this regard is somewhat anomalous in the deflationist tradition, seems to hold that the equivalence schema actually explains or is explained by correspondence, as he says, “What is true is the sentence, but its truth consists in the world’s being as the sentence says.”[12]  Frege holds that the property of being true is irreducible and primitive, so it cannot be reduced to assertion.   But a proposition’s being true can be explained as adding nothing that is not already contained in the concept of its being asserted.   Assertion on this explanation has the peculiar property that it implicitly includes the idea of being true but that this need never be made explicit.   Assertions are truth claims.  As Engel puts it, “la vérité est interne à l’assertion ou au jugement,” an idea he equates with the idea that “un énoncé ou une croyance sont vrais n’est pas autre chose qu’asserter” (49).   So it is superfluous when asserting a proposition to add that it is true.   This is why Engel says that on the one hand the word “true” does have a meaning, but “une phrase dans lequel ‘est vrai’ a une occurrence comme prédicat n’aurait pas de sens non plus” (35). This is not quite right: it has a meaning, but curiously the predicate has a meaning which it does not contribute to the sentence but which is present without it: “le mot ‘vrai’ a un sens qui ne contribue en rien au sens de la phrase entière dans laquelle elle figure comme prédicat” (35).[13] 

But if we don’t need to add to a proposition that we assert that it is true, since an assertion just is a truth claim, something does need to be added to a statement for it to be taken for true or taken as the sort of thing which could equally be said to be true: in addition to being articulated, it has to be expressed “seriously.”  Or if we speak of “thoughts” as the content of propositions, something else needs to be added which secures their seriousness or the fact that they make truth claims, and this is precisely the function of assertion, which is given by the statement’s grammatical form.  

An interrogative sentence and an indicative one contain the same thought: but the indicative contains something else as well, namely, the assertion. . . . Therefore two things must be distinguished in an indicative sentence: the content, which it has in common with the corresponding sentence-question [and other speech acts such as commands and requests], and the assertion.[14]

Strawson[15] provides another version of the redundancy theory: to assert that a proposition is true is not to make a statement about the proposition. (Strawson denies, as Horwich claims Frege does as well, that: “’x is true’ makes a statement of any kind about x.”)[16] Rather, it is to make the same statement with the addition of an indication of assent. So assertion or holding for true amounts to affirming.   This explanation comports the advantage that because it makes no implicit appeal to correspondence, ethical and aesthetic truths (which I take up in section IV below) are not a priori excluded ¾ but that is only a consequence of the fact that this explanation of what a statement that a proposition is true means fails to explain what makes the statement true – for if it just means to affirm, one could affirm a false proposition, though to affirm a proposition one holds to be false would entail Moore’s paradox, so it seems that affirmation is at least part of what is meant by presenting something as true.

We could lay down a series of conditions for utterances to be truth candidates.  First, they must have a sense; they must say something. Perhaps there must also be an addressor, who believes the statement and affirms it, and an addressee posited by the addressor, who is expected to share the belief. The last two conditions can be captured by saying that the statement is said “seriously,” which Frege gives as a condition for a statement being considered true. Must they also have a reference, whether this is to an object or state of affairs that really exists or that might just be thought to exist (since the question of what it is for a statement to be true is being understood semantically, in terms of what it means to say that something is true)? (I get this fourfold schema of sense, referent, addressor, and addressee from Jean-François Lyotard, Le Différend).[17] This is what is at issue in asking whether deflationist theories provide an alternative to correspondence theories or must be understood as providing a version thereof.   It may be that these aspects of statements are all internal to them, including reference; that is, there may be a constitutive relationship between existing and being true, which amounts to saying that a proposition’s being true correlates with the existence of a corresponding state of affairs.  

