Erkenntnis

, Volume 75, Issue 1, pp 113–122

Deflationism and the Dependence of Truth on Reality

Original Article

DOI: 10.1007/s10670-011-9277-z

Cite this article as:
Thomas, A. Erkenn (2011) 75: 113. doi:10.1007/s10670-011-9277-z

Abstract

A common objection against deflationism is that it cannot account for the fact that truth depends on reality. Consider the question ‘On what does the truth of the proposition that snow is white depend?’ An obvious answer is that it depends on whether snow is white. Now, consider what answer, if any, a deflationist can offer. The problem is as follows. A typical deflationary analysis of truth consists of biconditionals of the form ‘The proposition that p is true iff p’. Such biconditionals tell us nothing about what the truth of the proposition that p might depend on. Therefore, it seems that a typical deflationist cannot give an answer. Since we know that an answer is available, this throws doubt over the adequacy of deflationism as an account of truth. Articulated here is a defence of deflationism against this objection. It is argued that although biconditionals of the sort mentioned do not explicitly state a dependency between truth and reality, they nevertheless convey one. The reason is that, given the context in which a deflationist invokes the biconditionals, such a dependency is implicated. A potential problem with this defence is that it leaves the deflationist still unable to give an account of what it is for truth to depend on reality. One might think that a deflationist can offer such an account by appealing to truthmaker theory but, it is argued below, truthmaker theory is unavailable to a deflationist. Instead, the deflationist should question the assumption that an account is available.

1  

According to a typical deflationary account (hereafter ‘TD’), an adequate analysis of truth consists of the instances of E:
E

<p> is true iff p.1

This is often defended as follows.2 TD maintains that the reason we have a truth predicate is to enable us to express certain propositions (I will refer to this as the ‘expressive’ function of truth). Consider, for instance, the law of excluded middle. One can begin to express this law by writing down a fragment of an infinite conjunction:
(1)

Everything is red or not red, and happy or not happy, and square or not square, etc.

Clearly, this way of expressing the law is imperfect, because one can only write down a fragment of an infinite conjunction. The truth predicate enables the use of a quantifier to create a finite expression of the law: namely ‘Every proposition of the form <Everything is F or not F> is true’.

In order to explain the expressive function of truth, TD continues, one need not assume a substantive theory of truth (such as the correspondence theory): an explanation that invokes the instances of E suffices.3 Consider again the law of excluded middle. Given the instances of E, the conjuncts of (1) are equivalent to sentences such as ‘<Everything is red or not red> is true’ and ‘<Everything is square or not square> is true’. Since the form of the propositions to which truth is being attributed in each conjunct is the same (i.e. <Everything is F or not F>), one can quantify over those propositions and obtain a finite expression of (1): ‘Every proposition of the form <Everything is F or not F> is true’.

In sum, TD argues as follows: since the function of truth is entirely expressive, and since that function can be explained on the basis of the instances of E, those instances constitute an adequate analysis of truth.

Those who object to this analysis of truth generally agree that truth has an expressive role, but argue that there are other facts about truth that cannot be accounted for on the basis of the instances of E.4 According to one much-discussed objection, the fact that truth depends on reality is one such example: the one on which this paper will focus.5

Consider the question ‘On what does the truth of <Snow is white> depend?’ An obvious answer is that the truth of <Snow is white> depends on whether snow is white: if the proposition is true, then it is true because snow is white.6 Now, consider what answer a proponent of TD can supply. All TD has to say about the truth of <Snow is white> is the following biconditional:
(2)

<Snow is white> is true iff snow is white.

