Finally it is time for our study of aletheic properties to start paying dividends in the discussion of deflationism. Now that we have some sense of which aletheic properties exist and how they differ from what we intuitively take the property of being true to be like, we can turn to the question of what these aletheic properties are like. In particular, we can think about the question of whether deflationism is right about any of these aletheic properties.

Deflationism about truth has been influential in analytic philosophy for decades now, but there has been renewed interest in what deflationists should say about the property of being true. First generation deflationists tended to deny that there was any property denoted by ‘true’, but the subsequent debate made it clear that most of them meant instead that there is no substantive property denoted by ‘true’.Footnote 47 Even so, most of the attention was on what form a deflationary theory of truth should take and on what a deflationist should say about the role of truth predicates in our linguistic practice. However, the debate has now shifted to deflationary views on the property of being true, with the result being that earlier characterizations have been seen as inadequate. There is a new sense that the debate over deflationism about truth might well be adjudicated best by evaluating what deflationists say about the property of being true.

Wyatt’s (2015) paper, “The Many (Yet Few) Faces of Deflationism,” catalogs five deflationary theses about the property of being true:

(Transparency) Being true is a metaphysically transparent property, (Non-explanatory) Being true is a non-explanatory property, (Unconstituted) Being true is not constituted by any other property, [Wyatt claims that (Unconstituted) should not count because Horwich rejects it, but I include it because it is prominent in the literature and adds to the discussion.] (Abundant) Being true is an abundant property, and (Logical) Being true is a logical property.

These need not be accepted by every deflationist, but each has considerable support. A few clarificatory comments on these deflationary theses are in order.

First, being true is a metaphysically transparent property if and only if anyone who possesses the concept of truth is in a position to know all the essential facts about the property of being true. In other words, the property of being true does not have some hidden essence to be discovered by some investigation. Simply having the concept of truth is enough to be in a position to know everything important about the property of being true (but not, obviously, which things have that property).

Second, being true is a non-explanatory property iff there are no facts that are explained by facts about the property of being true.Footnote 48 It is important to stress that ‘true’ might occur in a theory only in its expressive role as a device of generalization despite the fact that the theory in question is genuinely explanatory. The word ‘true’ serves as a device of generalization when it changes a sentence position into a singular term position in a sentence. For example, one might say the following sentences. If grass is green and Sarah says that grass is green, then we should trust Sarah about this. If snow is white and Sarah says that snow is white, then we should trust Sarah about this. And so on. But one might want to state the general point and say if __________ and Sarah says that _____________, then we should trust Sarah (for whatever can be put in the sentence spaces). But that isn’t a sentence. Whether English has anything that functions like those sentence spaces is contentious. But deflationists claim that the word ‘true’ helps us state the general point by turning those sentence gaps into singular term gaps, which might be filled in by a name or a description or a variable. For example: if for all things x, x is true and Sarah says that x is true, then we should trust Sarah. The word ‘true’ turns those sentence spaces into something we can use. That is it. (Non-explanatory) entails that the word ‘true’ does not (or should not) play any role in any explanatory theory other than this generalizing role.

Third, the property of being true is not constituted by any other property iff it is not the case that there is some property, being F, such that all and only things that have the property of being true have the property of being F, and anything that has the property of being true has it because it has the property of being F. For example, if truth is properly analyzed as correspondence with the facts, then true things have the property of being true because they have the property of corresponding with the facts. Deflationists deny that truth is constituted by correspondence or by anything else. We could say that, together, (Non-explanatory) and (Unconstituted) imply that the property of being true doesn’t explain anything and nothing explains it.

A property is abundant iff it is to some extent unnatural, in Lewis’s sense. Naturalness, for Lewis, is objective, and it explains objective similarities among things.Footnote 49 Natural properties “cut nature at its joints,” in Plato’s phrase. Most metaphysicians accept that there are degrees of naturalness, but it is not clear whether deflationists endorsing (Abundant) mean that being true is merely not perfectly natural or they mean that it is highly unnatural.Footnote 50

A property is logical iff it is invariant under certain one–one transformations of the world onto itself.Footnote 51 There are other ways to define ‘logical’, but Wyatt follows Tarski, who was inspired by Klein, and this invariance tradition is one of the most respected when it comes to defining what is logical. A one–one transformation of the world maps every thing in the world to some thing in the world. For example, the identity transformation maps everything to itself. If the distribution of a property is unaffected by any such transformation, then the property is logical.