Deflationist theories have an at least superficial resemblance to correspondence theories: as mentioned, they explain what being true means by providing something like a semantic equivalent to correspondence in which what is correlated is not propositions and states of affairs but named propositions said to be true and the same propositions functioning as descriptions of states of affairs.  The schema of equivalence correlates the name of a situation in the world (a proposition that describes it) with the name of the proposition, and the existence of the situation described with the truth of the named proposition.  It can do this because there is a peculiar constitutive relationship between existence and empirical truth.   That is, I am suggesting, just as truth is internal to assertion on the deflationist view, so reference must be understood to be internal to truth.   Part of the meaning of saying that an empirical proposition is true lies in its reference to the existence of the state of affairs that the proposition identifies.  As Quine puts it, “What is true is the sentence, but its truth consists in the world’s being as the sentence says.”[18]  (At any rate, whether or not the world’s being as the sentence says is what makes the sentence true or what it means, clearly if the sentence is true, the world is as the sentence says.  But if we say that the cat’s being on the mat plays no role in the truth of the proposition, “The cat is on the mat,” is it not possible to suppose that, the latter being independent of the former, the proposition might be true even if the cat is not on the mat?   The way to put the possibility of the world’s not being as the sentence says and the sentence nonetheless being true is to say something like, “’The cat is on the mat’ is true and the cat is not on the mat,” which we would of course recognize as a contradiction precisely because the schema of equivalence assures that if the proposition is true, the cat is on the mat.  There need be nothing mysterious about the kind of minimal correspondence that is being invoked here, and no special metaphysical theory is called for; when I say “’The cat is on the mat’ is true if and if only if the cat is on the mat” (an application of the schema of equivalence), two things are identified and correlated: a proposition, which is named and said to be “true,” and a fact, reality, or whatever we want to call it which is not a mysterious entity but is nothing more or less than the being-on-the-matness of the cat.    There is no way of denying this without escaping into idealism by denying that it is part of the meaning of words and sentences that they have referents.  This is particularly a danger with decitationalism, because as we saw if it is statements and not propositions that are true or false, we do not seem to need the statement to have a sense, let alone a reference (and meaningful statements, unlike names, have both).  However, to say that reference to a reality is an aspect of truth is in fact to say nothing more than that when I say that the proposition is true I assert the proposition. This is because when we say that the cat is on the mat we are saying something about (real) cats and mats.   Assertion makes an implicit reference to truth, which embeds an implicit reference to the situation identified in the proposition asserted or said to be true.   This account of correspondence avoids the objection of Frege discussed above (that if one gives a reason why a proposition is true, one can ask of that explanation if it is true) because reference isn’t related to truth as something external that grounds it. We could of course say that it is because the cat is on the mat that “The cat is on the mat” is true, which is to say that the “fact” (to use a term that is misleading because it suggests some mysterious third entity) that the cat is on the mat is what makes the proposition true. That is true, but only because when we say that the proposition is true we are saying that the cat is on the mat.  The force of Frege’s objection evaporates on a deflationist account because Frege’s skeptical question, which can be phrased as, “If p is true because X, is X true?” becomes, simply, “If it is true that p if and only if p, is it true that p?” and the question can be seen to merely reiterate itself and so not to be a genuine question that expresses any kind of uncertainty.  

Even Horwich seems not to want to deny that correspondence exists:  “minimalism . . . does not deny that truths do correspond ¾ in some sense ¾ to the facts; it acknowledges that statements owe their truth to the nature of reality.”[19] What it denies is that this correspondence is what explains truth.  Further, Horwich seems to hold that an objective reality is what makes a true proposition true, though this relationship does not constitute part of its meaning.  For

It is indeed undeniable that whenever a proposition or an utterance is true, it is true because something in the world is a certain way ¾ something typically external to the proposition or utterance.  For example,

(1)        <Snow is white>’s being true is explained by snow’s being white.

That is to say,

(2)        <Snow is white> is true because snow is white.”[20] 

However, we do not need to know this to know what it means to say that “snow is white” is true.  On the other hand, we do of course need to know that snow is white.   The idea here seems to be that by sticking to an interpretation of the equivalence schema as giving the meaning of truth attributions rather than the conditions of their satisfaction, implicit reliance on a notion of correspondence is avoided.  Perhaps this can be put better by saying that rather than correspondence explaining the equivalence schema, the equivalence schema explains correspondence.  

Since the problems of classical correspondence theories seem to derive in part from the attempt to say, in terms other than those given in the proposition, what reality its truth might consist in, it is tempting to say that true propositions do correspond with states of affairs but that these propositions themselves give us all the resources we need to identify those states of affairs, so that there is no mystery about what they might be.   The equivalence schema lends itself readily to this solution.  Ramsey for one seems to provide an explanation along these lines.   With regard to “He asserts aRb,” “We can, if we like, say that it is true if there exists a corresponding fact that a has R to b, i.e., it is true if aRb, but this is essentially not an analysis but a paraphrase, for “The fact that a has R to b exists is no different from ‘a has R to b’.”[21] Ramsey takes this to mean that “if we have analyzed judgment we have solved the problem of truth.”[22] We might even hold that instead of a proposition’s truth being determined by the existence of a fact, that the existence of a fact is determined by the truth of a proposition.   However, while the efforts of logical atomism to identify the constituents of the facts that correspond to propositions seemed to lead to deep puzzles about the nature of facts, these puzzles seem to emerge with any theory that correlates propositions and facts, because if we say that the language of our propositions determines what facts there can be, then it becomes hard to explain how different descriptions could be different ways of describing the same circumstance: to use Engel’s example, cited above, the fact that “le chat est sur le tapis” becomes a different fact than “la minotte est sur la carpette”; thus, it seems “qu’il a autant de faits que de manières équivalents de décrire des objets” (22). The strategy mentioned above of locating propositions within a web of interrelated propositions and getting clear about the relationships between interdependent terms and propositions that give us various complex ways of referring to circumstances applies here as well, but then we cannot say that a description gives us all the information we need to determine what state of affairs it is the existence of which satisfies the description.   

