Performative Theory Of Truth Definition Essay

1. History of Deflationism

The deflationary theory has been one of the most popular approaches to truth in the twentieth century, having received explicit defense by Frege, Ramsey, Ayer, and Quine, as well as sympathetic treatment from many others. (According to Dummett 1959, the view originates with Frege.) The following passages all contain recognizable versions of the doctrine, though they differ on points of detail.

It is worthy of notice that the sentence ‘I smell the scent of violets’ has 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. (Frege 1918)

Truth and falsity are ascribed primarily to propositions. The proposition to which they are ascribed may be either explicitly given or described. Suppose first that it is explicitly given; then it is evident that ‘It is true that Caesar was murdered’ means no more than that Caesar was murdered, and ‘It is false that Caesar was murdered’ means no more than Caesar was not murdered. They are phrases which we sometimes use for emphasis or stylistic reasons, or to indicate the position occupied by the statement in our argument….In the second case in which the proposition is described and not given explicitly we have perhaps more of a problem, for we get statements from which we cannot in ordinary language eliminate the words ‘true’ or ‘false’. Thus if I say ‘He is always right’, I mean that the propositions he asserts are always true, and there does not seem to be any way of expressing this without using the word ‘true’. But suppose we put it thus ‘For all p, if he asserts p, p is true’, then we see that the propositional function p is true is simply the same as p, as e.g. its value ‘Caesar was murdered is true’ is the same as ‘Caesar was murdered’. (Ramsey 1927)

…it is evident that a sentence of the form "p is true" or "it is true that p" the reference to truth never adds anything to the sense. If I say that it is true that Shakespeare wrote Hamlet, or that the proposition "Shakespeare wrote Hamlet" is true, I am saying no more than that Shakespeare wrote Hamlet. Similarly, if I say that it is false that Shakespeare wrote the Iliad, I am saying no more than that Shakespeare did not write the Iliad. And this shows that the words ‘true’ and ‘false’ are not used to stand for anything, but function in the sentence merely as assertion and negation signs. That is to say, truth and falsehood are not genuine concepts. Consequently there can be no logical problem concerning the nature of truth. (Ayer 1935).

The truth predicate is a reminder that, despite a technical ascent to talk of sentences, our eye is on the world. This cancellatory force of the truth predicate is explicit in Tarski's paradigm:

‘Snow is white’ is true if and only if snow is white.

Quotation marks make all the difference between talking about words and talking about snow. The quotation is a name of a sentence that contains a name, namely ‘snow’, of snow. By calling the sentence true, we call snow white. The truth predicate is a device for disquotation. (Quine 1970).

In addition to being popular historically, the deflationary theory has been the focus of much recent work. Perhaps its most vociferous contemporary defenders are Hartry Field and Paul Horwich.

One reason for the popularity of deflationism is its anti-metaphysical stance. Deflationism seems to deflate a grand metaphysical puzzle, a puzzle about the nature of truth, and much of modern philosophy is marked by a profound scepticism of metaphysics. Another reason for the popularity of deflationism concerns the fact that truth is a semantic notion, and therefore takes its place along with other semantic notions, such as reference, meaning, and content. Many philosophers are concerned with trying to understand these semantic notions. The deflationary theory is attractive since it suggests that, at least in the case of truth, there is less to be puzzled about here than one might expect.

2. The Equivalence Schema

Perhaps because of the widespread interest in deflationism, the theory has received many different formulations. The result is that there is not so much a deflationary theory of truth as many. In recent times, however, the deflationary theory has most often been presented with the help of a schema, which is sometimes called the equivalence schema:

(ES) <p> is true if and only if p.

In this schema angle brackets indicate an appropriate name-forming device, e.g. quotation marks or ‘the proposition that …’, and occurrences of ‘p’ are replaced with sentences to yield instances of the schema. With the help of (ES), we can formulate deflationism as the view, roughly, that the instances of this schema capture everything significant that can be said about truth. Theories which depart from deflationism deny that the equivalence schema tells us the whole truth about truth. Since such theories add to the equivalence schema, they are often called inflationary theories of truth. (The equivalence schema is associated with Alfred Tarski (1944, 1958), but it is far from obvious that Tarski was any sort of deflationist. We will largely set Tarski aside here.)

Formulated in this way, deflationism does not give an explicit definition of truth, for (ES) is not a definition of anything. Indeed, some deflationists (most notably Horwich 1998b) do not provide an explicit definition of truth at all. Instead, they provide an explicit definition of having the concept of truth. To be more precise, the suggestion is that someone has the concept of truth just in case he or she is disposed to accept all (noncontroversial) instances of the equivalence schema, i.e., every sentence of the form ‘<p> is true if and only if p’ that is not paradoxical or in some other way deviant. Of course, such deflationists may think that, in saying something about what it is to have the concept of truth, they have told us what the concept of truth is. But the latter is a by-product of the former; for this reason, we can say that these deflationists are proposing an implicit definition of the concept of truth.

Are there versions of deflationism, or positions allied to deflationism, which do not employ the equivalence schema or some similar device? Yes, but we shall mention them here only to set them aside. One such view — which may be called expressivism — is the analogue of emotivism in ethics. (This view of truth is often associated with Strawson 1950, though the attribution is a difficult one.) According to emotivism, at least in one of its most traditional forms, utterances of the form ‘torture is wrong’ do not, despite appearances, predicate ‘is wrong’ of torture; rather utterances of ‘torture is wrong’ merely indicate a negative attitude on the part of the speaker toward torture. Expressivism is the parallel position about truth. According to expressivism, utterances of the form ‘S is true’ do not, despite appearances, predicate ‘is true’ of S; rather ‘S is true’ merely indicates preparedness on the part of the speaker to assert S.

Another such view is the prosentential theory of truth advanced by Dorothy Grover (see Grover, Camp and Belnap 1973, and Grover 1992) . According to this theory, sentences formed with the predicate ‘is true’ are prosentences, where a prosentence is a device for achieving anaphoric cross-reference to sentences uttered previously in a conversation, just as pronouns are devices for achieving anaphoric cross-reference to names uttered previously in a conversation. According to the prosentential theory, for example, just as in

(1) Mary wanted to buy a car, but she could only afford a motorbike.

we interpret ‘she’ as a pronoun anaphorically dependent on ‘Mary’, so too in

(2) Snow is white. That is true, but it rarely looks white in Pittsburgh.

we interpret ‘That is true’ as a prosentence anaphorically dependent on ‘Snow is white’.

Expressivism and the prosentential theory are close cousins of deflationism, and, in some uses of the term, might reasonably be called deflationary. However, they are also sufficiently different from those versions of deflationism that utilize the equivalence schema to be set aside here. The important difference between expressivism and the prosentential theory on the one hand, and deflationism as we are understanding it on the other, concerns the logical structure of sentences such as ‘S is true’. For the deflationist, the structure of such sentences is very straightforward: ‘S is true’ predicates the property expressed by ‘is true’ of the thing denoted by ‘S’. We might express this by saying that, according to deflationism, ‘S is true’ says ofS that it is true, just as ‘apples are red’ says, of apples, that they are red or ‘John sleeps’ says, of John, that he sleeps. Both expressivism and the prosentential theory deny this, though for different reasons. According to expressivism, ‘S is true’ is properly interpreted not even of subject-predicate form; rather it has the structure ‘Hooray to S’. Obviously, therefore, it does not say, ofS, that it is true. According to prosententialism, by contrast, while ‘S is true’ has a subject-predicate structure, it would still be mistaken to interpret it as being about S. For consider: according to the prosentential theory, ‘S is true’ is a prosentence which stands in for the sentence denoted by S just as ‘she’ in (1) is a pronoun which stands in for the name ‘Mary’. But we do not say that ‘she’ in (1) is about the name ‘Mary’; similarly, according to the prosentential theory, we should not say that ‘S is true’ is about S. To suppose otherwise would be to misconstrue the nature of anaphora.

3. Varieties of Deflationism

Different interpretations of the equivalence schema yield different versions of deflationism.

One important question concerns the issue of what instances of the equivalence schema are assumed to be about (equivalently: to what the names in instances of the equivalence schema are assumed to refer). According to one view, instances of the equivalence schema are about sentences, where a name for a sentence can be formulated simply by quoting the sentence — thus "‘Brutus killed Caesar’" is a name for ‘Brutus killed Caesar’. In other words, for those who hold what might be called a sententialist version of deflationism the equivalence schema has instances like (3):

(3) ‘Brutus killed Caesar’ is true if and only if Brutus killed Caesar.

To make this explicit, we might say that, according to sententialism, the equivalence schema is (ES-sent):

(ES-sent) The sentence ‘s’ is true if and only if s

Notice that in this schema, the angle-brackets of (ES) have been replaced by quotation marks.

According to those who hold what might be called a propositionalist version of deflationism, by contrast, instances of the equivalence schema are about propositions, where names of propositions are, or can be taken to be, expressions of the form ‘the proposition that p’ — thus, ‘the proposition that Brutus killed Caesar’ is a name for the proposition that Brutus killed Caesar. For the propositionalist, in other words, instances of the equivalence schema are properly interpreted not as being about sentences but about propositions, i.e., more like (4) than (3):

(4) The proposition that Brutus killed Caesar is true if and only if Brutus killed Caesar.

To make this explicit, we might say that, according to propositionalism, the equivalence schema is (ES-prop):

(ES-prop) The proposition that p is true if and only if p.

To interpret the equivalence schema as (ES-sent) rather than (ES-prop), or vice versa, is to yield a different deflationary theory of truth. Hence sententialism and propositionalism are different versions of deflationism. (There are also some further ways to interpret the equivalence schema, but we shall set them aside here.)

The other dimension along which deflationary theories vary concerns the nature of the equivalence that the theories interpret instances of the equivalence schema as asserting. On one view, the right hand side and the left hand side of such instances are analytically equivalent. Thus, for sententialists, (3) asserts that, "‘Brutus killed Caesar’ is true" means the same as ‘Brutus killed Caesar’; while for propositionalists (4) asserts that ‘the proposition that Brutus killed Caesar is true’ means the same as ‘Brutus killed Caesar’. A second view is that the right hand side and the left hand side of claims such as (3) and (4) are only materially equivalent; this view interprets the ‘if and only if’ in both (3) and (4) as the biconditional of classical logic. And a third view is that claims such as (3) and (4) assert a necessary equivalence between their right hand sides and their left hand sides; that is, both (3) and (4) are to be interpreted as material biconditionals that hold of necessity.

This tripartite distinction between analytic, necessary, and material equivalence, when combined with the distinction between sententialism and propositionalism, yields six different versions of deflationism:


It is this variegated nature of deflationism that to a large extent dictates the many names that have been used for the theory. The labels ‘redundancy theory’, ‘disappearance theory’ and ‘no-truth theory’ have been used mainly to apply to analytic versions of deflationism: positions A or B. The label ‘disquotational theory’ tends to apply to sententialist versions, and in fact to material sentential deflationism: position C. The label ‘minimalist theory’ is a label used recently by Paul Horwich (1998b) to apply to necessary versions, and in fact to necessary propositional deflationism: position F. It will not be important for us to examine all of these versions of deflationism in detail; to a large extent philosophers prefer one or other versions of these views on the basis of views from other parts of philosophy, views about the philosophy of language and metaphysics. However, it will be convenient here to settle on one version of the view. We will therefore follow Horwich in concentrating mainly on position F. Horwich calls this view ‘minimalism’, but we will continue simply with ‘deflationism’.

4. The Utility of Deflationary Truth

The deflationist idea that the equivalence schema (ES-prop) provides an implicit definition of the concept of truth suggests that truth is, as the label ‘redundancy theory’ suggests, a redundant concept, a concept that we could do without. On the contrary, however, advocates of the deflationary theory (particularly those influenced by Ramsey) are at pains to point out that anyone who has the concept of truth in this sense is in possession of a very useful concept indeed; in particular, anyone who has this concept is in a position to form generalizations that would otherwise require logical devices of infinite conjunction.

Suppose, for example, that Jones for whatever reason decides that Smith is an infallible guide to the nature of reality. We might then say that Jones believes everything Smith says. To say this much, however, is not to capture the content of Jones's belief. In order to do that we need some way of expressing an infinite conjunction of something like the following form:

If Smith says that snow is white, then snow is white, and if he says snow is pink, then snow is pink, and if he says that snow is chartreuse, then snow is chartreuse,…and so on.

The equivalence schema (ES-prop) allows us to capture this infinite conjunction. For, on the basis of the schema, we can reformulate the infinite conjunction as:

If Smith says that snow is white, then the proposition that snow is white is true, and if he says snow is pink, then the proposition that snow is pink is true, and if he says that snow is chartreuse, then the proposition that snow is chartreuse is true,…and so on.

In turn, this reformulated infinite conjunction can be expressed as a statement whose universal quantifier ranges over propositions:

For every proposition x, if what Smith said = x, then x is true.

Or, to put the same thing more colloquially:

Everything Smith says is true.

This statement give us the content of Jones's belief. And the important point for deflationists is that we could not have stated the content of this belief unless we had the concept of truth as described by the deflationary theory. In fact, for most deflationists, it is this feature of the concept of truth — its role in the formation of generalizations — that explains why we have a concept of truth at all. This is, as it is often put, the raison d'être of the concept of truth.

Given deflationists place such heavy emphasis on the role of the concept of truth in expressing generalizations, it is ironic that some versions of deflationism have been criticized for being constitutionally incapable of accounting for generalizations about truth (Gupta 1993, Halbach 1999, Soames 1999, Armour-Garb 2004). For example, theories that implicitly define truth using only the instances of (ES-prop) do not allow us to derive a generalization like (Conjunction).

(Conjunction) For all propositions p, q (the conjunction of p and q is true if and only if p is true and q is true).

Since the instances of (ES-prop) are a collection of particular propositions and (Conjunction) is a universal generalization, it is not possible to derive (Conjunction) from the instances of (ES-prop). Yet it is plausible that a theory of truth should allow us to derive general truths about truth, like (Conjunction). This suggests that deflationary theories of truth formulated using only the instances of (ES-prop) are inadequate.

It is for this reason that some deflationists use a version of (Gen) to formulate their theory of truth.

(Gen) For all x, x is true if and only if there is some p such that x = <p>, and p.

There are two things to notice about (Gen). First, unlike (ES-prop) it is not a schema, but a universally quantified formula. For this reason, it is possible to derive (Conjunction) from it. That (Gen) is universally quantified also means it can be used as an explicit definition of truth. So although deflationists often only implicitly define truth, it is possible for a deflationist to offer an explicit definition. Thus we have another dimension along which deflationary theories can vary.