What are we to make of these deflationary theses? And do any of the aletheic properties canvassed count as deflationary in any of these ways?

Given what we have seen so far, it is hard to be more wrong than (Transparency). Even if we assume that anyone who possesses the concept of truth has some access to the logical platitudes, that person would probably have no idea that they were inconsistent. As we have seen, the only reasonable response to the vast amount of inconsistency among the truth platitudes is that there is no property of being true. Nothing even comes close to satisfying even small subsets of the platitudes for the concept of truth. Hence, simply possessing the concept of truth does not put one in a position to know everything essential about the property of being true.

If a theorist denied this result and picked one of the aletheic properties to be the property of being true, then that aletheic property would be nothing like what the concept of truth would lead us to think it is like. Moreover, it has taken the accumulated effort of dozens of experts building on each others’ work to figure this out. Even on a liberal reading of ‘in a position to know’, (Transparency) fails. For every inconsistent concept of X, if it has an associated property of being X, then being X is not a transparent property.

What about the aletheic properties themselves?Footnote 52 For example, the property of being FSAtrue. Is it metaphysically transparent? Is anyone who possesses the concept of FSAtruth in a position to know all the essential facts about the property of being FSAtrue? This depends on what one takes to be essential to the property of being FSAtrue. If we assume that possessing the concept requires some kind of acceptance of the axioms in subset A of Friedman–Sheard criteria, then the answer is clearly No.Footnote 53 One might understand and accept these axioms without being able to figure out that there is only one model for this subset whose domain is the natural numbers and whose arithmetic vocabulary have their standard interpretations. And such a person might also not be in a position to figure out that everything is in the extension of ‘true’ in this model. The fact that every sentence of the object language has the property of being FSA true seems essential to me, but people differ on what is essential even in obvious cases, much less on esoteric subjects like this one. This result is even necessary in some sense because it holds in all the relevant models. The same sort of thing can be said for the other aletheic concepts and properties. I doubt that any of them is transparent.

(Non-explanatory) should be treated as highly dubious. The concept of truth shows up in truth conditional semantic theories, which are among the most widely accepted theories for doing natural language semantics in the science of linguistics.Footnote 54 Denying that these theories have explanatory power would be like denying that Newton’s theory of mechanics or Maxwell’s theory of electrodynamics has explanatory power. It is an open question as to whether any of the aletheic properties (or their related concepts) have this explanatory power, but they might work in the same sorts of semantic theories just as well as we thought truth would.Footnote 55

Although we now know that there is no property of being true, the verdict on the explanatory power of the genuine aletheic properties is complex. Truth conditional semantic theories come in a dizzying variety, and they are often tailored to the specific linguistic expressions under consideration. Are any of the alethic properties we canvassed up to the task? In the vast majority of cases, the clauses of a truth-conditional semantic theory could be added consistently to any of the axiomatic theories we have studied. The reason is that these semantic theories are not designed to apply to language fragments that contain truth predicates. Instead, semantic theories for epistemic modals, for example, apply to language fragments that contain epistemic modals, and semantic theories for conditionals apply to language fragments that contain conditionals. The problems in which we are interested crop up only for a truth-conditional semantic theory when they are interpreted as applying to sentences in which truth predicates occur. Hence, in this sense, any of our aletheic properties would be up to the task of satisfying the principles of most truth-conditional semantic theories.

But there is a catch. If we ask ourselves whether any of the aletheic properties studied so far could satisfy all the principles of a truth-conditional semantic theory when it is interpreted as applying to a language with a truth predicate and the resources to construct liar sentences, then the answer is No. There are plenty of paradoxes hiding among these principles and so no aletheic property is going to satisfy all of them. [For a detailed argument, see Scharp (2013)]. Therefore, any of the aletheic properties could serve an explanatory role in virtually any truth-conditional semantic theory, but when it comes to a truth-conditional semantic theory for a truth predicate, none of them are up to the task. Never fear, because there is a way to fix this problem, which is a topic of the next section.