In addition to an addressor, an addressee, a sense, and perhaps a referent, the assertion of a proposition, in so far as this explains or is equivalent to presenting it as true, also seems to implicitly contain something else, which is conformity to a norm that governs assertions and classifies them as correct or incorrect, which is part of what is meant by being true.   One of the features of the truth of assertions that an adequate theory needs to account for is the fact that truth is a normative concept: “la notion de vérité est normative ou évaluative: son usage suppose qu’il y a des normes épistémiques d’évaluation de nos assertions” (50). 

Failure to give this normativity its due entails relativist consequences. Explaining truth in terms of assertion poses the dangers of relativism if one understands this to mean that to say a proposition is true is just to accept it.   Then anything someone is prepared to accept could be taken for “true.”  (Strawson’s theory has this liability because “is true” seems to be basically a way of saying “yes.”) Thus, Engel represents the deflationist as wanting to say that “un énoncé est jugé vrai parce qu’on l’asserte” (49).  But one can, for example, assert a proposition haphazardly without a good reason.   Saying that a proposition is to be considered true because we accept it, a view Engel attributes to Rorty, reverses the order of explanation.  “Pourquoi acceptons-nous des énoncés ou des théories comme ‘vrais’?” (if not because we believe them to be true), Engel asks.  “Tout simplement, selon Rorty, parce que nous les acceptons” (51).   This relativist conclusion (anything anyone accepts can be considered true, at least “for them”) results if one says that to assert that p is true is to affirm p but does not understand asserting p as already implying that p is true.   (That is, if one interprets the biconditional of the equivalence schema as unidirectional.) Otherwise, it could make sense to assert p and hold that p is false, but that clearly would entail a Moore-like paradox. 

But it may be that to avoid this implication we do not need a theory of truth as correspondence, but only of truth as a norm that governs assertions. Engel explains what is wrong with Rorty’s position in terms not of the failure to maintain a correspondence theory of the correctness of propositions, but of the perhaps more basic failure to maintain truth as a norm governing assertions (and thus of the absence of any theory of the correctness of propositions).   To be precise, he says “Rorty ne nie pas non plus que la notion de vérité soit foncièrement normative et evaluative . . . mais il nie que cette valeur ait un fondement” (51).  But this is critical: to avoid a relativist conclusion, the correctness of an assertion must be understood to be intended as part of its sense.   Hence, “Rorty … est parfaitement prêt à admettre le lien entre vérité et assertabilité, mais il n’admet pas le lien entre assertabilité et assertabilité garantie” (51), for warranted assertability is a notion that is tied to the normativity of statements: a statement seems to us correct if we believe it is justified.[23]   

Truth also seems irreducible to assertion for reasons that have to do with the semantics of what is asserted when we say that a proposition is true or when we merely assert it.   “Truth” if it is redundant ceases to be part of the meaning of the analyzed phrase.  Engel points out that if “p est vrai” reduces to “p” and “q est vrai” to “q”, then the two statements seem to have nothing in common: one asserts p, the other q.  Then, “dans chacun de ces cas le mot ‘vrai’ signifie des choses distinctes.  C’est en ce sens que ‘vrai’ n’exprime aucune propriété commune à ces phrases.  Il y a autant de verités qu’il a de significations, autant de vérités qu’il a de choses dont on parle” (40).  And yet truth, Engel notes, doesn’t seem any more ambiguous than “exists”, though we can say of many different things and kinds of things that they exist (41). 