Second, the existential quantifier in (Gen) must be a higher-order quantifier that quantifies into sentential position. Wolfgang Künne (2003) takes the existential quantifier to be an objectual (domain and values) quantifier ranging over propositions. A different approach would be to take the existential quantifier as a substitutional quantifier where the substitution class consists of sentences. Christopher Hill (2002) offers a further, idiosyncratic, alternative and treats the existential quantifier as a substitutional quantifier whose substitution class is the set of all propositions. However, all these approaches have drawn criticism on the grounds that the use of higher-order quantifiers to define truth is circular (Platts 1980, Horwich 1998b, McGrath 2000), and may get the extension of the concept of truth wrong (Sosa 1993). Unfortunately, we cannot assess these criticisms here. We shall continue to concentrate mainly on those versions of deflationism formulated using instances of (ES-prop).

An alternative deflationist approach to the generalization problem is to attempt to show that, despite appearances, theories that only appeal to the instances of (ES-prop) nevertheless do have the resources to derive the problematic generalizations. Field (1994a), for example, suggests that we allow reasoning with schemas and proposes rules that would allow the derivation of generalizations. Horwich (1998b) suggests a more informal approach according to which we are justified in deriving (Conjunction) since an informal inspection of a derivation of some instance of (Conjunction) shows us that we could derive any instance of it.

5. Is Truth A Property?

It is commonly said that, according to the deflationary theory, truth is not a property and therefore that, according to the theory, if a proposition is true, it is mistaken to say that the proposition has a property, the property of being true. There is something right and something wrong about this view, and to see what is wrong and right about it will help us to understand the deflationary theory.

Consider the two true propositions (5) and (6):

(5) Caracas is the capital of Venezuela.

(6) The earth revolves around the sun.

Do these propositions share a property of being true? Well, in one sense of course they do: since they are both true, we can say that there both have the property of being true. In this sense, the deflationary theory is not denying that truth is a property: truth is the property that all true propositions have.

On the other hand, when we say that two things share a property F, we often mean more than simply that they are both F; we mean in addition that there is intuitively a common explanation as to why they are both F. It is in this second sense in which deflationists are denying that truth is a property. Thus, in the case of our example, what explains the truth of (5) is that Caracas is the capital of Venezuela; and what explains this is the political history of Venezuela. On the other hand, what explains the truth of (6) is that the earth revolves around the sun; and what explains this is the nature of the solar system. The nature of the solar system, however, has nothing to do with the political history of Venezuela (or if it does the connections are completely accidental!) and to that extent there is no shared explanation as to why (5) and (6) are both true. Therefore, in this stronger sense, they have no property in common.

It will help to bring out the contrast being invoked here if we consider two properties that have nothing to do with truth, the property of being, i.e. the property of having existence, and the property of being a mammal. Consider Hillary Rodham Clinton and the Great Wall of China. Do these objects have the property of existence? Well, in one sense, they do: they both exist so they both have the property of existence. On the other hand, however, there is no common explanation as to why they both exist. What explains the existence of the Great Wall is the architectural and defense policies of classical China; what explains the existence of Hillary Rodham Clinton is Mr and Mrs Rodham. We might then say that existence is not a property and mean by this that it does not follow from the fact that two things exist that there is a common explanation as to why they exist. But now compare the property of existence with the property of being a mammal. If two things are mammals, they have the property of being a mammal, but in addition there is some common explanation as to why they are both mammals — both are descended from the same family of creatures, say. According to deflationism, the property of being true is more like the property of existence than it is like the property of being a mammal.

Depending on one's views about what it takes to be a property, then, one might be tempted to say here that being true is not a property, because it is not like being a mammal. But in fact most contemporary deflationists, pursuing the analogy between truth and existence, describe truth as a logical property (for example, Field 1992: 322; Horwich 1998a: 37; Künne 2003: 91).

6. The Deflationary Theory of Falsity

Truth and falsity are a package deal. It would be hard to imagine someone having the concept of truth without also having the concept of falsity. One obvious question to ask the proponent of the deflationary theory of truth, then, is how the theory is to be extended to falsity.

A natural account of the concept of falsity defines it in terms of the concept of truth. Thus, someone has the concept of falsehood just in case they accept instances of the schema:

(F-prop) The proposition that P is false if and only if the proposition that P is not true

A second, and initially slightly different, account of falsity defines it directly in terms of negation. According to this view, someone has the concept of falsity just in case they accept instances of the schema:

(F-prop*) The proposition that P is false if and only if it is not the case that P

Many deflationists suppose that that (F-prop) and (F-prop*) in fact implicitly define the same concept of falsity (cf Horwich 1994). The key idea here is that there seems no reason to distinguish being true from being the case. If there is no distinction between being true and being the case, presumably there is also no distinction between ‘It is not the case that p’ and ‘It is not true that p’. In addition, however, ‘It is not true that p’ is plausibly synonymous with ‘the proposition that p is not true’; and this means that (F-prop) and (F-prop*) are equivalent. As we will shortly see, this account of falsity, though certainly a natural one, leaves the deflationary theory open to an important objection concerning truth-value gaps.

7. Objections to Deflationism

Our concern to this point has been only with what the deflationary theory is. In the remainder of this article, we consider six objections. These are by no means the only objections that have been advanced against deflationism — Horwich (1998b) considers thirty-nine different objections! — but they do seem particularly obvious and important.

7.1 Objection #1: Propositions Versus Sentences.

We noted earlier that deflationism can be presented in either a sententialist version or a propositionalist version. Some philosophers have suggested, however, that the choice between these two versions constitutes a dilemma for deflationism (Jackson, Oppy and Smith 1994). The objection is that if deflationism is construed in accordance with propositionalism, then it is trivial, but if it is construed in accordance with sententialism it is false. To illustrate the dilemma, consider the following claim:

(7) Snow is white is true if and only if snow is white

Now, does snow is white refer to a sentence or a proposition? If, on the one hand, we take (7) to be about a sentence, then, assuming (7) can be interpreted as making a necessary claim, (7) is false. On the face of it, after all, it takes a lot more than snow's being white for it to be the case that ‘snow is white’ is true. In order that ‘snow is white’ be true, it must be the case not only that snow is white, it must in addition be the case that ‘snow is white’ means that snow is white. But this is a fact about language that (7) ignores. On the other hand, suppose we take snow is white to denote a proposition; in particular, suppose we take it to denote the proposition that snow is white. Then the theory looks to be trivial, since the proposition that snow is white is defined as being true just in case snow is white. In short, the deflationist is faced with a dilemma: take deflationism to be a theory of sentences and it is false; take it to be a theory of propositions, on the other hand, and it is trivial.

Of the two horns of this dilemma, it might seem that the best strategy for deflationists is to remain with the propositionalist version of their doctrine and accept its triviality. A trivial doctrine, after all, at least has the advantage of being true. Moreover, the charge of triviality is something that deflationists might well be expected to wear as a badge of honor: since deflationists are advocating their theory as following from mundane facts about which everyone can agree, it is no wonder that the theory they advocate is trivial.

However, there are a number of reasons why deflationists have typically not endorsed this option. First, the triviality at issue here does not have its source in the concept of truth, but rather in the concept of a proposition. Second, a trivial version of deflationism says nothing about the theory of meaning, where by ‘theory of meaning’ we mean an account of the connections between sentences of natural language and the propositions they express. After all, if deflationists are attending only to propositions, they are evidently not attending to the relation between sentences and propositions. Of course, one might point out that other theories of truth are also silent on the theory of meaning — why then can deflationism not be? However, the fact is that many deflationists present their doctrine as a central part of a much bigger philosophical project, viz., to provide a deflationary account of all the semantic notions, that is, notions such as truth, reference, and meaning. The problem for deflationists who grasp the second horn of the dilemma is that they must admit that there is no way to complete this project: the deflationary theory of truth can only be maintained by remaining silent about the theory of meaning. And this means that deflationism should be understood as a much more modest project than it is often taken to be.

The other possible response to this dilemma is to accept that deflationism applies inter alia to sentences, but to argue that the sentences to which it applies must be interpreted sentences, i.e., sentences which have meaning. Of course, if the sentences to which deflationism applies are interpreted sentences, then there will be no force to the objection that deflationism is ignoring the fact that sentences have meaning. Deflationism, on this interpretation, is not so much ignoring this fact as assuming it.

On either plausible response to the dilemma, then, the deflationist makes use of the notion of meaning to explain truth. This fact has led a number of philosophers to argue that, on pain of circularity, deflationism cannot be combined with theories of meaning that make use of the notion of truth to explain meaning — in particular, that deflationism is incompatible with truth-conditional theories of meaning (e.g. Dummett 1959, Davidson 1990, Horwich 1998b, Kalderon 1999, Collins 2002). Other philosophers have also suggested that deflationism is incompatible with truth-conditional theories of meaning on the grounds that granting truth any kind of explanatory role is inconsistent with deflationism (Davidson 1990, Field 1986, 1994).

If deflationism is inconsistent with truth-conditional theories of meaning, this is not obviously an objection to deflationism. After all, there are alternative theories of meaning available: both Paul Horwich and Hartry Field have in different ways defended a version of a use theory of meaning (see Field 1994a, Horwich 1998a). There is, however, a lot of work to be done before a use theory can be regarded as a successful theory of meaning.

What about the claim that deflationism is inconsistent with truth-conditional theories of meaning? As William G. Lycan notes (Bar-On et al 2005), the charges of circularity in the literature have been impressionistic and so remain difficult to evaluate. Moreover, on the surface at least, the circularity charge would seem to show that even inflationism about truth is inconsistent with truth-conditional theories of meaning, since all theories of truth will have to take meaning for granted in some sense — for example, in deciding which sentences are truth-apt (For criticisms of the circularity charge, see Gupta 1993, Horisk 2008, Lance 1997, Williams 1999.)

On the other hand, worries about the explanatory role truth plays in truth-conditional theories of meaning can only be evaluated if we know, first, what sort of explanatory role truth plays in such theories, and, second, what sort of explanatory roles are ruled out by deflationism. It seems clear, for example, that if the concept of truth is only employed in truth-conditional theories of meaning as a device of generalization, there is no inconsistency with deflationary theories of truth. But does truth have only this role in truth-conditional theories of meaning? The compatibility of deflationism about truth and truth-conditional theories of meaning seems to us an important and unanswered question. (For recent discussion, see Williams 1999, Bar-On et al 2005, Collins 2002, Gupta and Martinez-Fernandez 2005, Horisk 2007 and Field 2005.)

7.2 Objection #2: Correspondence

It is often said that what is most obvious about truth is that truth consists in correspondence to the facts — for example, that the truth of the proposition that the earth revolves around the sun consists in its correspondence to the fact that the earth revolves around the sun. The so-called correspondence theory of truth is built around this intuition, and tries to explain the notion of truth by appeal to the notions of correspondence and fact. Even if one does not build one's theory of truth around this intuition however, many philosophers regard it as a condition of adequacy on any theory of truth that the theory accommodates the correspondence intuition.

It is often objected to deflationism, however, that the doctrine has particular trouble meeting this adequacy condition. One way to bring out the problem here is by focusing on a particular articulation of the correspondence intuition, an articulation favoured by deflationists themselves (Horwich 1998b). According to this way of spelling it out, the intuition that a certain sentence or proposition ‘corresponds to the facts’ is the intuition that the sentence or proposition is true because of a certain way the world is; that is, the truth of the proposition is explained by some contingent fact which is usually external to the proposition itself. We might express this by saying that someone who endorses the correspondence intuition so understood would endorse:

(8) The proposition that snow is white is true because snow is white

Now, the problem with (8) is that, when we combine it with the deflationary theory-or at least with a necessary version of that theory-we can derive something that is plainly false. Someone who holds a necessary version of deflationism would clearly be committed to the necessary truth of:

(9) The proposition that snow is white is true iff snow is white.

And, since (9) is a necessary truth, it is very plausible to suppose that (8) and (9) together entail:

(10) Snow is white because snow is white.

Unfortunately, however, (10) is false. The reason is that the relation reported by ‘because’ in (8) and (10) is a causal or explanatory relation, and such relations must obtain between distinct relata. But the relata in (10) are (obviously) not distinct. Hence (10) is false. But this means that the conjunction of (8) and (9) must be false, and that deflationism is inconsistent with the correspondence intuition. To borrow a phrase of Mark Johnston's — who mounts a similar argument in a different context — we might put the point differently by saying that, if deflationism is true, then what seems to be a perfectly good explanation in (8) goes missing; if deflationism is true, after all, then (8) is equivalent to (10), and (10) is not an explanation of anything.

How might a deflationist respond to this objection? One response is to provide a different articulation of the correspondence intuition. For example, one might point out that the connection between the proposition that snow is white and snow's being white is not a contingent connection, and suggest that this rules out (8) as a successful articulation of the correspondence intuition. That intuition (one might continue) is more plausibly given voice by (8*):

(8*) ‘Snow is white’ is true because snow is white.

However, when (8*) is conjoined with (9), one cannot derive the problematic (10), and thus, one might think, the objection from correspondence might be avoided. Now certainly this is a possible suggestion; the problem with it, however, is that a deflationist who thinks that (8*) is true is most plausibly construed as holding a sententialist, rather than a propositionalist, version of deflationism. A sententialist version of deflationism, on the other hand, will in turn supply a version of (9), viz.:

(9*) ‘Snow is white’ is true iff snow is white

which, at least it is interpreted as a necessary truth, will conspire with (8*) to yield (10). And we are back where we started.

Another response would be to object that ‘because’ creates an opaque context — that is, the kind of context within which one cannot substitute co-referring expressions and preserve truth. If ‘because’ creates an opaque context, then it would be illegitimate to suppose that (8) and (9) entail (10). This too is a possibility; however, it is not clear that ‘because’ creates opaque context of the right kind. In general we can distinguish two kinds of opaque context: intensional contexts, which allow the substitution of necessarily co-referring expressions but not contingently co-referring expressions; and hyper-intensional contexts, which do not even allow the substitution of necessarily co-referring expressions. If the inference from (8) and (9) to (10) is to be successfully blocked, it is necessary that ‘because’ creates a hyper-intensional context. However, it is open to a friend of the correspondence objection to argue that, while ‘because’ creates an intensional context, it does not create a hyper-intensional context.