The problem is that (2) appears to tell us nothing that could be used as an answer. One might think that if snow’s being white is necessary and sufficient for the truth of <Snow is white>, then the latter depends on the former. However, that would be mistaken. For if the truth of (2) is enough to guarantee that the truth of <Snow is white> depends on snow’s being white, then, since it invokes the symmetric connective ‘iff’, it should also guarantee that snow’s being white depends on the truth of <Snow is white>. Since no sensible account of truth wants to suggest that reality depends on truth, a proponent of TD ought not to suggest that the truth of the instances of E guarantee the dependency of truth on reality.7 In any case, we know that the truth of a biconditional—even the necessary truth of one—is no guarantee of a dependency, in either direction, between that stated on the RHS and LHS, as the following reveals:
(3)

2 + 2 = 4 iff bachelors are unmarried men.

(3) is necessarily true, yet neither is it the case that whether 2 + 2 = 4 depends on whether bachelors are unmarried men, nor vice versa.

This is a problem not only for TD. Consider the following passage from Quine:

…truth should hinge on reality, and it does. No sentence is true but reality makes it so. The sentence ‘Snow is white’ is true, as Tarski has taught us, if and only if real snow is really white. (Quine 1970, p. 10)

If the sentence ‘Snow is white’ is made true by reality, then its truth depends on reality. Quine seems to account for this by citing the following biconditional:
(4)

‘Snow is white’ is true iff [real] snow is [really] white.

As we have seen, the truth of (4) is consistent with there being no dependency between the truth of ‘Snow is white’ and snow’s being white, and so it seems that Quine cannot appeal to (4) to account for the fact that ‘Snow is white’ is made true by snow’s being white.8

One should be suspicious of any objection that has as a consequence Quine committing such an obvious mistake. In the next section I will argue that it is the objection that is mistaken. TD does convey a dependence of truth on reality.

2  

Of course, it is consistent with the necessary truth of (2) that the truth of <Snow is white> does not depend on whether snow is white:
(2)

<Snow is white> is true iff snow is white.

However, there are ways of conveying dependencies other than explicitly stating them. Suppose we have some information that states a connection between two phenomena, but that does not explicitly state a dependency. A dependency might nevertheless be implicated given the context in which that information is invoked. For example, consider the following scenario:

Gill asks: ‘Why is Fred giving his entire month’s wages to Oxfam?’ Jack responds: ‘Fred only gives money away if there’s something in it for him.’

Jack’s response does not explicitly state a dependency between Fred’s giving money away and there being something in it for him. To say that Fred only gives money away if there’s something in it for him is not to say that he gives money away because there’s something in it for him (or vice versa).9 However, a dependency is implicated given the context in which Jack makes his remark. It is implicated that Jack only gives money away because there is something in it for him. One can imagine Gill commenting, in response to Jack: ‘That is a little unfair. I don’t think that he gives money away just because there is something in it for him. He can be gracious.’
For a second example, consider the following scenario:

Tim, a politics student on a school trip to Westminster, asks his tutor, Mr. Taylor: ‘Why is the Royal Standard flying from Victoria Tower?’ His tutor responds: ‘The Royal Standard is shown from Victoria Tower just in case the Monarch is present in the Palace of Westminster.’

Mr. Taylor’s response does not explicitly state a dependency between the Royal Standard flying from Victoria Tower and the Monarch’s presence in the Palace of Westminster. To say that the Royal Standard is shown from Victoria Tower just in case the Monarch is present in the Palace of Westminster is not to say that the Royal Standard is shown from Victoria Tower because the Monarch is present in the Palace of Westminster (or vice versa). However, a dependency is implicated given the context in which Mr. Taylor makes his remark. It is implicated that the Royal Standard is shown from Victoria Tower because the Monarch is present in the Palace of Westminster. One can imagine, if asked by a fellow student: ‘What did Mr. Taylor say? Why is the Royal Standard flying from Victoria Tower?’, Tim would respond: ‘Because the Monarch is present in the Palace of Westminster.’