Truth may be a mere quasi-logical function, an operator that gives a certain value to a proposition (a view I will examine shortly).   But then, as Frege notes, the content of “p is true” (or the assertion that p) includes more than just “p”; it includes, precisely, the fact that p is asserted or said to be true.  We cannot reduce the truth of “p is true” to the assertion that p unless we are clear about what the function of assertion or being taken for true involves.   That is why, when properly understood, the possibility that in the assertions “p is true” and “q is true” what is asserted is just p and q does not in fact entail the problem Engel raises here that “true” means many different things.  For in the assertion is contained more than just p; it also includes the application of the assertion- or truth-function.  

A third form of deflationism, the semantic theory of Tarski, does not explain truth in terms of assertion. The two statements that are correlated in Tarski’s use of the decitational schema are not the same statement, despite their similarity of form; they are not even understood to be part of the same language.  Tarski understands the decitational schema as giving a proposition in a metalanguage with the predicate “is true” attached to a proposition (using the same words or a translation of them) in an object language.   Examples include “The proposition expressed by the German sentence ‘Schnee ist Weiss’ is true if and only if snow is white” and “The proposition expressed by the English sentence ‘Snow is white’ is true if and only if snow is white.”[24]  The latter is of course the decitational schema with the addition of specification of a language to which the truth of the statement is relative.  By separating object language and metalanguage, Tarski avoids self-referential paradoxes.   As Strawson points out, this makes a proposition that includes “is true” a proposition about a proposition. Tarski’s intention is to define truth without presupposing it.   It is a question, thus, of defining truth by giving the meaning of statements that a statement is true in terms of claims that, as the Internet Encyclopedia of Philosophy puts it, are not claims about truth at all but claims “about the nature of the world.”[25]   Does this work?   Can the meaning of statements ascribing truth to other statements be defined in terms of statements that merely describe a state of affairs?   If so, it is because of a peculiar feature of statements about states of affairs, which is that there seems to be a constitutive relationship between a situation existing and a statement that it exists being true.   This is why we seem to be able to explain the truth of a proposition just by stating the proposition.   This is what is peculiar about assertion in its relationship with truth.   

In sum, it seems to me that, in the first place, it cannot be sufficient to say that “dire que ‘p’ est vrai, c’est simplement asserter que p,” as Engel puts it, unless by “assert” one means, precisely, to assert that p is true.   For it is certainly not sufficient to say “p”: as Frege has explained, it is necessary that I say it seriously and not as an extract of poetry, for example.  It must be understand that I say “p” in such a manner that (a) I believe that p (which is to say, I hold it for true), (b) I want the listener to believe that p, (c) I assert something which has a meaning in my language, and (c) at least in the case of empirical statements, my statement refers to a reality outside it in which it is as my statement says it is.  The first two conditions render my statement a truth claim; the latter two render it the kind of thing of which we can meaningfully say that it is true or false.  The simplest way of indicating all of these things is to say that I say “p” with the intention of being understood to say that “p” is true.    Of course – and this is the truth of deflationism – when I say “The cat is on the mat’ is true” I make the same assertion as if I say, simply, “The cat is on the mat,” but this is because when we assert a proposition it is understood that we are affirming its truth.   Truth cannot be reduced to assertion unless the meaning of being-true is understood to be part of the meaning of asserting; in this sense, being true is irreducible.

Secondly, a deflationist theory cannot be an alternative to a theory of correspondence, but must be understood as explaining, in strictly linguistic terms, this relationship. Deflationist theories do not explain what makes a proposition true or what it is for a statement or proposition to be true; they explain, rather, what we are saying when we say that a proposition is true.  Deflationist theories make the sense that they do because it is propositions that at the same time are true or false and that describe the states of affairs whose existence or non-existence is what makes them true or false.   The same words that we use to describe a situation can be used, in quotes, to name the proposition that describes the situation and assert that that proposition is true (or false).  A statement is true if there is a state of affairs which is as the statement indicates: it is in this sense that « The cat is on the mat » is true if and only if the cat is on the mat.  

III

It is perhaps not altogether mistaken to regard “truth” as a kind of semantic, grammatical, or logical function (this is the topic of the third paragraph of the passage),  since it seems to be an operator that transforms or contributes to the meaning of a phrase in a certain way, and it is a semantically curious notion because, as the deflationists have pointed out, in ordinary uses it is superfluous, which is to say that the function can do its work without having to be explicitly invoked: it is normally transparent.[26] 