A final, and most radical, response would be to reject the correspondence intuition outright. This response is not in fact as drastic as it sounds. In particular, the deflationist does not have to say that someone who says ‘the proposition that snow is white corresponds to the facts’ is speaking falsely. Deflationists would do better to say that such a person is simply using a picturesque or ornate way of saying that the proposition is true, where truth is understood in accordance with the deflationary theory. Indeed, the deflationist can even agree that for certain rhetorical or conversational purposes, it might be more effective to use the ‘correspondence to the facts’ talk. Nevertheless, it is important to see that this response does involve a burden, since it involves rejecting a condition of adequacy that many regard as binding on a theory of truth

7.3 Objection #3: Truth-value Gaps.

Philosophy of language has isolated a class of propositions that are supposed to fail of truth-value. According to some moral philosophers, for example, moral propositions — such as the injunction that one ought to return people's phone calls — are neither true nor false. The same thing is true, according to some philosophers of language, about propositions which presuppose the existence of something which does not in fact exist — such as the claim that the present King of France is bald; about propositions that are vague — such as the proposition that wall hangings are furniture; and about propositions that are paradoxical, such as those that arise in connection with the liar paradox. Let us call this thesis the gap, since it finds a gap in the class of propositions between those that are true and those that are false.

The deflationary theory of truth is inconsistent with there being a gap in the class of propositions, and this has been thought by many to be an objection to the theory. The reason for the inconsistency is very simple, and flows directly from the deflationist theory of falsity that we considered earlier. Suppose, for reductio, that the gap is correct and thus that there is a proposition Q which lacks a truth-value. Obviously, since Q lacks a truth-value, it is not the case that it is true or false. But now consider the equivalence schema (F-prop):

(F-prop) The proposition that P is false if and only if the proposition that P is not true

It is clear from (F-prop) that if it is not the case that Q is true or false, then it is not the case that Q is true or not true. But that is a contradiction: it must be the case that Q is true or not true. We have been led to this contradiction by accepting the following: the claims that all the instances of (ES-prop) and (F-prop) are true, the gap, and classical logic. Clearly, then, we must give up one of these things. But which? And which can we give up consistently with deflationism?

One strategy that is obviously consistent with deflationism is the rejection of classical logic (perhaps rejecting or restricting the law of excluded middle, for example). We shall largely ignore this approach here. Another strategy would be to restrict (ES-prop), so that it is not asserted that all instances of (ES-prop) are true (Horwich 1998b). However, there are reasons to be suspicious of such a restriction. To see this, consider the following two propositions:

(11) All inclusive disjunctions are true if and only if one of the disjuncts is true.
(12) All the propositions asserted by the Pope are true.

Both (11) and (12) are generalizations we express with the help of the truth predicate. And yet both seem to require the truth of all instances of (ES-prop). In particular, we may use (12) as a way of acknowledging our agreement with everything the Pope said, even if some of the propositions he asserted were moral propositions. This suggests that we need to use a notion of truth according to which instances of (ES-prop) hold even for moral statements, and even if they are neither true nor false.

A third strategy modifies deflationism by jettisoning the account of falsity that the deflationist offers, while hanging on to the account of truth. This strategy is a fairly desperate one, however. To begin with, if we give up the account of falsehood, it is not clear that we have an account of truth. Truth and falsehood are, as we have said, a package deal. Moreover, the deflationary theories of falsity that we considered are motivated in large part by classical logic. Presumably, it would be desirable to maintain classical logic if at all possible, and this means that we should maintain the deflationist account of falsity. Finally, one can generate a problem for the gap even if we operate without falsity, and only with truth (Rescher 1969). Suppose, again for reductio, that there is a proposition Q that is neither true nor false. Now, if Q is neither true nor false, then the proposition that Q is true will be false. But this means that for at least one instance of the equivalence schema, one side of the biconditional will be false, and the other side will be neither true nor false. On all logics that involve truth-value gaps, however, such a biconditional will be counted either as false or else as neither true nor false. Either way, the result is that the equivalence schema is not true in all instances.

A fourth strategy argues that the gap, as we have presented it, is malformed. According to this strategy, one should not respond to the phenomena that prompt the gap by suggesting that certain propositions lack truth values; one should rather suggest that certain declarative sentences lack truth values, i.e., because they fail to express propositions at all. Thus, if we take presupposition failure as our example, the suggestion is that instead of supposing that the proposition that the present King of France is bald does not have a truth value if the King of France does not exist, one should rather suppose that the sentence ‘the present King of France is bald’ does not express a proposition, and therefore fails to have a truth value. This kind of approach removes any conflict between the gap and deflationism. The gap says, or implies, that certain sentences fail to express propositions; deflationism says, or implies, that if those sentences did express propositions, they would have truth values. But there is clearly no contradiction in supposing, on the one hand, that a certain sentence fails to express a proposition and, on the other, that if it did, it would have a truth value.

This strategy for dealing with the gap returns us to the problems we mentioned earlier concerning which theories of meaning are compatible with deflationism. For example, some have argued that deflationism is incompatible with truth-conditional theories of meaning and so cannot accept that some declarative sentences do not have truth-conditions or express propositions (e.g. Field 1994a, Armour-Garb 2001). Even if this is true, however, the deflationist can maintain that only meaningful declarative sentences have truth-conditions or express a proposition and that a use theory of meaning will distinguish the meaningful sentences from the meaningless. Still, it is unclear whether any use theory of meaning can make the appropriate distinctions — for example, whether it can distinguish ‘The present King of France is bald’ from ‘The present Prime Minister of Australia is bald’.

A fifth strategy is to reject the gap entirely, and to simply agree that there is no gap that divides either propositions or sentences. This may initially seem to be an overreaction to the inconsistency of deflationism and the gap; however, what lies behind this strategy is the thought that it is not clear that the various phenomena that motivate the gap ought to be regarded as phenomena which involve failure of truth value, whether of sentences or propositions. In the case of presupposition failure, for example, it is not clear that the problem is best explained by a failure of certain sentences to have truth values, or by the presence of conventional or conversational implicatures that govern utterances of those sentences. The possibility of a broadly pragmatic account of the phenomena suggests that one might accommodate the intuitions behind the gap without supposing that there is a gap in the class of propositions (for an example, see Stalnaker 1975). Similarly, in the case of vague propositions, one might adopt epistemicism: the position that vague words like ‘bald’ in fact have precise extensions, but that we can never know what these precise extensions are (see Williamson 1994, Horwich 1998b). Like the previous strategy, however, more work is required to show that this approach is able to account for the various linguistic phenomena that prompt the gap.

A final strategy for dealing with the gap takes seriously the deflationist idea that attributions of truth to a proposition have the same semantic value as the propositions to which truth is attributed. So far we have assumed that attributions of truth to the proposition Q, where Q lacks a truth value, are false. However, an alternative approach is to suppose that if Q lacks a truth value, then both the proposition that Q is true and the proposition that Q is false lack truth values too. This allows us to accept that the instances of (ES-prop) involving propositions that lack truth value are true, since the two sides of the biconditional will have the same semantic value. Of course, if we accept the law of excluded middle — that is, we accept that either Q or not-Q — then we must also accept that either Q is true or not-Q is true. Given that, by hypothesis, Q lacks a truth value, this may seem odd. In particular, it is unclear how we can express the fact that Q lacks a truth value. For we cannot describe this case by saying that Q is neither true nor false.

To avoid this consequence, we may wish to distinguish two notions of truth at this point. One notion of truth, call it the weak notion (Yablo 1985, Field 1994b), is implicitly defined by the instances of (weak-ES), all of which are asserted to hold.

(weak-ES) the proposition that p is weakly true if and only if p

Because all instances of (weak-ES) are true, it is the weak notion that is required to express (11).

(11) All inclusive disjunctions are true if and only if one of the disjuncts is true.

In short, weak truth is such that attributions of weak truth to a truth-bearer have the same semantic value as the truth-bearer itself. In contrast, a strong notion of truth will not make all instances of (strong-ES) hold.

(strong-ES) the proposition that p is strongly true if and only if p.

In particular, propositions that lack truth value will falsify (strong-ES). This strong notion of truth appears to be required if we wish to say that it is neither true that Q nor true that not-Q. For these sorts of reasons, some have suggested that ordinary truth-talk vacillates between using a weak and a strong notion of truth (see Field 1994b, McGee 2005). If this is right, then perhaps deflationists can focus on the weak notion of truth as primary, and try to define up a strong notion of truth from it and additional resources consistent with their position (see Field 1994b for an attempt).

There are, then, a number of strategies for dealing with the gap that are prima facie compatible with deflationism. However, in each case there are reasons to worry about either the plausibility of the strategy, or about whether, on closer inspection, deflationism will turn out to be inconsistent with the strategy.

7.4 Objection #4: Consistency and Adequacy

One of the major tasks of philosophical logic in the twentieth century has been to provide a theory of truth that can deal with the ancient problem of the liar paradox. Consider the following proposition.

(The Liar) The Liar is not true.

If we accept the relevant instance of (ES-prop) for The Liar, and classical logic, then contradiction quickly follows. Moreover, since deriving this contradiction does not rely on the supposition that some proposition is neither true nor false, appealing to a weak notion of truth will not help with this problem. Indeed, since the weak notion of truth implies that all instances of (ES-prop) are true, it is precisely this notion of truth that allows the contradiction to be derived. A stronger notion of truth that restricted (ES-prop) in certain ways might be able to avoid the liar paradox.

Partly for this reason, a number of philosophers have recently argued that The Liar poses a special problem for deflationary theories of truth (see Beall and Armour-Garb (eds.) 2005). That is, since it is unclear whether deflationists can appeal to a strong notion of truth, they seem to be at a special disadvantage in dealing with the liar paradox. Moreover, it has been argued that one particular way of motivating a restriction of (ES-prop) is incompatible with deflationism: namely, that paradoxical sentences like The Liar are meaningless, or do not express propositions. (Armour-Garb 2001; but see Beall 2001 for a contrary view.)

However, as we mentioned above, not all deflationary theories are committed to the truth of all instances of (ES-prop). Horwich's minimal theory of truth, for example, only consists of all the non-pathological instances of (ES-prop). One possible deflationist response to The Liar, then, is to simply bar the problematic instances of (ES-prop) from the theory of truth. There are several problems with this strategy. For one, by making this ad hoc manoeuvre we lose the ability to explain why the pathological instances of (ES-prop) are pathological. After all, it is surely something about the concept of truth, and in particular the role of the relevant instances of (ES-prop), that explains why the liar paradox arises (Soames 1999, Gupta 2006). Another problem is that it is very difficult, if not impossible, to spell out in advance which instances of (ES-prop) are paradoxical (Kripke 1975, McGee 1992, Yablo 1993). A final problem is that it appears we need to assume that the paradoxical instances of (ES-prop) are true if we are to assert (11) (Armour-Garb 2004, Gupta 2006).

(11) All inclusive disjunctions are true if and only if one of the disjuncts is true.

These problems facing accounts that merely restrict the instances of the equivalence schema suggest an alternative deflationist response to the liar. For both the fact that The Liar's instance of (ES-prop) is required to explain its (The Liar's) pathology, and the fact that we need The Liar's instance of (ES-prop) to assert (11), give us good reason to suppose that even the paradoxical instances of (ES-prop) are true. Moreover, these reasons hold whether we are deflationists or inflationists. If this is right, then, since the paradox is generated merely from the relevant instance of (ES-prop) by classical logic, The Liar poses no special problem for deflationists (Gupta 2006). And since everyone's problem is no one's, the liar paradox cannot be used against deflationists. This defence of deflationism can be bolstered by noting that, like inflationists, deflationists can try to deal with the liar paradox by modifying classical logic (Field 2003), by adopting epistemicism (Restall 2006), or by adopting a revision theory (Gupta and Belnap 1993). (See also Maudlin 2004.)

However, there is a further line of argument that suggests there is a special problem for deflationists in this vicinity. The ideal theory of truth will be both consistent (e.g. avoids the liar paradox) and adequate (e.g. allows us to derive all the essential laws of truth, like (11)). Yet it has been recently argued that even if deflationists can give a consistent theory of truth, they cannot provide an adequate theory. The argument for this conclusion turns on the notion of a conservative extension of a theory. Informally, a conservative extension of a theory is one that does not allow us to prove any sentences that couldn't be proved from the original, unextended theory. More formally, and applied to theories of truth, a truth theory, Tr is conservative over some theory T formulated in language L if and only if for every sentence φ of L in which the truth predicate doesn't occur, if TrL  ⊢  φ, then L  ⊢  φ. As is well known, certain truth theories are conservative over arithmetic — e.g. theories that implicitly define truth using only the instances of (ES-prop) — and certain truth theories are not — e.g. Tarski's compositional theory (Tarski 1944). Specifically, the addition of certain truth theories allows us to prove that arithmetic is consistent, something we famously can't do if we are confined to arithmetic itself.

Now, it has recently been argued (a) that conservative truth theories are inadequate and (b) deflationists are committed to conservative truth theories (Shapiro 1998, Ketland 1999). The details of the arguments for (a) are complicated and we will pass over them here (but see Field 1999 for criticism). To get a flavour of the arguments for (b), consider Shapiro's rhetorical question: ‘How thin can the notion of arithmetic truth be, if by invoking it we can learn more about the natural numbers?’ Shapiro is surely right to press deflationists on their frequent claims that truth is 'thin' or 'insubstantial'. It might also be a worry for deflationists if any adequate truth theory allowed us to derive non-logical truths, given the common deflationist assertion that truth is a logical property. On the other hand, deflationists themselves insist that truth is an expressively useful device, and so they cannot be faulted merely for promoting a theory of truth that allows us to say more about matters not involving truth. Whether there is more of a worry for deflationists in the non-conservativeness of certain truth-theories depends on subtle questions about what sort of axioms count as essential laws of truth and whether all conservative truth theories are inadequate (Shapiro 1998, Field 1999, Ketland 1999). Perhaps most importantly, though, the debate over conservativeness highlights how unclear we are about the commitments of deflationism.

7.5 Objection #5: Normativity.

It is commonly said that our beliefs and assertions aim at truth. The idea here, of course, is not that our beliefs and assertions are always true in a statistical sense, or even that they are mostly true. The idea is rather that truth is a norm of assertion. This fact about assertion and truth has often been seen to suggest that deflationism must be false. However, the felt contradiction between normativity and deflationism is difficult to make precise.

The first thing to say is that there is certainly a sense in which deflationism is not inconsistent with the idea that truth is a norm of assertion. To illustrate this, notice that we can obtain an intuitive understanding of the content of this idea without mentioning truth at all, so long as we focus on a particular case. Suppose for whatever reason that Mary sincerely believes that snow is green, has good evidence for this belief, and on the basis of this belief and evidence asserts that snow is green. We might say that there is a norm of assertion which implies that Mary is in this case open to criticism. After all, since snow is evidently not green, there must be something incorrect or defective about Mary's assertion that it is. It is this incorrection or defectiveness that the idea that truth is a norm of assertion is trying to capture.