Are any of the aletheic properties unconstituted? This is hard to say because it is not obvious how to individuate properties and it isn’t clear what kind of dependence is invoked with the claim that the property of being true is constituted by some other property. If something like a reductive explanation is given as the reading of ‘constituted’, then the answer is probably going to be No because uncontroversial reductive explanations (think thermodynamics and statistical mechanics) are rare in philosophy. If the standard is somewhat relaxed, say, to a weak supervenience claim, then perhaps the odds are a bit better, but probably not by much. What kind of explanatorily powerful property is going to explain any one of these aletheic properties? They are each hopelessly gerrymandered –their extensions zigzagging around to avoid the plethora of impossibility results. Hence it looks like all of the aletheic properties are unconstituted.

One might protest this conclusion: but we already have such properties! Correspondence to the facts or coherence, or superwarrant maybe. My reply: none of the classic analyses of truth are remotely plausible in light of the results of our attempted Canberra plan. First of all, there is no property of being true. That result is inconsistent with every purported constitution theory for the property of being true. Second, even if one denies this conclusion, it is hard to see that the property of corresponding to the facts could constitute any one of the aletheic properties. Consider the property of being FSFtrue (i.e., satisfying subset F of Friedman–Sheard critera). This property fails to obey (¬T-Enter). Hence, even if one can prove a theorem from subset F of form ¬p, one cannot conclude that ¬Tp. For example, it would be like proving ‘snow is not white’ but failing to prove ‘‘snow is white’ is not true’. Does the property of corresponding to the facts behave just like this? Highly doubtful.

What about abundance? All of the aletheic properties are highly unnatural in one sense. Naturalness is supposed to explain the objective similarities between things. If we intuitively think of all the truths as having some kind of objective similarity, then every aletheic property is going to violate this in myriad ways. And it is hard to believe that anyone thinks that all the KFtruths or all the VFtruths have objective similarity. So in this sense all the aletheic properties are deflationary.

Logicality? Wyatt argues that no deflationist should accept this thesis because it is easily refuted.Footnote 56 His argument is that some transformations will map some true proposition onto a false proposition, so truth is not preserved under all transformations. But Wyatt assumes that propositions are things in a particular world, whereas it is much more common to assume that propositions are sets of possible worlds, and so they are not members of any particular possible world. If that is right, then propositions are not among the things in a world, and so Wyatt’s argument fails.

Certainly some aletheic properties count as logical: when the predicates that denote them get their own clauses in the semantic theory for languages in which they occur, just like negation and the rest of the logical vocabulary. If that is the case, then the interpretation of the predicate is by definition invariant across all models. For example, one can do this for ascending truth and descending truth.Footnote 57 So at least some aletheic properties count as logical properties.

We can summarize the results in this section:

i. No aletheic properties are transparent, so versions of deflationism committed to (Transparency) are false. ii. No aletheic properties are non-explanatory, so versions of deflationism committed to (Non-Explanatory) are false. iii. All aletheic properties are unconstituted (depending on how one individuates properties), so insofar as they are committed to (Unconstituted), deflationist views of alethic properties are acceptable. iv. All aletheic properties are abundant, so insofar as they are committed to (Abundant), deflationist views of aletheic properties are acceptable. v. Some aletheic properties are logical (depending on how one understands logical expressions and how one formulates a semantic theory for a language with expressions that denote these properties), so insofar as they are committed to (Logical), deflationist views of aletheic properties might be acceptable.

It deserves to be emphasized that deflationist theories of truth have multiple aspects or parts, some of which pertain to the property of being true, some to the concept of truth, some to the word ‘true’, and some to the structure of any acceptable theory of truth. Moreover, there is no property of being true, so any theory, deflationist or not, that entails that there is such a property is false. At present, we are evaluating only deflationist views of aletheic properties, not deflationist views as a whole. As such, even those versions of deflationism that come out as acceptable on the present inquiry might be false for some other reason (e.g., because deflationist theories are typically taken to consist of all and only the non-paradoxical instances of (Schema T), but it is difficult or impossible to specify in advance which instances these will be).