Indeed, that a dependency is implicated in both scenarios is to be expected. Paul Grice’s influential account of conversational implicatures suggests that there are maxims that govern conversational exchanges. One such maxim—the one that is pertinent here—is that one is relevant [which is termed ‘relation’ (Grice 1975, pp. 27)]. Grice argues that, providing certain other conditions obtain, if person a says that p, and if the supposition that q is required to make a’s saying that p consistent with the presumption that a is observing the conversational maxims, then a has conversationally implicated that q.10 Applying this to the second scenario (involving Tim and Mr. Taylor), unless it is supposed that Mr. Taylor thinks that the Royal Standard’s being shown from Victoria Tower depends on the Monarch’s being present in the Palace of Westminster, he would be violating the maxim ‘relation’. Given that there is no reason to believe that Mr. Taylor is opting out of the conversational maxims, and assuming that he feels that it is within Tim’s competence to work out that the supposition mentioned in the previous sentence is required, the aforementioned dependency is implicated. Similarly for the first scenario.

Similarly also for the following situation:
 

Ed, a philosophy student, asks his deflationist friend: ‘Why is <Snow is white> true?’ His friend responds: ‘Well, <Snow is white> is true just in case snow is white.’

Unless it is supposed that Ed’s friend thinks that the truth-value of <Snow is white> depends on snow’s being white, he would be infringing the maxim ‘relation’. Given that there is no reason to think that Ed’s friend is opting out of the conversational maxims, and assuming that he feels that Ed is able to work out that the supposition mentioned in the previous sentence is required, a dependence of the truth of <Snow is white> on snow’s being white is implicated. Suppose that, having overheard the conversation between Ed and his tutor, a fellow student asks Ed: ‘So, why is <Snow is white> true?’ Providing he believes his deflationist friend, surely it would be natural for Ed to respond: ‘Because snow is white.’11, 12

In sum, the reason the instances of E implicate dependencies is because of the context in which they are invoked (i.e. the context of an explanation of truth). The reason they are asymmetric in the sense that they implicate a dependence of truth on reality and not vice versa is because they are offered in the context of an explanation of truth, not in the context of an explanation of reality.13

The objection that prompted this response was that TD seems unable to supply an answer to the question ‘On what does the truth of <Snow is white> depend?’ We have now seen that TD does supply an answer: one that is conveyed via an implicature.14 This also allows us to make sense of the above quote from Quine. Recall that Quine uses the following biconditional in accounting for the fact that ‘Snow is white’ is made true by reality:
(4)

‘Snow is white’ is true iff [real] snow is [really] white.

One can point out that if (4) is invoked in an explanation of the truth of ‘Snow is white’ then it is implicated that the truth of ‘Snow is white’ depends on snow’s being white. Finally, one can point out that Quine mentions Tarski, who did indeed take biconditionals similar to (4) as (partial) explanations of truth [he referred to them as ‘partial definitions’ of truth (Tarski 1944, p. 335)].

3  

The fact that TD implicates a dependence of truth on reality doesn’t enable it to provide an account of what it is for (say) the truth of <Snow is white> to depend on snow’s being white. Therefore, those who insist on there being such an account are likely to be unsatisfied. In particular, I have in mind certain proponents of truthmaker theory, who argue that for the truth of <Snow is white> to depend on snow’s being white is for the proposition to be made true by the existence of at least one entity (or ‘truthmaker’), such as the fact that snow is white.15

It might be thought that TD can appeal to truthmaker theory, and thus provide the aforementioned account. I will examine (and reject) two reasons why one might think this. The first is David Lewis’ suggestion that truthmaker theory isn’t really about truth, which I will argue is mistaken. The second is the suggestion that truthmaker theory need not be understood as an analysis of truth. I will argue that even a version of truthmaker theory that is not understood as an analysis of truth is unavailable to TD.

In light of this, I recommend that a proponent of TD should not attempt to give an account of what it is for truth to depend on reality, but question the assumption that such an account can be given at all.

3.1  

It might be thought that, as Lewis suggests, truthmaker theory isn’t really about truth, and thus consistent with a deflationary account such as TD (Lewis 2001, pp. 278–279). Consider the following truthmaker principle and an instance of it:
TM

(For all <p>)(<p> is true iff there exists at least one thing such that the existence of that thing implies <p>).