But now let us see if we can give a general statement of the norm that lies behind this particular case. The problem of providing a general statement seems to be difficult, and for reasons that by now should be familiar. To state the norm in general we would need to be able to do something we cannot really do, namely, to complete an infinite conjunction of something like the following form:

If someone asserts that snow is green, and snow is not green then he or she is open to criticism, and if someone asserts that grass is purple, and grass is not purple then he or she is open to criticism,…and so on.

Given the equivalence schema (F-prop*) provided by the deflationary theory of falsity, however, this infinite conjunction can be reformulated as:

If someone asserts that snow is green and the proposition that snow is green is false, then he or she is open to criticism, and if someone asserts that grass is purple and the proposition that grass is purple is false, then he or she is open to criticism, and so on.

In turn, this reformulated infinite conjunction can be reformulated as a statement whose universal quantifier ranges over propositions:

For all propositions p, if someone asserts that p, and p is false, then he or she is open to criticism

Or, to put it as some philosophers might:

Truth is a norm of assertion.

For after all, if truth is a norm of assertion, then, if you assert something false, you are open to criticism. In short, then, deflationists are certainly not denying that truth is a norm of assertion; on the contrary, the concept of truth is required to state that very generalization.

If the problem of normativity is not the straightforward one that deflationists cannot account for the idea that truth is a norm of assertion, what is the problem? Crispin Wright argues that the problem is not so much that deflationists cannot account for normativity; rather, he suggests that the problem is twofold: first, that any theory of truth that does account for normativity is ipso facto not a deflationary theory properly so-called, and second, that any theory of truth which employs the equivalence schemas can account for normativity (Wright 1992; and see Price 1998 for discussion). The result is that, since most contemporary varieties of deflationism evidently employ the equivalence schemas, most contemporary varieties of deflationism are not varieties of deflationism properly so-called.

Wright's objection from normativity is a difficult one to assess. For one thing, it is difficult to find Wright's reason for supposing that the equivalence schemas play such a central role in the explanation of normativity. As we have seen, the equivalence schemas are crucial in providing a general statement of the idea that truth is a norm of assertion, but there seems for all that no internal connection between truth and the norm in question, and thus no internal connection between the equivalence schemas and that norm (cf. Price 1998). Nor is it clear what role normativity plays in the distinction between an inflationary and a deflationary theory of truth. Certainly it is not good enough to simply define deflationism so that any deflationary theory cannot account for normativity. Of course, it is a consequence of a definition of this sort that a theory of truth is either inflationary or false; but then again, no deflationist will accept the definition.

Whatever one thinks of the details of Wright's objection, however, it does have far-reaching consequences for deflationism about truth. What the objection forces us to consider is the possibility that there is no very clear distinction between an inflationary and a deflationary theory of truth. Indeed, this possibility — that there is no clear inflationary/deflationary distinction — is the topic of the final objection to deflationism that we will discuss.

7.6 Objection #6: Inflationist Deflationism?

The final objection begins by drawing attention to a little known doctrine about truth that G.E. Moore held at the beginning of the century. Richard Cartwright describes the view as follows: “a true proposition is one that has a certain simple unanalyzable property, and a false proposition is one that lacks the property” (1987, p. 73). This doctrine about truth is, of course, to be understood as the analogue for truth of the doctrine that Moore held about good, namely that good is a simple, unanalyzable quality.

The problem that this Moorean view about truth presents for the deflationary theory might best be expressed in the form of a question: what is the difference between the Moorean view and deflationism? Of course, there is a sense in which the flavour of the Moorean view is very different from the flavour of the deflationist theory about truth. After all, what could be more inflationary than thinking that truth is a property of a proposition that is unanalyzable? Certainly Moore's view about good has been viewed in this light. However, the fact that one view has a different flavour from another does not mean that, at bottom, they are not the same view. One might perhaps suggest that, according to the deflationary theory, the concept of truth has an important logical role, i.e., to capture generalizations. However, this doesn't really answer our question. For one thing, it isn't clear that Moore's notion might not also capture generalizations. For another, the idea that the deflationary concept of truth plays an important logical role doesn't distinguish the metaphysics of deflationism from the metaphysics of the Moorean view; and it is the metaphysics of the matter that the present objection really brings into focus. Alternatively, one might suggest that the distinction between truth according to deflationism and truth according to Moore's view is the distinction between having a simple unanalyzable nature, and not having a nature at all. However, what is that distinction? It is certainly not obvious that there is any distinction between having a nature about which nothing can be said and having no nature at all.

The problem is particularly acute in light of the fact that deflationism has often been discussed in the context of various claims about reductionism. In many discussions of deflationism, for example, the opponent is assumed to be a particular version of a correspondence theory that attempts to reduce the correspondence relation to certain relations of causation (Field 1986 is a good example). However, it should be noted that this kind of view is also opposed to the kind of position that takes semantic facts-such as a proposition's being true-as primitive (Field 1972 is a good example). And the problem that we are considering for deflationism is that these two views are not simply identical in being opposed to the kind of view that explains correspondence in terms of causation: it is that they are identical simpliciter. The suggestion, in short, is that deflationism is identical to what initially seems to be its complete opposite, Moorean inflationism.

The decision to be an inflationist or a deflationist about truth has been called “the biggest decision a theorist of truth must make” (Boghossian 1990). Certainly this is true at an intuitive level. But it is sobering also to realize that it is not exactly clear what this decision amounts to when subjected to philosophical scrutiny. And this suggests that there is still a lot of work to be done before we can arrive at a final evaluation of the deflationary theory of truth.


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  • Yablo, S., 1993. ‘Paradox Without Self-Reference’, Analysis, 53: 251–2.


We would like to express our thanks to Stewart Candlish, James Chase, Jacob Hohwy, Graham Oppy, and Huw Price for help in constructing this entry.

1. History of the Correspondence Theory

The correspondence theory is often traced back to Aristotle’s well-known definition of truth (Metaphysics 1011b25): “To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true”—but virtually identical formulations can be found in Plato (Cratylus 385b2, Sophist 263b). It is noteworthy that this definition does not highlight the basic correspondence intuition. Although it does allude to a relation (saying something of something) to reality (what is), the relation is not made very explicit, and there is no specification of what on the part of reality is responsible for the truth of a saying. As such, the definition offers a muted, relatively minimal version of a correspondence theory. (For this reason it has also been claimed as a precursor of deflationary theories of truth.) Aristotle sounds much more like a genuine correspondence theorist in the Categories (12b11, 14b14), where he talks of underlying things that make statements true and implies that these things (pragmata) are logically structured situations or facts (viz., his sitting and his not sitting are said to underlie the statements “He is sitting” and “He is not sitting”, respectively). Most influential is Aristotle’s claim in De Interpretatione (16a3) that thoughts are “likenessess” (homoiomata) of things. Although he nowhere defines truth in terms of a thought’s likeness to a thing or fact, it is clear that such a definition would fit well into his overall philosophy of mind. (Cf. Crivelli 2004; Szaif 2006.)

1.1 Metaphysical and Semantic Versions

In medieval authors we find a division between “metaphysical” and “semantic” versions of the correspondence theory. The former are indebted to the truth-as-likeness theme suggested by Aristotle’s overall views, the latter are modeled on Aristotle’s more austere definition from Metaphysics 1011b25.

The metaphysical version presented by Thomas Aquinas is the best known: “Veritas est adaequatio rei et intellectus” (Truth is the equation of thing and intellect), which he restates as: “A judgment is said to be true when it conforms to the external reality”. He tends to use “conformitas” and “adaequatio”, but also uses “correspondentia”, giving the latter a more generic sense (De Veritate, Q.1, A.1-3; cf. Summa Theologiae, Q.16). Aquinas credits the Neoplatonist Isaac Israeli with this definition, but there is no such definition in Isaac. Correspondence formulations can be traced back to the Academic skeptic Carneades, 2nd century B.C., whom Sextus Empiricus (Adversos Mathematicos, vii, 168) reports as having taught that a presentation “is true when it is in accord (symphonos) with the object presented, and false when it is in discord with it”. Similar accounts can be found in various early commentators on Plato and Aristotle (cf. Künne 2003, chap. 3.1), including some Neoplatonists: Proklos (In Tim., II 287, 1) speaks of truth as the agreement or adjustment (epharmoge) between knower and the known. Philoponus (In Cat., 81, 25-34) emphasizes that truth is neither in the things or states of affairs (pragmata) themselves, nor in the statement itself, but lies in the agreement between the two. He gives the simile of the fitting shoe, the fit consisting in a relation between shoe and foot, not to be found in either one by itself. Note that his emphasis on the relation as opposed to its relata is laudable but potentially misleading, because x’s truth (its being true) is not to be identified with a relation, R, between x and y, but with a general relational property of x, taking the form (∃y)(xRy & Fy). Further early correspondence formulations can be found in Avicenna (Metaphysica, 1.8-9) and Averroes (Tahafut, 103, 302). They were introduced to the scholastics by William of Auxerre, who may have been the intended recipient of Aquinas’ mistaken attribution (cf. Boehner 1958; Wolenski 1994).

Aquinas’ balanced formula “equation of thing and intellect” is intended to leave room for the idea that “true” can be applied not only to thoughts and judgments but also to things or persons (e.g. a true friend). Aquinas explains that a thought is said to be true because it conforms to reality, whereas a thing or person is said to be true because it conforms to a thought (a friend is true insofar as, and because, she conforms to our, or God’s, conception of what a friend ought to be). Medieval theologians regarded both, judgment-truth as well as thing/person-truth, as somehow flowing from, or grounded in, the deepest truth which, according to the Bible, is God: “I am the way and the truth and the life” (John 14, 6). Their attempts to integrate this Biblical passage with more ordinary thinking involving truth gave rise to deep metaphysico-theological reflections. The notion of thing/person-truth, which thus played a very important role in medieval thinking, is disregarded by modern and contemporary analytic philosophers but survives to some extent in existentialist and continental philosophy.

Medieval authors who prefer a semantic version of the correspondence theory often use a peculiarly truncated formula to render Aristotle’s definition: A (mental) sentence is true if and only if, as it signifies, so it is (sicut significat, ita est). This emphasizes the semantic relation of signification while remaining maximally elusive about what the “it” is that is signified by a true sentence and de-emphasizing the correspondence relation (putting it into the little words “as” and “so”). Foreshadowing a favorite approach of the 20th century, medieval semanticists like Ockham (Summa Logicae, II) and Buridan (Sophismata, II) give exhaustive lists of different truth-conditional clauses for sentences of different grammatical categories. They refrain from associating true sentences in general with items from a single ontological category. (Cf. Moody 1953; Adams McCord 1987; Perler 2006.)

Authors of the modern period generally convey the impression that the correspondence theory of truth is far too obvious to merit much, or any, discussion. Brief statements of some version or other can be found in almost all major writers; see e.g.: Descartes 1639, ATII 597; Spinoza, Ethics, axiom vi; Locke, Essay, 4.5.1; Leibniz, New Essays, 4.5.2; Hume, Treatise, 3.1.1; and Kant 1787, B82. Berkeley, who does not seem to offer any account of truth, is a potentially significant exception. Due to the influence of Thomism, metaphysical versions of the theory are much more popular with the moderns than semantic versions. But since the moderns generally subscribe to a representational theory of the mind (the theory of ideas), they would seem to be ultimately committed to spelling out relations like correspondence or conformity in terms of a psycho-semantic representation relation holding between ideas, or sentential sequences of ideas (Locke’s “mental propositions”), and appropriate portions of reality, thereby effecting a merger between metaphysical and semantic versions of the correspondence theory.

1.2 Object-Based and Fact-Based Versions

It is helpful to distinguish between “object-based” and “fact-based” versions of correspondence theories, depending on whether the corresponding portion of reality is said to be an object or a fact (cf. Künne 2003, chap. 3).

Traditional versions of object-based theories assumed that the truth-bearing items (usually taken to be judgments) have subject-predicate structure. An object-based definition of truth might look like this:

A judgment is true if and only if its predicate corresponds to its object (i.e., to the object referred to by the subject term of the judgment).

Note that this actually involves two relations to an object: (i) a reference relation, holding between the subject term of the judgment and the object the judgment is about (its object); and (ii) a correspondence relation, holding between the predicate term of the judgment and a property of the object. Owing to its reliance on the subject-predicate structure of truth-bearing items, the account suffers from an inherent limitation: it does not cover truthbearers that lack subject-predicate structure (e.g. conditionals, disjunctions), and it is not clear how the account might be extended to cover them. The problem is obvious and serious; it was nevertheless simply ignored in most writings. Object-based correspondence was the norm until relatively recently.

Object-based correspondence became the norm through Plato’s pivotal engagement with the problem of falsehood, which was apparently notorious at its time. In a number of dialogues, Plato comes up against an argument, advanced by various Sophists, to the effect that false judgment is impossible—roughly: To judge falsely is to judge what is not. But one cannot judge what is not, for it is not there to be judged. To judge something that is not is to judge nothing, hence, not to judge at all. Therefore, false judgment is impossible. (Cf. Euthydemus 283e-288a; Cratylus 429c-e; Republic 478a-c; Theaetetus 188d-190e.) Plato has no good answer to this patent absurdity until the Sophist (236d-264b), where he finally confronts the issue at length. The key step in his solution is the analysis of truthbearers as structured complexes. A simple sentence, such as “Theaetetus sits.”, though simple as a sentence, is still a complex whole consisting of words of different kinds—a name (onoma) and a verb (rhema)—having different functions. By weaving together verbs with names the speaker does not just name a number of things, but accomplishes something: meaningful speech (logos) expressive of the interweaving of ideas (eidon symploken). The simple sentence is true when Theaetetus, the person named by the name, is in the state of sitting, ascribed to him through the verb, and false, when Theaetetus is not in that state but in another one (cf. 261c-263d; see Denyer 1991; Szaif 1998). Only things that are show up in this account: in the case of falsehood, the ascribed state still is, but it is a state different from the one Theaetetus is in. The account is extended from speech to thought and belief via Plato’s well known thesis that “thought is speech that occurs without voice, inside the soul in conversation with itself” (263e)—the historical origin of the language-of-thought hypothesis. The account does not take into consideration sentences that contain a name of something that is not (“Pegasus flies”), thus bequeathing to posterity a residual problem that would become more notorious than the problem of falsehood.