Truth’s being a function is conceived as an alternative to its being a property, or at least a “substantive property,” which Horwich understands to mean “reducible to non-semantic terms.”[27]  Truth’s being a property would mean, as Horwich explains it, that “x’s being true consists in x’s having property F,” which is a variant of the position that “’’true’ means ‘F’,” where F is some expression composed of terms that are more basic than the truth predicate.”[28] The idea of truth not being a substantive property is seen by deflationists as a way of avoiding the metaphysical quandaries that seem to be entailed otherwise.  Thus, Horwich describes the “deflationary attitude toward truth” as “a reaction against the natural and widespread idea that the property of truth has some sort of underlying nature and that our problem as philosophers is to say what that nature is . . . ”[29] The deflationist theory of truth does not entail truth being a substantive property on Horwich’s view in the sense that “it does not say explicitly what truth is: it contains no principle of the form ‘(x)(x is true iff . . . x . . . )’, or ‘What makes a proposition true is its having characteristic P.”[30] This is analogous to the fact that logical operators are not defined except in terms of their functional role, which can be explained in terms of the input and output of values that have strictly speaking no meaning, in the sense that a number by itself really has no meaning but is a pure form.  Truth’s functional status is given in the first place by its role in the equivalence schema itself, which provides what Horwich calls a “contextual definition,” i.e., “a set of rules that would allow the conversion of any sentence containing the word ‘true’ into a synonymous sentence that does not contain it” (and vice-versa).[31]

Truth could be understood as a function in the mathematical sense of being an operation that transforms an input into an output and gives a value of an output for each input.   Since truth cannot be defined as a function of itself, perhaps the truth function could be defined as a function that takes propositions about states of affairs that would otherwise be merely (logically) possible and transforms them into propositions that we are prepared to affirm or believe.   A proposition to which the truth-function or operator has not been applied corresponds (at least if it is an empirical proposition) to a logically possible state of affairs; it is, in Frege’s terms, a thought but one which has not been asserted and might equally well be the object of a question, an order, or request, or a statement in a work of literary or dramatic art.   Also, the truth function transforms the logical status of a statement partly by assigning it a logical status, since statements only have a logical status in terms of functions that are defined in relation to possibilities of truth and falsity. 

The truth predicate is also a function that enables certain forms of oblique reference, as in “Everything the Pope says is true” or “Einstein’s theory is true”[32] or “Physicists would like to believe only what is true”[33]  The latter is explicable as a generalization of an infinite set of propositions of the form “Physicists would like to believe that there are black holes only if the belief that there are black holes is true.”[34]  The schema of equivalence explains the meaning of the truth function, which can in turn be applied meaningfully and non-superfluously to refer to propositions that are not being immediately presented.  So there are at least two roles for the truth function, or two functions, one of which is defined in terms of the other: affirming a given proposition and affirming a proposition or set of propositions that is not given but referred to by way of generalization; as Horwich puts it, “the function of the truth predicate is to enable the explicit formulation of schematic generalizations.”[35]  This makes it possible to state certain general truths such as the law of the excluded middle, which derives from an infinite series of disjunctive statements of the form “The proposition that everything is red or not-red is true” a generalized statement such as “Every proposition of the form: <Everything is F or not-F> is true.”[36]  This is a genuine contribution of the truth operator to the meaning of statements, because without it we cannot make these general claims.

The logical functions (negation, conjunction, disjunction, the conditional and the biconditional) can be given a purely syntactic and non-semantic definition. But it is questionable whether this can be done with truth.  Non-semantic definitions define terms in terms of properties other than their meanings.  What is wrong with saying that “true” is just a logical operator not essentially different from “and,” “or,” or “not” is that these operators all enable us to make complex statements that are defined in terms of consequences for their truth or falsity, but they leave unexplained what that truth or falsity consists of because they do not say what it means.   Truth cannot be understood as a logical function that is strictly analogous to negation, conjunction, and disjunction and defined syntatictally in the way that they are, because the syntactic functions of these operators is defined in terms of their relation to truth.  We cannot explain truth as a truth-function.  To say that the predicate “is true” has an inferential role is true but circular, because inferences are truth-producing judgments.  The assertion that a statement or proposition is true or false is more than just a transformation of one type of statement into another, thought it is also that; at issue is what it is to make a statement in the first place.   Perhaps it is best to say that truth is a syntatic, logical function but not one that has no semantic value or requires no semantic explanation.   Of course, “and,” “or,” and “not” have a semantic value, but their meaning can be given in syntactic terms alone ; with truth, a semantic theory seems to be necessary.