TM1

<Roses are red> is true iff there exists at least one thing such that the existence of that thing implies <Roses are red>.

TM1 is equivalent, given the relevant instance of E, to something that does not invoke the truth-predicate:
TM1

Roses are red iff there exists at least one thing such that the existence of that thing implies <Roses are red>.

Lewis argues that since the instances of TM are equivalent to biconditionals that are “not about truth”, TM similarly is not about truth. Indeed, in his view, truth enters into TM only to enable the finite expression of the following infinite conjunction:

Roses are red iff there exists at least one thing such that the existence of that thing implies <Roses are red>; and snow is white iff there exists at least one thing such that the existence of that thing implies <Snow is white>; etc.

However, it seems implausible to suggest that TM is not about truth. As the infinite conjunction makes clear, only certain propositions have truthmakers (i.e. <p> has a truthmaker iff p). What TM makes explicit is that it is all and only those propositions that instantiate the property of truth that have truthmakers. This, surely, is enough to conclude that the infinite conjunction implicitly concerns truth.

3.2  

Alternatively, it might be thought that, even if truthmaker theory is about truth, it need not be taken as part of an analysis of truth, and thus is available to a proponent of TD. For instance, one might endorse TM1 and argue that it is a consequence of the relevant instance of E and TM1’, where the relevant instance of E is the analysis of the truth of <Roses are red>.

Even if truthmaker theory is not taken as part of an analysis of truth, it is still unavailable to a proponent of TD. Suppose we have two ‘packages’ (labeled ‘A’ and ‘B’), each consisting of an account of truth and a version of truthmaker theory that has TM as its truthmaker principle. The difference between the two packages is that A understands TM as part of a substantive (correspondence) theory of truth, whereas B does not. According to package B, an adequate analysis of truth is as outlined in TD.

Package B contains a deflationary account of truth and a substantive explanation of the idea that propositions are made true by something. But why suppose that this renders the ‘deflationary’ account of truth less interesting? Deflationism about truth is based, in part, on a concern about the content of an account of truth. Deflationists believe that the traditional theories of truth (e.g. the correspondence and coherence theories) employ too many ontological and conceptual resources.16 This also constitutes part of the appeal of a deflationary account of truth: i.e. the appeal of providing an adequate account of truth using minimal resources. Now, the resources employed by the correspondence theory contained in package A consists of that invoked by TM: propositions, truthmakers, and a relation between the latter and true propositions. Package B, even though it endorses a ‘deflationary’ account of truth, employs the same resources. Since it employs the same resources, part of the appeal of the deflationary account it endorses is lost. Those resources might not be invoked as part of an account of truth, but they are invoked nevertheless. The gains in theoretical economy that the deflationary account of truth promises to deliver are lost elsewhere.

Furthermore, package B endorses a truthmaker principle (TM) that looks precisely the same as the sort of principle defended by a typical correspondence theory. The only difference is that TM, according to package B, ought not to be taken as part of an account of truth. This makes the dispute between the deflationist and the correspondence theorist seem somewhat thin.

3.3  

I submit that the prospects of TD giving an account of what it is for truth to depend on reality by appealing to truthmaker theory are dim. Instead, a proponent of TD ought to reply in a way that is similar to the reply often made to a different but related objection. TD is also incapable of providing an answer to the question ‘What is it for a proposition to be true?’ The reason is that, according to TD, there is nothing common to all true propositions in which their truth consists. At best, a proponent of TD can say that the truth of <Snow is white> consists in snow’s being white; the truth of <Roses are red> consists in roses being red; and so on. Instead, the proponent of TD challenges the assumption that the aforementioned question has an answer. It is that assumption, the proponent suggests, that has led to theories of truth that attempt to discern an underlying structure common to all truths, resulting in an analysis that is inflated beyond plausibility.17