Aristotle, in De Interpretatione, adopts Plato’s account without much ado—indeed, the beginning of De Interpretatione reads like a direct continuation of the passages from the Sophist mentioned above. He emphasizes that truth and falsehood have to do with combination and separation (cf. De Int. 16a10; in De Anima 430a25, he says: “where the alternative of true and false applies, there we always find a sort of combining of objects of thought in a quasi-unity”). Unlike Plato, Aristotle feels the need to characterize simple affirmative and negative statements (predications) separately—translating rather more literally than is usual: “An affirmation is a predication of something toward something, a negation is a predication of something away from something” (De Int. 17a25). This characterization reappears early in the Prior Analytics (24a). It thus seems fair to say that the subject-predicate analysis of simple declarative sentences—the most basic feature of Aristotelian term logic which was to reign supreme for many centuries—had its origin in Plato’s response to a sophistical argument against the possibility of falsehood. One may note that Aristotle’s famous definition of truth (see Section 1) actually begins with the definition of falsehood.

Fact-based correspondence theories became prominent only in the 20th century, though one can find remarks in Aristotle that fit this approach (see Section 1)—somewhat surprisingly in light of his repeated emphasis on subject-predicate structure wherever truth and falsehood are concerned. Fact-based theories do not presuppose that the truth-bearing items have subject-predicate structure; indeed, they can be stated without any explicit reference to the structure of truth-bearing items. The approach thus embodies an alternative response to the problem of falsehood, a response that may claim to extricate the theory of truth from the limitations imposed on it through the presupposition of subject-predicate structure inherited from the response to the problem of falsehood favored by Plato, Aristotle, and the medieval and modern tradition.

The now classical formulation of a fact-based correspondence theory was foreshadowed by Hume (Treatise, 3.1.1) and Mill (Logic, 1.5.1). It appears in its canonical form early in the 20th century in Moore (1910-11, chap. 15) and Russell: “Thus a belief is true when there is a corresponding fact, and is false when there is no corresponding fact” (1912, p. 129; cf. also his 1905, 1906, 1910, and 1913). The self-conscious emphasis on facts as the corresponding portions of reality—and a more serious concern with problems raised by falsehood—distinguishes this version from its foreshadowings. Russell and Moore’s forceful advocacy of truth as correspondence to a fact was, at the time, an integral part of their defense of metaphysical realism. Somewhat ironically, their formulations are indebted to their idealist opponents, F. H. Bradley (1883, chaps. 1&2), and H. H. Joachim (1906), the latter was an early advocate of the competing coherence theory, who had set up a correspondence-to-fact account of truth as the main target of his attack on realism. Later, Wittgenstein (1921) and Russell (1918) developed “logical atomism”, which introduces an important modification of the fact-based correspondence approach (see below, Section 7.1). Further modifications of the correspondence theory, bringing a return to more overtly semantic and broadly object-based versions, were influenced by Tarski’s (1935) technical work on truth (cf. Field 1972, Popper 1972).

2. Truthbearers, Truthmakers, Truth

2.1 Truthbearers

Correspondence theories of truth have been given for beliefs, thoughts, ideas, judgments, statements, assertions, utterances, sentences, and propositions. It has become customary to talk of truthbearers whenever one wants to stay neutral between these choices. Five points should be kept in mind:

  1. The term “truthbearer” is somewhat misleading. It is intended to refer to bearers of truth or falsehood (truth-value-bearers), or alternatively, to things of which it makes sense to ask whether they are true or false, thus allowing for the possibility that some of them might be neither.
  2. One distinguishes between secondary and primary truthbearers. Secondary truthbearers are those whose truth-values (truth or falsehood) are derived from the truth-values of primary truthbearers, whose truth-values are not derived from any other truthbearers. Consequently, the term “true” is usually regarded as ambiguous, taking its primary meaning when applied to primary truthbearers and various secondary meanings when applied to other truthbearers. This is, however, not a brute ambiguity, since the secondary meanings are supposed to be derived, i.e. definable from, the primary meaning together with additional relations. For example, one might hold that propositions are true or false in the primary sense, whereas sentences are true or false in a secondary sense, insofar as they express propositions that are true or false (in the primary sense). The meanings of “true”, when applied to truthbearers of different kinds, are thus connected in a manner familiar from what Aristotelians called “analogical” uses of a term—nowadays one would call this “focal meaning”; e.g., “healthy” in “healthy organism” and “healthy food”, the latter being defined as healthy in the secondary sense of contributing to the healthiness (primary sense) of an organism.
  3. It is often unproblematic to advocate one theory of truth for bearers of one kind and another theory for bearers of a different kind (e.g., a deflationary theory of truth, or an identity theory, applied to propositions, could be a component of some form of correspondence theory of truth for sentences). Different theories of truth applied to bearers of different kinds do not automatically compete. The standard segregation of truth theories into competing camps (found in textbooks, handbooks, and dictionaries) proceeds under the assumption—really a pretense—that they are intended for primary truthbearers of the same kind.
  4. Confusingly, there is little agreement as to which entities are properly taken to be primary truthbearers. Nowadays, the main contenders are public language sentences, sentences of the language of thought (sentential mental representations), and propositions. Popular earlier contenders—beliefs, judgments, statements, and assertions—have fallen out of favor, mainly for two reasons:
    1. The problem of logically complex truthbearers. A subject, S, may hold a disjunctive belief (the baby will be a boy or the baby will be a girl), while believing only one, or neither, of the disjuncts. Also, S may hold a conditional belief (if whales are fish, then some fish are mammals) without believing the antecedent or the consequent. Also, S will usually hold a negative belief (not everyone is lucky) without believing what is negated. In such cases, the truth-values of S’s complex beliefs depend on the truth-values of their constituents, although the constituents may not be believed by S or by anyone. This means that a view according to which beliefs are primary truthbearers seems unable to account for how the truth-values of complex beliefs are connected to the truth-values of their simpler constituents—to do this one needs to be able to apply truth and falsehood to belief-constituents even when they are not believed. This point, which is equally fundamental for a proper understanding of logic, was made by all early advocates of propositions (cf. Bolzano 1837, I.§§22, 34; Frege 1879, §§2-5; Husserl 1900, I.§11; Meinong 1902, §6). The problem arises in much the same form for views that would take judgments, statements, or assertions as primary truthbearers. The problem is not easily evaded. Talk of unbelieved beliefs (unjudged judgments, unstated statements, unasserted assertions) is either absurd or simply amounts to talk of unbelieved (unjudged, unstated, unasserted) propositions or sentences. It is noteworthy, incidentally, that quite a few philosophical proposals (concerning truth as well as other matters) run afoul of the simple observation that there are unasserted and unbelieved truthbearers (cf. Geach 1960 & 1965).
    2. The duality of state/content a.k.a. act/object. The noun “belief” can refer to the state of believing or to its content, i.e., to what is believed. If the former, the state of believing, can be said to be true or false at all, which is highly questionable, then only insofar as the latter, what is believed, is true or false. Similarly for nouns referring to mental acts or their objects (contents), such as “judgment”, “statement”, and “assertion”.
  5. Mental sentences were the preferred primary truthbearers throughout the medieval period. They were neglected in the first half of the 20th century, but made a comeback in the second half through the revival of the representational theory of the mind (especially in the form of the language-of-thought hypothesis, cf. Fodor 1975). Somewhat confusingly (to us now), for many centuries the term “proposition” (propositio) was reserved exclusively for sentences, written, spoken or mental. This use was made official by Boethius in the 6th century, and is still found in Locke’s Essay in 1705 and in Mill’s Logic in 1843. Some time after that, e.g., in Moore’s 1901-01, “proposition” switched sides, the term now being used for what is said by uttering a sentence, for what is believed, judged, stated, assumed (etc.)—with occasional reversions to medieval usage, e.g. in Russell (1918, 1919).

2.2 Truthmakers

Talk of truthmakers serves a function similar, but correlative, to talk of truthbearers. A truthmaker is anything that makes some truthbearer true. Different versions of the correspondence theory will have different, and often competing, views about what sort of items true truthbearers correspond to (facts, states of affairs, events, things, tropes, properties). It is convenient to talk of truthmakers whenever one wants to stay neutral between these choices. Four points should be kept in mind:

  1. The notion of a truthmaker is tightly connected with, and dependent on, the relational notion of truthmaking: a truthmaker is whatever stands in the truthmaking relation to some truthbearer. Despite the causal overtones of “maker” and “making”, this relation is usually not supposed to be a causal relation.
  2. The terms “truthmaking” and “truthmaker” are ambiguous. For illustration, consider a classical correspondence theory on which x is true if and only if x corresponds to some fact. One can say (a) that x is made true by a fact, namely the fact (or a fact) that x corresponds to. One can also say (b) that x is made true by x’s correspondence to a fact. Both uses of “is made true by” are correct and both occur in discussions of truth. But they are importantly different and must be distinguished. The (a)-use is usually the intended one; it expresses a relation peculiar to truth and leads to a use of “truthmaker” that actually picks out the items that would normally be intended by those using the term. The (b)-use does not express a relation peculiar to truth; it is just an instance (for “F” = “true”) of the generic formula “what makes an F-thing an F” that can be employed to elicit the definiens of a proposed definition of F. Compare: what makes an even number even is its divisibility by 2; what makes a right action right is its having better consequences than available alternative actions. Note that anyone proposing a definition or account of truth can avail themselves of the notion of truthmaking in the (b)-sense; e.g., a coherence theorist, advocating that a belief is true if and only if it coheres with other beliefs, can say: what makes a true belief true is its coherence with other beliefs. So, on the (b)-use, “truthmaking” and “truthmaker” do not signal any affinity with the basic idea underlying the correspondence theory of truth, whereas on the (a)-use these terms do signal such an affinity.
  3. Talk of truthmaking and truthmakers goes well with the basic idea underlying the correspondence theory; hence, it might seem natural to describe a traditional fact-based correspondence theory as maintaining that the truthmakers are facts and that the correspondence relation is the truthmaking relation. However, the assumption that the correspondence relation can be regarded as (a species of) the truthmaking relation is dubious. Correspondence appears to be a symmetric relation (if x corresponds to y, then y corresponds to x), whereas it is usually taken for granted that truthmaking is an asymmetric relation, or at least not a symmetric one. It is hard to see how a symmetric relation could be (a species of) an asymmetric or non-symmetric relation (cf. David 2009.)
  4. Talk of truthmaking and truthmakers is frequently employed during informal discussions involving truth but tends to be dropped when a more formal or official formulation of a theory of truth is produced (one reason being that it seems circular to define or explain truth in terms of truthmakers or truthmaking). However, in recent years, the informal talk has been turned into an official doctrine: “truthmaker theory”. This theory should be distinguished from informal truthmaker talk: not everyone employing the latter would subscribe to the former. Moreover, truthmaker theory should not simply be assumed to be a version of the correspondence theory; indeed, some advocates present it as a competitor to the correspondence theory (see below, Section 8.5).

2.3 Truth

The abstract noun “truth” has various uses. (a) It can be used to refer to the general relational property otherwise referred to as being true; though the latter label would be more perspicuous, it is rarely used, even in philosophical discussions. (b) The noun “truth” can be used to refer to the concept that “picks out” the property and is expressed in English by the adjective “true”. Some authors do not distinguish between concept and property; others do, or should: an account of the concept might differ significantly from an account of the property. To mention just one example, one might maintain, with some plausibility, that an account of the concept ought to succumb to the liar paradox (see the entry on the liar paradox), otherwise it wouldn’t be an adequate account of our concept of truth; this idea is considerably less plausible in the case of the property. Any proposed “definition of truth” might be intend as a definition of the property or of the concept or both; its author may or may not be alive to the difference. (c) The noun “truth” can be used, finally, to refer to some set of true truthbarers (possibly unknown), as in: “The truth is out there”, and: “The truth about this matter will never be known”.

3. Simple Versions of the Correspondence Theory

The traditional centerpiece of any correspondence theory is a definition of truth. Nowadays, a correspondence definition is most likely intended as a “real definition”, i.e., as a definition of the property, which does not commit its advocate to the claim that the definition provides a synonym for the term “true”. Most correspondence theorists would consider it implausible and unnecessarily bold to maintain that “true” means the same as “corresponds with a fact”. Some simple forms of correspondence definitions of truth should be distinguished (“iff” means “if and only if”; the variable, “x”, ranges over whatever truthbearers are taken as primary; the notion of correspondence might be replaced by various related notions):

(1)x is true iff x corresponds to some fact;
x is false iff x does not correspond to any fact.
(2)x is true iff x corresponds to some state of affairs that obtains;
x is false iff x corresponds to some state of affairs that does not obtain.

Both forms invoke portions of reality—facts/states of affairs—that are typically denoted by that-clauses or by sentential gerundives, viz. the fact/state of affairs that snow is white, or the fact/state of affairs of snow’s being white. (2)’s definition of falsehood is committed to there being (existing) entities of this sort that nevertheless fail to obtain, such as snow’s being green. (1)’s definition of falsehood is not so committed: to say that a fact does not obtain means, at best, that there is no such fact, that no such fact exists. It should be noted that this terminology is not standardized: some authors use “state of affairs” much like “fact” is used here (e.g. Armstrong 1997). The question whether non-obtaining beings of the relevant sort are to be accepted is the substantive issue behind such terminological variations. The difference between (2) and (1) is akin to the difference between Platonism about properties (embraces uninstantiated properties) and Aristotelianism about properties (rejects uninstantiated properties).

Advocates of (2) hold that facts are states of affairs that obtain, i.e., they hold that their account of truth is in effect an analysis of (1)’s account of truth. So disagreement turns largely on the treatment of falsehood, which (1) simply identifies with the absence of truth.

The following points might be made for preferring (2) over (1): (a) Form (2) does not imply that things outside the category of truthbearers (tables, dogs) are false just because they don’t correspond to any facts. One might think this “flaw” of (1) is easily repaired: just put an explicit specification of the desired category of truthbearers into both sides of (1). However, some worry that truthbearer categories, e.g. declarative sentences or propositions, cannot be defined without invoking truth and falsehood, which would make the resultant definition implicitly circular. (b) Form (2) allows for items within the category of truthbearers that are neither true nor false, i.e., it allows for the failure of bivalence. Some, though not all, will regard this as a significant advantage. (c) If the primary truthbearers are sentences or mental states, then states of affairs could be their meanings or contents, and the correspondence relation in (2) could be understood accordingly, as the relation of representation, signification, meaning, or having-as-content. Facts, on the other hand, cannot be identified with the meanings or contents of sentences or mental states, on pain of the absurd consequence that false sentences and beliefs have no meaning or content. (d) Take a truth of the form ‘p or q’, where ‘p’ is true and ‘q’ false. What are the constituents of the corresponding fact? Since ‘q’ is false, they cannot both be facts (cf. Russell 1906-07, p. 47f.). Form (2) allows that the fact corresponding to ‘p or q’ is an obtaining disjunctive state of affairs composed of a state of affairs that obtains and a state of affairs that does not obtain.