Secondly, we are not concerned merely with meaningless mathematical transformations (in which “truth” and “falsity” might be reduced to “1” and “0” and the logical calculus suitably redefined, a move which might still allow to logic certain practical uses (e.g., in electronics and computer science), but which could not be held to explain what our intuitions about something being true amount to, for this is precisely a semantic question (wherein philosophy is incompletely served by the resources of mathematics and logic): what do we mean by a proposition’s being true?   It is not incorrect but incomplete to say that truth is a function that transforms the value of a proposition or assigns a value to it; the whole question is what that value means.   We need to know this in order to know what is being said.   At a purely syntactic level, we could only understand the formal relationships between “true” propositions and other propositions or elements thereof.   At least some element in this system on which the others depend must be given a semantic characterization, and that element can only be truth, because of the privileged relationship between truth and reference, and between meaning and reference, which gives truth a semantic role.       

Frege suggests how we might begin to think about truth as like a logical function when he says that an indicative sentence contains a thought plus an assertion. It is possible to express the thought “without laying it down as true.” Assertion is absent in questions, and “when we do not speak seriously” as happens in poetry, and in statements made by an actor on a stage.  “In poetry we have the case of thoughts being expressed without being actually put forward as true.”[37] The “logical” function indicated by “is true” is just the function of asserting that marks the distinction between a proposition that we are inclined or expected to believe and one that is not uttered “seriously.”  This seems to be what Engel understands the function to consist of, for he associates here the otherwise suggestive but unexplained and perhaps inexact notion that truth is a logical function with the deflationist idea that truth reduces to assertion: “dire que ‘p’ est vrai, c’est simplement asserter que p.”  From this it seems to follow that truth is just a linguistic function, the function of asserting.    (It is somewhat misleading to call it a logical function, as it has some but not all of the aspects of a logical term; it would be better to call it a pragmatic function).  It is important to note that it is more than just the pragmatic function of indicating assent or affirmation, which seems to be Strawson’s understanding of it.

So then is truth the marker of assertion, but where assertion means that the phrase is said seriously, which means that belief is entailed, which in turn means the statement is taken for true?   This seems not incorrect, but it is more of an explication than an explanation, as it is unfortunately circular.   The error, perhaps, lies in moving from the observation that there is a truth-function which is connected with assertion and that when applied transforms propositions we do not believe into ones we do, or thoughts into assertions, in Frege’s terms, to the claim that this function suffices to explain what it is for a proposition to be true, or to be considered true.   This is analogous to the error of moving from the observation that ascribing truth to a proposition and asserting it are semantically equivalent to the claim that saying that is asserted it suffices in some non-circular way to explain what it means to say that it is true.   

IV

One property, alluded to above, that the truth function would seem to need to satisfy is normativity: When we say “ The proposition that p is true,” part of what we mean by this is that it is correct to affirm it.   We could understand this to mean that it is correct because it is true, but this is really circular because “correct” seems to be part of the meaning of “true.”   Another way of saying this is to say that we are justified in affirming that it is true. However, in Western culture at least, justified is understood to be not just a synonym for correct but a relation that holds when there is an appropriate ground for the belief or action which provides its justification: something is justified when it is rendered just by something else. And so this seems to be saying too much, although this intuition that justified means having a justifying ground or reason together with the intuition that the meaning of true includes that of “correct” motivates the belief that the sense of a statement’s being true includes its warranted assertability.

It is easy to see that this notion of justification that refers something to be justified to something else that justifies it is also involved in correspondence theories and is part of their basis. Thus, we could certainly say that among the things that are implied or meant by the proposition, “’The cat is on the mat’ is true iff the cat is on the mat” is that the proposition referred to in the sentence is justified by the cat being on the mat. What prevents us from declaring that it is really justification and not reference that is basic is that it seems to be not only a matter of justification, for at least when the original proposition is an empirical statement, about objects and states of affairs in the world, there seems to be a peculiarly transparent relationship between what is given by that proposition and what is given by the further proposition that it is true.   Saying that “The cat is on the mat” is true because it is justified by the cat’s being on the mat seems to get it backwards: surely, we are justified in saying it precisely and only because it is true.    

However, a theory that focuses on something like “warranted assertability” (or Crispin Wright’s version of it, “superassertability”) has at least one pertinent advantage, which it shares with deflationist theories in so far as they can be understood independently of correspondence.   For if understood to explain rather than provide an alternative to correspondence theories, deflationist theories share with the latter the defect that their explanatory power is limited to empirical propositions, or at least, propositions about objects and states of affairs in the world; they cannot explain how a statement about an action being good or an object being beautiful might be true, and so, if asserting is equivalent to claiming as true, what someone could mean in affirming such a statement.  