Similarly, the proponent of TD ought to point out that the assumption that there is an account of what it is for truth to depend on reality is questionable. Gonzalo Rodriguez-Pereyra is an example of someone who makes this assumption in defending the existence of truthmakers. Having observed that the truth of a substantial class of propositions is grounded in reality (to use his example: <The rose is red> is true because the rose is red), he argues that grounding is a relation between a true proposition and its truthmaker(s) (Rodriguez-Pereyra 2005, pp. 20–31). In so doing, he challenges anyone who denies that grounding is a relation to provide an alternative account of what it is for the truth of <The rose is red> to be grounded in the rose’s being red:

But if grounding is not a relation—what is it? That is, how can the truth of the proposition that the rose is red be grounded in the rose’s being red if grounding is not a relation? What is it, then, for the proposition that the rose is red to be true because the rose is red? (Ibid. p. 27)

Rodriguez-Pereyra considers a number of alternative accounts, finds them to be unsatisfactory, and concludes that grounding is a relation.

Clearly, Rodriguez-Pereyra’s argument relies on the assumption that there is an account of what it is for the truth of <The rose is red> to depend on the rose’s being red: an assumption that requires justification. We certainly have the intuition that truth depends on reality, as demonstrated by our propensity to assent to sentences such as ‘<The rose is red> is true because the rose is red’. Since TD conveys the idea that the truth of <The rose is red> depends on the rose’s being red, it surely accommodates that intuition. But why suppose that that intuition points to a genuine feature of truth, of which an account must be provided?18 Rather, TD suggests, the only feature of truth requiring explanation is its ability to facilitate the expression of certain propositions (such as the law of excluded middle). That feature can be explained (as demonstrated above) merely by supposing that from ‘<p> is true’ one can infer ‘p’ and vice versa.

4  

The objection to which this paper responds is that typical deflationism (TD) cannot provide an answer to a question such as ‘On what does the truth of <Snow is white> depend?’ Since we know that an answer is available, if the objection turns out to be correct, one would have to conclude that the instances of E provide an inadequate analysis of truth. We have seen that the objection is mistaken: TD conveys via an implicature that the truth of <Snow is white> depends on snow’s being white. We have also considered the potential difficulty that this leaves a proponent of TD still unable to give an account of what it is for truth to depend on reality, and found that difficulty to rely on the questionable assumption that such an account is available. This removes a much-discussed problem for deflationism (and saves Quine from the suggestion that he has made an obvious blunder).

Footnotes
1

Angle-brackets denote propositions. The instances of E are typically restricted to those that do not give rise to paradox, and supplemented by the extra axiom ‘(For all x)(x is true → x is a proposition)’ (e.g. Horwich 1998, pp. 40–42 and p. 23, fn. 7). For ease of expression, I won’t repeat this in the rest of this paper.

 
2

See, for instance, Horwich 1998, pp. 2–5 and Williams 2002, p. 148.

 
3

I do not mean to imply that such an explanation consists merely of the instances of E. Indeed, in the following example one must also introduce a quantifier to obtain ‘Every proposition of the form <Everything is F or not F> is true’. The point is that the explanation does not require a substantive theory of truth.

 
4

For instance, Davidson argues that truth has a role in explaining meaningfulness, and Putnam argues that truth has a causal role (Davidson 1996; Putnam 1978, pp. 100–103).

 
5

Vision 2005 and Newman 2002, pp. 34–37 are examples of those who raise this objection; Hill 2002, Horwich 1998, Chap. 7 and McGrath 2003 are examples of those who defend deflationism against it.

 
6

For a more formal treatment of the dependence of truth (particularly in relation to the semantic paradoxes) see Yablo 1982; Leitgeb 2005; and Fine 2010. I am grateful to an anonymous referee for bringing these papers to my attention.

 
7

A similar line of reasoning is found in Rodriguez-Pereyra 2005, p. 27 and Künne 2003, p. 152.