The main point in favor of (1) over (2) is that (1) is not committed to counting non-obtaining states of affairs, like the state of affairs that snow is green, as constituents of reality.

(One might observe that, strictly speaking, (1) and (2), being biconditionals, are not ontologically committed to anything. Their respective commitments to facts and states of affairs arise only when they are combined with claims to the effect that there is something that is true and something that is false. The discussion assumes some such claims as given.)

Both forms, (1) and (2), should be distinguished from:

(3)x is true iff x corresponds to some fact that exists;
x is false iff x corresponds to some fact that does not exist,

which is a confused version of (1), or a confused version of (2), or, if unconfused, signals commitment to Meinongianism, i.e., the thesis that there are things/facts that do not exist. The lure of (3) stems from the desire to offer more than a purely negative correspondence account of falsehood while avoiding commitment to non-obtaining states of affairs. Moore at times succumbs to (3)’s temptations (1910-11, pp. 267 & 269, but see p. 277). It can also be found in the 1961 translation of Wittgenstein (1921, 4.25), who uses “state of affairs” (Sachverhalt) to refer to (atomic) facts. The translation has Wittgenstein saying that an elementary proposition is false, when the corresponding state of affairs (atomic fact) does not exist—but the German original of the same passage looks rather like a version of (2). Somewhat ironically, a definition of form (3) reintroduces Plato’s problem of falsehood into a fact-based correspondence theory, i.e., into a theory of the sort that was supposed to provide an alternative solution to that very problem (see Section 1.2).

A fourth simple form of correspondence definition was popular for a time (cf. Russell 1918, secs. 1 & 3; Broad 1933, IV.2.23; Austin 1950, fn. 23), but seems to have fallen out of favor:

(4)x is true iff x corresponds (agrees) with some fact;
x is false iff x mis-corresponds (disagrees) with some fact.

This formulation attempts to avoid (2)’s commitment to non-obtaining states of affairs and (3)’s commitment to non-existent facts by invoking the relation of mis-correspondence, or disagreement, to account for falsehood. It differs from (1) in that it attempts to keep items outside the intended category of x’s from being false: supposedly, tables and dogs cannot mis-correspond with a fact. Main worries about (4) are: (a) its invocation of an additional, potentially mysterious, relation, which (b) seems difficult to tame: Which fact is the one that mis-corresponds with a given falsehood? and: What keeps a truth, which by definition corresponds with some fact, from also mis-corresponding with some other fact, i.e., from being a falsehood as well?

In the following, I will treat definitions (1) and (2) as paradigmatic; moreover, since advocates of (2) agree that obtaining states of affairs are facts, it is often convenient to condense the correspondence theory into the simpler formula provided by (1), “truth is correspondence to a fact”, at least as long as one is not particularly concerned with issues raised by falsehood.

4. Arguments for the Correspondence Theory

The main positive argument given by advocates of the correspondence theory of truth is its obviousness. Descartes: “I have never had any doubts about truth, because it seems a notion so transcendentally clear that nobody can be ignorant of it...the word ‘truth’, in the strict sense, denotes the conformity of thought with its object” (1639, AT II 597). Even philosophers whose overall views may well lead one to expect otherwise tend to agree. Kant: “The nominal definition of truth, that it is the agreement of [a cognition] with its object, is assumed as granted” (1787, B82). William James: “Truth, as any dictionary will tell you, is a property of certain of our ideas. It means their ‘agreement’, as falsity means their disagreement, with ‘reality’” (1907, p. 96). Indeed, The Oxford English Dictionary tells us: “Truth, n. Conformity with fact; agreement with reality”.

In view of its claimed obviousness, it would seem interesting to learn how popular the correspondence theory actually is. There are some empirical data. The PhilPapers Survey (conducted in 2009; cf. Bourget and Chalmers 2014), more specifically, the part of the survey targeting all regular faculty members in 99 leading departments of philosophy, reports the following responses to the question: “Truth: correspondence, deflationary, or epistemic?” Accept or lean toward: correspondence 50.8%; deflationary 24.8%; other 17.5%; epistemic 6.9%. The data suggest that correspondence-type theories may enjoy a weak majority among professional philosophers and that the opposition is divided. This fits with the observation that typically, discussions of the nature of truth take some version of the correspondence theory as the default view, the view to be criticized or to be defended against criticism.

Historically, the correspondence theory, usually in an object-based version, was taken for granted, so much so that it did not acquire this name until comparatively recently, and explicit arguments for the view are very hard to find. Since the (comparatively recent) arrival of apparently competing approaches, correspondence theorists have developed negative arguments, defending their view against objections and attacking (sometimes ridiculing) competing views.

5. Objections to the Correspondence Theory

Objection 1: Definitions like (1) or (2) are too narrow. Although they apply to truths from some domains of discourse, e.g., the domain of science, they fail for others, e.g. the domain of morality: there are no moral facts.

The objection recognizes moral truths, but rejects the idea that reality contains moral facts for moral truths to correspond to. Logic provides another example of a domain that has been “flagged” in this way. The logical positivists recognized logical truths but rejected logical facts. Their intellectual ancestor, Hume, had already given two definitions of “true”, one for logical truths, broadly conceived, the other for non-logical truths: “Truth or falsehood consists in an agreement or disagreement either to the real relations of ideas, or to real existence and matter of fact” (Hume, Treatise, 3.1.1, cf. 2.3.10; see also Locke, Essay, 4.5.6, for a similarly two-pronged account but in terms of object-based correspondence).

There are four possible responses to objections of this sort: (a) Noncognitivism, which says that, despite appearances to the contrary, claims from the flagged domain are not truth-evaluable to begin with, e.g., moral claims are commands or expressions of emotions disguised as truthbearers; (b) Error theory, which says that all claims from the flagged domain are false; (c) Reductionism, which says that truths from the flagged domain correspond to facts of a different domain regarded as unproblematic, e.g., moral truths correspond to social-behavioral facts, logical truths correspond to facts about linguistic conventions; and (d) Standing firm, i.e., embracing facts of the flagged domain.

The objection in effect maintains that there are different brands of truth (of the property being true, not just different brands of truths) for different domains. On the face of it, this conflicts with the observation that there are many obviously valid arguments combining premises from flagged and unflagged domains. The observation is widely regarded as refuting non-cognitivism, once the most popular (concessive) response to the objection.

In connection with this objection, one should take note of the recently developed “multiple realizability” view of truth, according to which truth is not to be identified with correspondence to fact but can be realized by correspondence to fact for truthbearers of some domains of discourse and by other properties for truthbearers of other domains of discourse, including “flagged” domains. Though it retains important elements of the correspondence theory, this view does not, strictly speaking, offer a response to the objection on behalf of the correspondence theory and should be regarded as one of its competitors (see below, Section 8.2).

Objection 2: Correspondence theories are too obvious. They are trivial, vacuous, trading in mere platitudes. Locutions from the “corresponds to the facts”-family are used regularly in everyday language as idiomatic substitutes for “true”. Such common turns of phrase should not be taken to indicate commitment to a correspondence theory in any serious sense. Definitions like (1) or (2) merely condense some trivial idioms into handy formulas; they don’t deserve the grand label “theory”: there is no theoretical weight behind them (cf. Woozley 1949, chap. 6; Davidson 1969; Blackburn 1984, chap. 7.1).

In response, one could point out: (a) Definitions like (1) or (2) are “mini-theories”—mini-theories are quite common in philosophy—and it is not at all obvious that they are vacuous merely because they are modeled on common usage. (b) There are correspondence theories that go beyond these definitions. (c) The complaint implies that definitions like (1) and/or (2) are generally accepted and are, moreover, so shallow that they are compatible with any deeper theory of truth. This makes it rather difficult to explain why some thinkers emphatically reject all correspondence formulations. (d) The objection implies that the correspondence of S’s belief with a fact could be said to consist in, e.g., the belief’s coherence with S’s overall belief system. This is wildly implausible, even on the most shallow understanding of “correspondence” and “fact”.

Objection 3: Correspondence theories are too obscure.

Objections of this sort, which are the most common, protest that the central notions of a correspondence theory carry unacceptable commitments and/or cannot be accounted for in any respectable manner. The objections can be divided into objections primarily aimed at the correspondence relation and its relatives (3.C1, 3.C2), and objections primarily aimed at the notions of fact or state of affairs (3.F1, 3.F2):

3.C1: The correspondence relation must be some sort of resemblance relation. But truthbearers do not resemble anything in the world except other truthbearers—echoing Berkeley’s “an idea can be like nothing but an idea”.

3.C2: The correspondence relation is very mysterious: it seems to reach into the most distant regions of space (faster than light?) and time (past and future). How could such a relation possibly be accounted for within a naturalistic framework? What physical relation could it possibly be?

3.F1: Given the great variety of complex truthbearers, a correspondence theory will be committed to all sorts of complex “funny facts” that are ontologically disreputable. Negative, disjunctive, conditional, universal, probabilistic, subjunctive, and counterfactual facts have all given cause for complaint on this score.

3.F2: All facts, even the most simple ones, are disreputable. Fact-talk, being wedded to that-clauses, is entirely parasitic on truth-talk. Facts are too much like truthbearers. Facts are fictions, spurious sentence-like slices of reality, “projected from true sentences for the sake of correspondence” (Quine 1987, p. 213; cf. Strawson 1950).

6. Correspondence as Isomorphism

Some correspondence theories of truth are two-liner mini-theories, consisting of little more than a specific version of (1) or (2). Normally, one would expect a bit more, even from a philosophical theory (though mini-theories are quite common in philosophy). One would expect a correspondence theory to go beyond a mere definition like (1) or (2) and discharge a triple task: it should tell us about the workings of the correspondence relation, about the nature of facts, and about the conditions that determine which truthbearers correspond to which facts.

One can approach this by considering some general principles a correspondence theory might want to add to its central principle to flesh out her theory. The first such principle says that the correspondence relation must not collapse into identity—“It takes two to make a truth” (Austin 1950, p. 118):

No truth is identical with a fact correspondence to which is sufficient for its being a truth.

It would be much simpler to say that no truth is identical with a fact. However, some authors, e.g. Wittgenstein 1921, hold that a proposition (Satz, his truthbearer) is itself a fact, though not the same fact as the one that makes the proposition true (see also King 2007). Nonidentity is usually taken for granted by correspondence theorists as constitutive of the very idea of a correspondence theory—authors who advance contrary arguments to the effect that correspondence must collapse into identity regard their arguments as objections to any form of correspondence theory (cf. Moore 1901/02, Frege 1918-19, p. 60).

Concerning the correspondence relation, two aspects can be distinguished: correspondence as correlation and correspondence as isomorphism (cf. Pitcher 1964; Kirkham 1992, chap. 4). Pertaining to the first aspect, familiar from mathematical contexts, a correspondence theorist is likely to adopt claim (a), and some may in addition adopt claim (b), of:

(a) Every truth corresponds to exactly one fact;
(b) Different truths correspond to different facts.

Together, (a) and (b) say that correspondence is a one-one relation. This seems needlessly strong, and it is not easy to find real-life correspondence theorists who explicitly embrace part (b): Why shouldn’t different truths correspond to the same fact, as long as they are not too different? Explicit commitment to (a) is also quite rare. However, correspondence theorists tend to move comfortably from talk about a given truth to talk about the fact it corresponds to—a move that signals commitment to (a).

Correlation does not imply anything about the inner nature of the corresponding items. Contrast this with correspondence as isomorphism, which requires the corresponding items to have the same, or sufficiently similar, constituent structure. This aspect of correspondence, which is more prominent (and more notorious) than the previous one, is also much more difficult to make precise. Let us say, roughly, that a correspondence theorist may want to add a claim to her theory committing her to something like the following:

If an item of kind K corresponds to a certain fact, then they have the same or sufficiently similar structure: the overall correspondence between a true K and a fact is a matter of part-wise correspondences, i.e. of their having corresponding constituents in corresponding places in the same structure, or in sufficiently similar structures.

The basic idea is that truthbearers and facts are both complex structured entities: truthbearers are composed of (other truthbearers and ultimately of) words, or concepts; facts are composed of (other facts or states of affairs and ultimately of) things, properties, and relations. The aim is to show how the correspondence relation is generated from underlying relations between the ultimate constituents of truthbearers, on the one hand, and the ultimate constituents of their corresponding facts, on the other. One part of the project will be concerned with these correspondence-generating relations: it will lead into a theory that addresses the question how simple words, or concepts, can be about things, properties, and relations; i.e., it will merge with semantics or psycho-semantics (depending on what the truthbearers are taken to be). The other part of the project, the specifically ontological part, will have to provide identity criteria for facts and explain how their simple constituents combine into complex wholes. Putting all this together should yield an account of the conditions determining which truthbearers correspond to which facts.

Correlation and Structure reflect distinct aspects of correspondence. One might want to endorse the former without the latter, though it is hard to see how one could endorse the latter without embracing at least part (a) of the former.

The isomorphism approach offers an answer to objection 3.C1. Although the truth that the cat is on the mat does not resemble the cat or the mat (the truth doesn’t meow or smell, etc.), it does resemble the fact that the cat is on the mat. This is not a qualitative resemblance; it is a more abstract, structural resemblance.

The approach also puts objection 3.C2 in some perspective. The correspondence relation is supposed to reduce to underlying relations between words, or concepts, and reality. Consequently, a correspondence theory is little more than a spin-off from semantics and/or psycho-semantics, i.e. the theory of intentionality construed as incorporating a representational theory of the mind (cf. Fodor 1989). This reminds us that, as a relation, correspondence is no more—but also no less—mysterious than semantic relations in general. Such relations have some curious features, and they raise a host of puzzles and difficult questions—most notoriously: Can they be explained in terms of natural (causal) relations, or do they have to be regarded as irreducibly non-natural aspects of reality? Some philosophers have claimed that semantic relations are too mysterious to be taken seriously, usually on the grounds that they are not explainable in naturalistic terms. But one should bear in mind that this is a very general and extremely radical attack on semantics as a whole, on the very idea that words and concepts can be about things. The common practice to aim this attack specifically at the correspondence theory seems misleading. As far as the intelligibility of the correspondence relation is concerned, the correspondence theory will stand, or fall, with the general theory of reference and intentionality.