While “It is true that ‘the cat is on the mat’ if and only if the cat is on the mat” seems to give a condition that could be objectively ascertained, “It is wrong to steal” is true if and only if it is wrong to steal” seems, although in terms of disquotation it is equally undeniably (and trivially) true, to be a pure tautology that explains nothing.    It seems trivially true and empty in a way that “The cat is on the mat” does not.   To say that what makes “The cat is on the mat” true is that a cat is on the mat is to give a condition that could in principle be seen to be met, thereby rendering the statement true.   This is because it reposes on a notion of correspondence with a reality, even if this is translated into a purely semantic relationship.   But to say that what makes “It is wrong to steal” true or correct is that it is wrong to steal appears to merely repeat the assertion rather to explain it or to identify a condition that makes it true.

It may be an advantage of seeing deflationist theories as an alternative to correspondence rather than an explanation of it that they are not restricted to empirical truths.   But there seems to be a link between deflationist theories and our intuitions that it is correspondence with something like the objective world that makes our statements true. Thus Quine can say, “What is true is the sentence, but its truth consists in the world’s being as the sentence says.”[38]   From the fact that a true empirical sentence describes something that exists, we can confirm the truth of an empirical proposition simply by looking or directing our attention: if we perceive that a cat is on the mat, we seem to be justified in saying that it is.   This is perhaps because there is an internal relationship between being truth and existence (and existence and perception), between a circumstance existing and a proposition about it being true in the empirical sense.  A deflationist or disquotationalist theory of the truth of axiological statements seems like an extension from the realm of objective realities, of things that just are, to that of ethics and aesthetics.  

But the peculiarity of axiological propositions with respect to empirical ones is rooted in a peculiarity of the domain, or rather the absence of the peculiar structure of the empirical domain, which is just that our empirical statements are true if they say how things are in reality, and if we try to extend this to statements about the correctness of an attribution of value, we find that the question of what makes the statement correct seems to be an unsolvable mystery. 

Perhaps this problem is solvable by distinguishing two different senses of “is true”: in a broad sense, truth is just a norm of correctness, which in this sense must be seen as aspect of truth as a logical function — which is another reason to hold that a deflationist theory or one which incorporates its insights can very well explain axiological and other non-empirical “truths.”  In another, restricted, sense, truth is correspondence, the obtaining of a state of affairs.   Clearly, it is something like this that we mean when we make empirical claims, and this is why when we say “’The cat is on the mat’ is true if and only if the cat is on the mat,” this seems to be all we need to or indeed can say about the matter: what makes the proposition “The cat is on the mat” true is just the “fact,” circumstance, or reality that is indeed adequately named by saying “The cat is on the mat” (calling this a fact or a reality is correct but superfluous). But we cannot so easily do this with axiological statements.

Part of the problem is that internal to the statement that something is good is a normative principle, “is good,” which is analogous in a way to “is true.”  Axiological statements have this feature of incorporating a normative predicate, and because true, like good or beautiful, is a term of evaluation, it may be that seeking to validate such a statement by asking if it is “true” is asking the wrong question.  “Good” and “true” are distinct norms that do not collapse into one another as “existence” and “truth” seem to do in statements about the truth of empirical statements. “Good” and “beautiful” are perhaps in their own way terms that are just as primitive and irreducible as “true.”[39] 

This is an advantage of Wright’s theory of superassertability as Engel describes it, as it explains “is true” as providing a norm of assertion, whereas deflationist theories seem to implicitly rely on intuitions of correspondence.  Of course, axiological propositions like epistemic ones can have warrants, and the principle of warranted assertability is neutral as to what type of warrant is involved. So to explain what it means to say that a proposition is true, do we need to say what makes it true, what counts as a satisfactory justification or warrant?  Or is it enough to say that we mean that we have a warrant that meets certain conditions?    It seems that with empirical propositions the warrant has to satisfy certain conditions, and these have to do at least partly with reference.

Conclusion

In summary, there is indeed something peculiar about assertions and truth that justifies affirming the schema of equivalence, not as an explanation of what makes a proposition true, but as clarifying what we mean by holding a proposition true, and even more, what we mean when we assert a proposition, which of course the schema presents as the same thing.   Problems emerge when we attempt to reduce the truth of propositions in some way to their being asserted, or when we suppose that deflationist theories give us an alternative to correspondence theories when in fact they, like every theory we have examined, seem to require a notion of correspondence for their full explication.   The concept of truth seems to be ineliminable, as Frege seemed to understand, and so does that of reference, at least for empirical propositions, which are after all understood to be propositions about the world.    