 
8

Künne articulates this criticism of Quine on p. 152 of his 2003. See also Vision 2005, pp. 366–367.

 
9

The reason is as follows. Jack has articulated a conditional (i.e. the conditional ‘If Fred gives money away then there’s something in it for him’), and a true conditional does not guarantee a dependency between the antecedent and consequent (e.g. ‘If Fred gives money away then 2 + 2 = 4’ is true, but 2 + 2 equalling 4 does not depend on Fred giving money away). If a true conditional does not guarantee a dependency between the antecedent and consequent, it cannot be the case that in articulating a conditional one says that there is such a dependency. Similarly for biconditionals.

 
10

The other conditions are twofold. The first is that the speaker is presumed to be observing the conversational maxims. The second concerns the supposition that q is required to make a’s saying that p consistent with the presumption that a is observing the conversational maxims: it is the condition that “the speaker thinks (and would expect the hearer to think that the speaker thinks) that it is within the competence of the hearer to work out, or grasp intuitively, that the supposition [mentioned at the beginning of this sentence] is required.” (Grice 1975, pp. 30–31).

 
11

Although all three scenarios above involve spoken conversations, this is not necessary for an implicature to be generated. Grice himself gives the example of a testimonial written about a student who is a candidate for a philosophy job. In virtue of the fact that the writer purposely flouts the maxim ‘quantity’, he manages to implicate what he is unwilling to write down. (Ibid. p. 33).

 
12

One might wonder what sort of dependency is implicated here. What can be said is that the implicated dependency between the truth of <Snow is white> and snow’s being white is such that the latter explains the former (in this sense, one could term it an ‘explanatory dependency’). This is unsurprising, because the response ‘Well, <Snow is white> is true just in case snow is white’ is uttered in the context of a request for an explanation of the truth of <Snow is white>. (Similarly for the implicated dependency between Fred’s giving money away and there being something in it for him; and between the Royal Standard’s flying from Victoria Tower and the Monarch’s being present in the Palace of Westminster.).

 
13

For instance, ‘<Snow is white> is true iff snow is white’ is offered in the context of an explanation of the truth of <Snow is white>, not in the context of an explanation of snow’s being white.

 
14

In light of this, it ought to be agreed that there is a sense in which it is incompatible with TD that truth does not depend on reality. Kent Bach distinguishes between the semantic content of a sentence and the content of an utterance of that sentence (2005, pp. 9–11). The truth-value of the former does not depend on the truth-value of any implicatures, but the truth-value of the latter does. Thus, for instance, although it is consistent with the content of ‘I saw Bill with a woman’ that the woman in question was his wife, it can still be incompatible with the content of an utterance of that sentence (if, say, that content includes the implicature that the woman was not his wife). Similarly, one can distinguish between the semantic content of (2), and what is conveyed when (2) is taken in the context of an explanation of truth. Since the latter includes the implicature that the truth of <Snow is white> depends on whether snow is white, in this sense it is incompatible with TD that the truth of <Snow is white> does not depend on reality.

 
15

See, for instance, Rodriguez-Pereyra 2005, p. 27.

 
16

For an example of a deflationist complaining about the tendency to use too many ontological resources in analysing truth, see Quine: facts “are projected from true sentences for the sake of correspondence” (1987, p. 213). See also David on the deflationists' attitude towards the conceptual resources employed by the correspondence theory of truth: “…the deflationist will charge that the notion of correspondence … is also a fabrication—that it has been invented for the sole purpose of binding the invented facts to the true sentences” (1994, p. 24).

 
17

See, for instance, Horwich 1998, pp. 1–5.

 
18

Liggins also questions why one must suppose that there is such an account (2008, p. 188 fn. 9).

 

Acknowledgments

Thanks to David Liggins, Rosanna Keefe and two anonymous referees for helpful comments.

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Woodford, Plympton, Plymouth, DevonUK

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