It should be noted, though, that these points concerning objections 3.C1 and 3.C2 are not independent of one’s views about the nature of the primary truthbearers. If truthbearers are taken to be sentences of an ordinary language (or an idealized version thereof), or if they are taken to be mental representations (sentences of the language of thought), the above points hold without qualification: correspondence will be a semantic or psycho-semantic relation. If, on the other hand, the primary truthbearers are taken to be propositions, there is a complication:

  1. On a broadly Fregean view of propositions, propositions are constituted by concepts of objects and properties (in the logical, not the psychological, sense of “concept”). On this view, the above points still hold, since the relation between concepts, on the one hand, and the objects and properties they are concepts of, on the other, appears to be a semantic relation, a concept-semantic relation.
  2. On the so-called Russellian view of propositions (which the early Russell inherited mostly from early Moore), propositions are constituted, not of concepts of objects and properties, but of the objects and properties themselves (cf. Russell 1903). On this view, the points above will most likely fail, since the correspondence relation would appear to collapse into the identity relation when applied to true Russellian propositions. It is hard to see how a true Russellian proposition could be anything but a fact: What would a fact be, if not this sort of thing? So the principle of Nonidentity is rejected, and with it goes the correspondence theory of truth: “Once it is definitely recognized that the proposition is to denote, not a belief or form of words, but an object of belief, it seems plain that a truth differs in no respect from the reality with which it was supposed merely to correspond” (Moore 1901-02, p. 717). A simple, fact-based correspondence theory, applied to propositions understood in the Russellian way, thus reduces to an identity theory of truth, on which a proposition is true iff it is a fact, and false, iff it is not a fact. See below, Section 8.3; and the entries on propositions, singular propositions, and structured propositions in this encyclopedia.

But Russellians don’t usually renounce the correspondence theory entirely. Though they have no room for (1) from Section 3, when applied to propositions as truthbearers, correspondence will enter into their account of truth for sentences, public or mental. The account will take the form of Section 3’s (2), applied to categories of truthbearers other than propositions, where Russellian propositions show up on the right-hand side in the guise of states of affairs that obtain or fail to obtain. Commitment to states of affairs in addition to propositions is sometimes regarded with scorn, as a gratuitous ontological duplication. But Russellians are not committed to states of affairs in addition to propositions, for propositions, on their view, must already be states of affairs. This conclusion is well nigh inevitable, once true propositions have been identified with facts. If a true proposition is a fact, then a false proposition that might have been true would have been a fact, if it had been true. So, a (contingent) false proposition must be the same kind of being as a fact, only not a fact—an unfact; but that just is a non-obtaining state of affairs under a different name. Russellian propositions are states of affairs: the false ones are states of affairs that do not obtain, and the true ones are states of affairs that do obtain.

The Russellian view of propositions is popular nowadays. Somewhat curiously, contemporary Russellians hardly ever refer to propositions as facts or states of affairs. This is because they are much concerned with understanding belief, belief attributions, and the semantics of sentences. In such contexts, it is more natural to talk proposition-language than state-of-affairs-language. It feels odd (wrong) to say that someone believes a state of affairs, or that states of affairs are true or false. For that matter, it also feels odd (wrong) to say that some propositions are facts, that facts are true, and that propositions obtain or fail to obtain. Nevertheless, all of this must be the literal truth, according to the Russellians. They have to claim that “proposition” and “state of affairs”, much like “evening star” and “morning star”, are different names for the same things—they come with different associations and are at home in somewhat different linguistic environments, which accounts for the felt oddness when one name is transported to the other’s environment.

Returning to the isomorphism approach in general, on a strict or naïve implementation of this approach, correspondence will be a one-one relation between truths and corresponding facts, which leaves the approach vulnerable to objections against funny facts (3.F1): each true truthbearer, no matter how complex, will be assigned a matching fact. Moreover, since a strict implementation of isomorphism assigns corresponding entities to all (relevant) constituents of truthbearers, complex facts will contain objects corresponding to the logical constants (“not”, “or”, “if-then”, etc.), and these “logical objects” will have to be regarded as constituents of the world. Many philosophers have found it hard to believe in the existence of all these funny facts and funny quasi-logical objects.

The isomorphism approach has never been advocated in a fully naïve form, assigning corresponding objects to each and every wrinkle of our verbal or mental utterings. Instead, proponents try to isolate the “relevant” constituents of truthbearers through meaning analysis, aiming to uncover the logical form, or deep structure, behind ordinary language and thought. This deep structure might then be expressed in an ideal-language (typically, the language of predicate logic), whose syntactic structure is designed to mirror perfectly the ontological structure of reality. The resulting view—correspondence as isomorphism between properly analyzed truthbearers and facts—avoids assigning strange objects to such phrases as “the average husband”, “the sake of”, and “the present king of France”; but the view remains committed to logically complex facts and to logical objects corresponding to the logical constants.

Austin (1950) rejects the isomorphism approach on the grounds that it projects the structure of our language onto the world. On his version of the correspondence theory (a more elaborated variant of (4) applied to statements), a statement as a whole is correlated to a state of affairs by arbitrary linguistic conventions without mirroring the inner structure of its correlate (cf. also Vision 2004). This approach appears vulnerable to the objection that it avoids funny facts at the price of neglecting systematicity. Language does not provide separate linguistic conventions for each statement: that would require too vast a number of conventions. Rather, it seems that the truth-values of statements are systematically determined, via a relatively small set of conventions, by the semantic values (relations to reality) of their simpler constituents. Recognition of this systematicity is built right into the isomorphism approach.

Critics frequently echo Austin’s “projection”-complaint, 3.F2, that a traditional correspondence theory commits “the error of reading back into the world the features of language” (Austin 1950, p. 155; cf. also, e.g., Rorty 1981). At bottom, this is a pessimistic stance: if there is a prima facie structural resemblance between a mode of speech or thought and some ontological category, it is inferred, pessimistically, that the ontological category is an illusion, a matter of us projecting the structure of our language or thought into the world. Advocates of traditional correspondence theories can be seen as taking the opposite stance: unless there are specific reasons to the contrary, they are prepared to assume, optimistically, that the structure of our language and/or thought reflects genuine ontological categories, that the structure of our language and/or thought is, at least to a significant extent, the way it is because of the structure of the world.

7. Modified Versions of the Correspondence Theory

7.1 Logical Atomism

Wittgenstein (1921) and Russell (1918) propose modified fact-based correspondence accounts of truth as part of their program of logical atomism. Such accounts proceed in two stages. At the first stage, the basic truth-definition, say (1) from Section 3, is restricted to a special subclass of truthbearers, the so-called elementary or atomic truthbearers, whose truth is said to consist in their correspondence to (atomic) facts: if x is elementary, then x is true iff x corresponds to some (atomic) fact. This restricted definition serves as the base-clause for truth-conditional recursion-clauses given at the second stage, at which the truth-values of non-elementary, or molecular, truthbearers are explained recursively in terms of their logical structure and the truth-values of their simpler constituents. For example: a sentence of the form ‘not-p’ is true iff ‘p’ is false; a sentence of the form ‘p and q’ is true iff ‘p’ is true and ‘q’ is true; a sentence of the form ‘p or q’ is true iff ‘p’ is true or ‘q’ is true, etc. These recursive clauses (called “truth conditions”) can be reapplied until the truth of a non-elementary, molecular sentence of arbitrary complexity is reduced to the truth or falsehood of its elementary, atomic constituents.

Logical atomism exploits the familiar rules, enshrined in the truth-tables, for evaluating complex formulas on the basis of their simpler constituents. These rules can be understood in two different ways: (a) as tracing the ontological relations between complex facts and constituent simpler facts, or (b) as tracing logico-semantic relations, exhibiting how the truth-values of complex sentences can be explained in terms of their logical relations to simpler constituent sentences together with the correspondence and non-correspondence of simple, elementary sentences to atomic facts. Logical atomism takes option (b).

Logical atomism is designed to go with the ontological view that the world is the totality of atomic facts (cf. Wittgenstein 1921, 2.04); thus accommodating objection 3.F2 by doing without funny facts: atomic facts are all the facts there are—although real-life atomists tend to allow conjunctive facts, regarding them as mere aggregates of atomic facts. An elementary truth is true because it corresponds to an atomic fact: correspondence is still isomorphism, but it holds exclusively between elementary truths and atomic facts. There is no match between truths and facts at the level of non-elementary, molecular truths; e.g., ‘p’, ‘p or q’, and ‘p or r’ might all be true merely because ‘p’ corresponds to a fact). The trick for avoiding logically complex facts lies in not assigning any entities to the logical constants. Logical complexity, so the idea goes, belongs to the structure of language and/or thought; it is not a feature of the world. This is expressed by Wittgenstein in an often quoted passage (1921, 4.0312): “My fundamental idea is that the ‘logical constants’ are not representatives; that there can be no representatives of the logic of facts”; and also by Russell (1918, p. 209f.): “You must not look about the real world for an object which you can call ‘or’, and say ‘Now look at this. This is ‘or’’”.

Though accounts of this sort are naturally classified as versions of the correspondence theory, it should be noted that they are strictly speaking in conflict with the basic forms presented in Section 3. According to logical atomism, it is not the case that for every truth there is a corresponding fact. It is, however, still the case that the being true of every truth is explained in terms of correspondence to a fact (or non-correspondence to any fact) together with (in the case of molecular truths) logical notions detailing the logical structure of complex truthbearers. Logical atomism attempts to avoid commitment to logically complex, funny facts via structural analysis of truthbearers. It should not be confused with a superficially similar account maintaining that molecular facts are ultimately constituted by atomic facts. The latter account would admit complex facts, offering an ontological analysis of their structure, and would thus be compatible with the basic forms presented in Section 3, because it would be compatible with the claim that for every truth there is a corresponding fact. (For more on classical logical atomism, see Wisdom 1931-1933, Urmson 1953, and the entries on Russell's logical atomism and Wittgenstein's logical atomism in this encyclopedia.)

While Wittgenstein and Russell seem to have held that the constituents of atomic facts are to be determined on the basis of a priori considerations, Armstrong (1997, 2004) advocates an a posteriori form of logical atomism. On his view, atomic facts are composed of particulars and simple universals (properties and relations). The latter are objective features of the world that ground the objective resemblances between particulars and explain their causal powers. Accordingly, what particulars and universals there are will have to be determined on the basis of total science.

Problems: Logical atomism is not easy to sustain and has rarely been held in a pure form. Among its difficulties are the following: (a) What, exactly, are the elementary truthbearers? How are they determined? (b) There are molecular truthbearers, such as subjunctives and counterfactuals, that tend to provoke the funny-fact objection but cannot be handled by simple truth-conditional clauses, because their truth-values do not seem to be determined by the truth-values of their elementary constituents. (c) Are there universal facts corresponding to true universal generalizations? Wittgenstein (1921) disapproves of universal facts; apparently, he wants to re-analyze universal generalizations as infinite conjunctions of their instances. Russell (1918) and Armstrong (1997, 2004) reject this analysis; they admit universal facts. (d) Negative truths are the most notorious problem case, because they clash with an appealing principle, the “truthmaker principle” (cf. Section 8.5), which says that for every truth there must be something in the world that makes it true, i.e., every true truthbearer must have a truthmaker. Suppose ‘p’ is elementary. On the account given above, ‘not-p’ is true iff ‘p’ is false iff ‘p’ does not correspond to any fact; hence, ‘not-p’, if true, is not made true by any fact: it does not seem to have a truthmaker. Russell finds himself driven to admit negative facts, regarded by many as paradigmatically disreputable portions of reality. Wittgenstein sometimes talks of atomic facts that do not exist and calls their very nonexistence a negative fact (cf. 1921, 2.06)—but this is hardly an atomic fact itself. Armstrong (1997, chap. 8.7; 2004, chaps. 5-6) holds that negative truths are made true by a second-order “totality fact” which says of all the (positive) first-order facts that they are all the first-order facts.

Atomism and the Russellian view of propositions (see Section 6). By the time Russell advocated logical atomism (around 1918), he had given up on what is now referred to as the Russellian conception of propositions (which he and G. E. Moore held around 1903). But Russellian propositons are popular nowadays. Note that logical atomism is not for the friends of Russellian propositions. The argument is straightforward. We have logically complex beliefs some of which are true. According to the friends of Russellian propositions, the contents of our beliefs are Russellian propositions, and the contents of our true beliefs are true Russellian propositions. Since true Russellian propositions are facts, there must be at least as many complex facts as there are true beliefs with complex contents (and at least as many complex states of affairs as there are true or false beliefs with complex contents). Atomism may work for sentences, public or mental, and for Fregean propositions; but not for Russellian propositions.

Logical atomism is designed to address objections to funny facts (3.F1). It is not designed to address objections to facts in general (3.F2). Here logical atomists will respond by defending (atomic) facts. According to one defense, facts are needed because mere objects are not sufficiently articulated to serve as truthmakers. If a were the sole truthmaker of ‘a is F’, then the latter should imply ‘a is G’, for any ‘G’. So the truthmaker for ‘a is F’ needs at least to involve a and Fness. But since Fness is a universal, it could be instantiated in another object, b, hence the mere existence of a and Fness is not sufficient for making true the claim ‘a is F’: a and Fness need to be tied together in the fact of a’s being F. Armstrong (1997) and Olson (1987) also maintain that facts are needed to make sense of the tie that binds particular objects to universals.

In this context it is usually emphasized that facts do not supervene on, hence, are not reducible to, their constituents. Facts are entities over and above the particulars and universals of which they are composed: a’s loving b and b’s loving a are not the same fact even though they have the very same constituents.

Another defense of facts, surprisingly rare, would point out that many facts are observable: one can see that the cat is on the mat; and this is different from seeing the cat, or the mat, or both. The objection that many facts are not observable would invite the rejoinder that many objects are not observable either. (See Austin 1961, Vendler 1967, chap. 5, and Vision 2004, chap. 3, for more discussion of anti-fact arguments; see also the entry facts in this encyclopedia.)

Some atomists propose an atomistic version of definition (1), but without facts, because they regard facts as slices of reality too suspiciously sentence-like to be taken with full ontological seriousness. Instead, they propose events and/or objects-plus-tropes (a.k.a. modes, particularized qualities, moments) as the corresponding portions of reality. It is claimed that these items are more “thingy” than facts but still sufficiently articulated—and sufficiently abundant—to serve as adequate truthmakers (cf. Mulligan, Simons, and Smith 1984).