Notes

[1] Pascal Engel, La vérité: Réflexions sur quelques truismes, Montmorillon, Hatier, pp. 35-36.  All subsequent page references in the text refer to this text.

[2] Although Engel uses this term differently to identify the “superassertability” theory of Crispin Wright.

[3]  Stanford Encyclopedia of Philosophy, s.v. « Truth », http://plato.stanford/edu

[4] Gottlob Frege, “The thought: A logical inquiry,” Mind, New Series, vol. 65, no. 259 (July 1956), p. 291. 

[5] Ibid.  This passage is cited in Engel, La Vérité, at p. 17.

[6] Bertrand Russell, Essais philosophiques, trans. F. Clementz and J.-P. Commetti, Paris, PUF, 1997, p. 173, quoted in Engel, op. cit., 29-30.

[7] Paul Horwich, Truth, 2nd ed., Oxford: Clarendon, 1998, pp. 120-21.

[8] “Si j’asserte ‘Il est vrai que l’eau est salée’, j’asserte la même chose que si j’asserte “L’eau de me rest salee’” (Gottlob Frege, Nachgelassene Schriften, F. Meiner Verlag, 1969, pp. 271-72, quoted in Engel, op cit., 35).

[9] Both conditions seem to be required.  It is not clear what it would mean to believe a statement without understanding it, for this is to say that one could believe it even if it doesn’t mean anything, at the limit if it were just a series of noises, whereas when we say we believe something we generally understand that there is a content to our belief, that could for example be explicated in different terms and that has implications for other beliefs.  But if we cannot believe a statement without understanding it, surely we also cannot hold it to be true without understanding it, because to believe just is to hold for true.

[10] Frege, op. cit., p. 293. 

[11] Horwich, op. cit., p. 36.

[12] W. V. O. Quine, Pursuit of Truth, rev. ed., Cambridge, MA: Harvard University Press, 1992, p. 81.

[13] This is a reference to Frege’s theory that the meaning of a sentence is a function of the meaning of its constituents, which in turn depends on their role in the sentence. If the term contributes nothing to the meaning of sentences in which it occurs, it is vacuous. See Gottlob Frege, “On Sinn and Bedeutung,” trans. Max Black, The Frege Reader, ed. Michael Beaney, Oxford: Blackwell, 1997, pp. 151-71.

[14] Id., 294.

[15] P. F. Strawson, “Truth,” Analysis, vol. 9, no. 4 (June 1949), pp. 83-97.

[16] Horwich, p. 38.

[17] Jean-François Lyotard, Le Différend, Paris: Ed. Minuit, 1983, 279 pp.

[18] Quine, op. cit., p. 81.

[19] Horwich, op. cit., p. 104.

[20] Id., pp. 104-105.

[21] F. P. Ramsey, “Facts and Propositions,” Philosophical Papers, ed. D. H. Mellor, Cambridge, UK: Cambridge University Press, 1990, p. 39. 

[22] Ibid.

[23] The question here is whether truth can be fully explained as a normative concept that requires justification.   If it is the only such concept, this would seem not to distinguish truth from moral rightness or aesthetic value, as these are also normative concepts that demand justification and can be said to be validated by the presentation of a warrant. I discuss this below.

[24] “Truth,” The Internet Encyclopedia of Philosophy, http://www.iep.utm.edu/truth/

[25] Ibid.

[26] It needs to be invoked in cases where the proposition or propositions said to be true are not given: e.g., “Einstein’s theory is true” or “Everything the Pope says is true.”  Deflationists hold that this is the only case in which it is not superfluous.   See below.

[27] Horwich, op. cit.,, p. 143.

[28] Id., 121. 

[29] Id., p. 120.

[30] Id., 21.

[31] Id., p. 34.

[32] Quine (op. cit., p. 81) gives this example.

[33] Horwich, op cit., p. 123.

[34] Ibid.

[35] Id., p. 37.

[36] Id., p. 4.

[37] Frege, op. cit., p. 294.

[38] Quine, op. cit., 1992. 

[39] The difference between empirical statements and statements governed by other norms of validity may be that only empirical statements, which can be true, have a referent, in which case some other kind of warrant must be needed; or it may be that the referent of moral and aesthetic claims is some “world” of values distinct from the objective world of objects and states of affairs.   Both possibilities seem to be problematic in ways (among them, that objects and states of affairs do figure in moral and aesthetic judgments) that lie outside the scope of this paper.