7.2 Logical “Subatomism”

Logical atomism aims at getting by without logically complex truthmakers by restricting definitions like (1) or (2) from Section 3 to elementary truthbearers and accounting for the truth-values of molecular truthbearers recursively in terms of their logical structure and atomic truthmakers (atomic facts, events, objects-plus-tropes). More radical modifications of the correspondence theory push the recursive strategy even further, entirely discarding definitions like (1) or (2), and hence the need for atomic truthmakers, by going, as it were, “subatomic”.

Such accounts analyze truthbearers, e.g., sentences, into their subsentential constituents and dissolve the relation of correspondence into appropriate semantic subrelations: names refer to, or denote, objects; predicates (open sentences) apply to, or are satisfied by objects. Satisfaction of complex predicates can be handled recursively in terms of logical structure and satisfaction of simpler constituent predicates: an object o satisfies ‘x is not F’ iff o does not satisfy ‘x is F’; o satisfies ‘x is F or x is G’ iff o satisfies ‘x is F’ or o satisfies ‘x is G’; and so on. These recursions are anchored in a base-clause addressing the satisfaction of primitive predicates: an object o satisfies ‘x is F’ iff o instantiates the property expressed by ‘F’. Some would prefer a more nominalistic base-clause for satisfaction, hoping to get by without seriously invoking properties. Truth for singular sentences, consisting of a name and an arbitrarily complex predicate, is defined thus: A singular sentence is true iff the object denoted by the name satisfies the predicate. Logical machinery provided by Tarski (1935) can be used to turn this simplified sketch into a more general definition of truth—a definition that handles sentences containing relational predicates and quantifiers and covers molecular sentences as well. Whether Tarski’s own definition of truth can be regarded as a correspondence definition, even in this modified sense, is under debate (cf. Popper 1972; Field 1972, 1986; Kirkham 1992, chaps. 5-6; Soames 1999; Künne 2003, chap. 4; Patterson 2008.)

Subatomism constitutes a return to (broadly) object-based correspondence. Since it promises to avoid facts and all similarly articulated, sentence-like slices of reality, correspondence theorists who take seriously objection 3.F2 favor this approach: not even elementary truthbearers are assigned any matching truthmakers. The correspondence relation itself has given way to two semantic relations between constituents of truthbearers and objects: reference (or denotation) and satisfaction—relations central to any semantic theory. Some advocates envision causal accounts of reference and satisfaction (cf. Field 1972; Devitt 1982, 1984; Schmitt 1995; Kirkham 1992, chaps. 5-6). It turns out that relational predicates require talk of satisfaction by ordered sequences of objects. Davidson (1969, 1977) maintains that satisfaction by sequences is all that remains of the traditional idea of correspondence to facts; he regards reference and satisfaction as “theoretical constructs” not in need of causal, or any, explanation.

Problems: (a) The subatomistic approach accounts for the truth-values of molecular truthbearers in the same way as the atomistic approach; consequently, molecular truthbearers that are not truth-functional still pose the same problems as in atomism. (b) Belief attributions and modal claims pose special problems; e.g., it seems that “believes” is a relational predicate, so that “John believes that snow is white” is true iff “believes” is satisfied by John and the object denoted by “that snow is white”; but the latter appears to be a proposition or state of affairs, which threatens to let in through the back-door the very sentence-like slices of reality the subatomic approach was supposed to avoid, thus undermining the motivation for going subatomic. (c) The phenomenon of referential indeterminacy threatens to undermine the idea that the truth-values of elementary truthbearers are always determined by the denotation and/or satisfaction of their constituents; e.g., pre-relativistic uses of the term “mass” are plausibly taken to lack determinate reference (referring determinately neither to relativistic mass nor to rest mass); yet a claim like “The mass of the earth is greater than the mass of the moon” seems to be determinately true even when made by Newton (cf. Field 1973).

Problems for both versions of modified correspondence theories: (a) It is not known whether an entirely general recursive definition of truth, one that covers all truthbearers, can be made available. This depends on unresolved issues concerning the extent to which truthbearers are amenable to the kind of structural analyses that are presupposed by the recursive clauses. The more an account of truth wants to exploit the internal structure of truthbearers, the more it will be hostage to the (limited) availability of appropriate structural analyses of the relevant truthbearers. (b) Any account of truth employing a recursive framework may be virtually committed to taking sentences (maybe sentences of the language of thought) as primary truthbearers. After all, the recursive clauses rely heavily on what appears to be the logico-syntactic structure of truthbearers, and it is unclear whether anything but sentences can plausibly be said to possess that kind of structure. But the thesis that sentences of any sort are to be regarded as the primary truthbearers is contentious. Whether propositions can meaningfully be said to have an analogous (albeit non-linguistic) structure is under debate (cf. Russell 1913, King 2007). (c) If clauses like “‘p or q’ is true iff ‘p’ is true or ‘q’ is true” are to be used in a recursive account of our notion of truth, as opposed to some other notion, it has to be presupposed that ‘or’ expresses disjunction: one cannot define “or” and “true” at the same time. To avoid circularity, a modified correspondence theory (be it atomic or subatomic) must hold that the logical connectives can be understood without reference to correspondence truth.

7.3 Relocating Correspondence

Definitions like (1) and (2) from Section 3 assume, naturally, that truthbearers are true because they, the truthbearers themselves, correspond to facts. There are however views that reject this natural assumption. They propose to account for the truth of truthbearers of certain kinds, propositions, not by way of their correspondence to facts, but by way of the correspondence to facts of other items, the ones that have propositions as their contents. Consider the state of believing that p (or the activity of judging that p). The state (the activity) is not, strictly speaking, true or false; rather, what is true or false is its content, the proposition that p. Nevertheless, on the present view, it is the state of believing that p that corresponds or fails to correspond to a fact. So truth/falsehood for propositions can be defined in the following manner: x is a true/false proposition iff there is a belief state B such that x is the content of B and B corresponds/fails to correspond to a fact.

Such a modification of fact-based correspondence can be found in Moore (1927, p. 83) and Armstrong (1973, 4.iv & 9). It can be adapted to atomistic (Armstrong) and subatomistic views, and to views on which sentences (of the language of thought) are the primary bearers of truth and falsehood. However, by taking the content-carrying states as the primary corresponders, it entails that there are no truths/falsehoods that are not believed by someone. Most advocates of propositions as primary bearers of truth and falsehood will regard this as a serious weakness, holding that there are very many true and false propositions that are not believed, or even entertained, by anyone. Armstrong (1973) combines the view with an instrumentalist attitude towards propositions, on which propositions are mere abstractions from mental states and should not be taken seriously, ontologically speaking.

8. The Correspondence Theory and Its Competitors

8.1 Traditional Competitors

Against the traditional competitors—coherentist, pragmatist, and verificationist and other epistemic theories of truth—correspondence theorists raise two main sorts of objections. First, such accounts tend to lead into relativism. Take, e.g., a coherentist account of truth. Since it is possible that ‘p’ coheres with the belief system of S while ‘not-p’ coheres with the belief system of S*, the coherentist account seems to imply, absurdly, that contradictories, ‘p’ and ‘not-p’, could both be true. To avoid embracing contradictions, coherentists often commit themselves (if only covertly) to the objectionable relativistic view that ‘p’ is true-for-S and ‘not-p’ is true-for-S*. Second, the accounts tend to lead into some form of idealism or anti-realism, e.g., it is possible for the belief that p to cohere with someone’s belief system, even though it is not a fact that p; also, it is possible for it to be a fact that p, even if no one believes that p at all or if the belief does not cohere with anyone’s belief system. Cases of this sort are frequently cited as counterexamples to coherentist accounts of truth. Dedicated coherentists tend to reject such counterexamples, insisting that they are not possible after all. Since it is hard to see why they would not be possible, unless its being a fact that p were determined by the belief’s coherence with other beliefs, this reaction commits them to the anti-realist view that the facts are (largely) determined by what we believe.

This offers a bare outline of the overall shape the debates tend to take. For more on the correspondence theory vs. its traditional competitors see, e.g., Vision 1988; Kirkham 1992, chaps. 3, 7-8; Schmitt 1995; Künne 2003, chap. 7; and essays in Lynch 2001. Walker 1989 is a book-lenght discussion of coherence theories of truth. See also the entries on pragmatism, relativism, the coherence theory of truth, in this encyclopedia.

8.2 Pluralism

The correspondence theory is sometimes accused of overreaching itself: it does apply, so the objection goes, to truths from some domains of discourse, e.g., scientific discourse and/or discourse about everyday midsized physical things, but not to truths from various other domains of discourse, e.g., ethical and/or aesthetic discourse (see the first objection in Section 5 above). Alethic pluralism grows out of this objection, maintaining that truth is constituted by different properties for true propositions from different domains of discourse: by correspondence to fact for true propositions from the domain of scientific or everyday discourse about physical things; by some epistemic property, such as coherence or superassertibility, for true propositions from the domain of ethical and aesthetic discourse, and maybe by still other properties for other domains of discourse. This suggests a position on which the term “true” is multiply ambiguous, expressing different properties when applied to propositions from different domains. However, contemporary pluralists reject this problematic idea, maintaining instead that truth is “multiply realizable”. That is, the term “true” is univocal, it expresses one concept or property, truth (being true), but one that can be realized by or manifested in different properties (correspondence to fact, coherence or superassertibility, and maybe others) for true propositions from different domains of discourse. Truth itself is not to be identified with any of its realizing properties. Instead, it is characterized, quasi axiomatically, by a set of alleged “platitudes”, including, according to Crispin Wright’s (1999) version, “transparency” (to assert is to present as true), “contrast” (a proposition may be true without being justified, and v.v.), “timelesness” (if a proposition is ever true, then it always is), “absoluteness” (there is no such thing as a proposition being more or less true), and others.

Though it contains the correspondence theory as one ingredient, alethic pluralism is nevertheless a genuine competitor, for it rejects the thesis that truth is correspondence to reality. Moreover, it equally contains competitors of the correspondence theory as further ingredients.

Alethic pluralism in its contemporary form is a relatively young position. It was inaugurated by Crispin Wright (1992; see also 1999) and was later developed into a somewhat different form by Lynch (2009). Critical discussion is still at a relatively nascent stage (but see Vision 2004, chap. 4, for extended discussion of Wright). It will likely focus on two main problem areas.

First, it seems difficult to sort propositions into distinct kinds according to the subject matter they are about. Take, e.g., the proposition that killing is morally wrong, or the proposition that immoral acts happen in space-time. What are they about? Intuitively, their subject matter is mixed, belonging to the physical domain, the biological domain, and the domain of ethical discourse. It is hard to see how pluralism can account for the truth of such mixed propositions, belonging to more than one domain of discourse: What will be the realizing property?

Second, pluralists are expected to explain how the platitudes can be “converted” into an account of truth itself. Lynch (2009) proposes to construe truth as a functional property, defined in terms of a complex functional role which is given by the conjunction of the platitudes (somewhat analogous to the way in which functionalists in the philosophy of mind construe mental states as functional states, specified in terms of their functional roles—though in their case the relevant functional roles are causal roles, which is not a feasible option when it comes to the truth-role). Here the main issue will be to determine (a) whether such an account really works, when the technical details are laid out, and (b) whether it is plausible to claim that properties as different as correspondence to a fact, on the one hand, and coherence or superassertibilty, on the other, can be said to play one and the same role—a claim that seems required by the thesis that these different properties all realize the same property, being true.

For more on pluralism, see e.g. the essays in Monnoyer (2007) and in Pedersen & Wright (2013); and the entry on pluralist theories of truth in this encyclopedia.

8.3 The Identity Theory of Truth

According to the identity theory of truth, true propositions do not correspond to facts, they are facts: the true proposition that snow is white = the fact that snow is white. This non-traditional competitor of the correspondence theory threatens to collapse the correspondence relation into identity. (See Moore 1901-02; and Dodd 2000 for a book-length defense of this theory and discussion contrasting it with the correspondence theory; and see the entry the identity theory of truth: in this encyclopedia.)

In response, a correspondence theorist will point out: (a) The identity theory is defensible only for propositions as truthbearers, and only for propositions construed in a certain way, namely as having objects and properties as constituents rather than ideas or concepts of objects and properties; that is, for Russellian propositions. Hence, there will be ample room (and need) for correspondence accounts of truth for other types of truthbearers, including propositions, if they are construed as constituted, partly or wholly, of concepts of objects and properties. (b) The identity theory is committed to the unacceptable consequence that facts are true. (c) The identity theory rests on the assumption that that-clauses always denote propositions, so that the that-clause in “the fact that snow is white” denotes the proposition that snow is white. The assumption can be questioned. That-clauses can be understood as ambiguous names, sometimes denoting propositions and sometimes denoting facts. The descriptive phrases “the proposition…” and “the fact…” can be regarded as serving to disambiguate the succeeding ambiguous that-clauses—much like the descriptive phrases in “the philosopher Socrates” and “the soccer-player Socrates” serve to disambiguate the ambiguous name “Socrates” (cf. David 2002).

8.4 Deflationism About Truth

At present the most noticeable competitors to correspondence theories are deflationary accounts of truth (or ‘true’). Deflationists maintain that correspondence theories need to be deflated; that their central notions, correspondence and fact (and their relatives), play no legitimate role in an adequate account of truth and can be excised without loss. A correspondence-type formulation like

(5) “Snow is white” is true iff it corresponds to the fact that snow is white,

is to be deflated to

(6) “Snow is white” is true iff snow is white,

which, according to deflationists, says all there is to be said about the truth of “Snow is white”, without superfluous embellishments (cf. Quine 1987, p. 213).

Correspondence theorists protest that (6) cannot lead to anything deserving to be regarded as an account of truth. It is concerned with only one particular sentence (“Snow is white”), and it resists generalization. (6) is a substitution instance of the schema

(7) “p” is true iff p,

which does not actually say anything itself (it is not truth-evaluable) and cannot be turned into a genuine generalization about truth, because of its essential reliance on the schematic letter “p”, a mere placeholder. The attempt to turn (7) into a generalization produces nonsense along the lines of “For every x, “x” is true iff x”, or requires invocation of truth: “Every substitution instance of the schema ““p” is true iff p” is true”. Moreover, no genuine generalizations about truth can be accounted for on the basis of (7). Correspondence definitions, on the other hand, do yield genuine generalizations about truth. Note that definitions like (1) and (2) in Section 3 employ ordinary objectual variables (not mere schematic placeholders); the definitions are easily turned into genuine generalizations by prefixing the quantifier phrase “For every x


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