Keywords

1 Truth Without Truthbearers?

In recent writings, Kevin Mulligan (2010, 2011) has argued against Künne (2003) that the latter should extend his ‘modest’ accounts of truth and of truthmaking without truthmakers to an account of truth without truthbearers urging—against Künne—the primacy of the truth connective ‘it is true that …’ over the truth predicate ‘…is true’.

In his magistral Conceptions of Truth (2003), Künne proposed what he calls a ‘modest’ account of truth, characterising the truth-predicate by any of:

Mod 1 :

∀ x (x is true ↔ things are as x has it)

Mod 2 :

∀ x (x is true ↔ things are as they are according to x)

Mod 3 :

∀ x (x is true ↔ for some ways things may be said to be, x is the proposition that things are that way, and things are that way) (2003, pp. 335–336) or rather, to avoid misunderstandings,Footnote 1

$$ \mathbf{Mod}~ \forall x( x \text{is true} \leftrightarrow \exists \text{p }( x=\text{ }[ \text{p} ]\text{ }\And \text{ p} ) ) $$

(2003, p. 337)

where ‘[…]’ abbreviates the singular term-forming operator ‘the proposition that …’. Künne claims that Mod improves on Horwich’s minimalism by being conceptually more economical and by stating what all truths have in common. Mod, however, also shares an important drawback of the minimalist theory: in particular, it applies only to propositions designated by singular terms of the form ‘the proposition that …’ (Künne 2003, p. 340). Künne says that these proper names are semantically structured in that they ‘contain’ the sentence of the second conjunct (2003, p. 342).

Künne (2003, p. 360) is explicit that his modest account presupposes the intelligibility of higher-order, but objectual, quantification over propositions and endorses the ontological commitment thereby incurred. This brings with it a familiar problem of circularity: Sundholm (2008, p. 364) , for example, thinks it is a ‘mystery how to explain [Künne’s] deviant quantifier without recourse to truth’. The circularity does not lie, as Künne (2008, p. 389) thinks, in the specification of the truth-conditions of the sentential quantification,Footnote 2 but rather in the only way of explaining the double role of the things quantified over, to wit propositions: They are characterised as entities which are not referred to, but expressed by permissible substituends for the nominal variable. They are things which exist (‘∃p(p)’), and thus can be named, but also are things that name themselves and, in general, are not ‘given to us’ by name but by some sentence which expresses them. They thus do double duty: They exist, and have properties, but they are also expressed, and the meaning s of sentences.Footnote 3

This is not quite Dummett’s argument that propositions are sentence-meanings and that the notion of a sentence-meaning cannot be explained independently of the notion of truth . Künne (2003, pp. 369–372) is right that objects of belief s need to be individuated more finely than sentence-meanings and that ‘proposition’ is better taken to stand for the former than for the latter.

The circularity worry, as I understand it, concerns the expression relation: what other, truth-independent, grasp do we have of what some sentence expresses than the familiar idea how the world would have to be like for it to be true?Footnote 4 This, I think, is a version of the ‘denial of intelligibility’ charge Davidson (1996) advanced against Horwich ,Footnote 5 to which Künne (2003, pp. 328–329) does not adequately reply. It is not primarily (or at least not only) a worry about the intelligibility of names for propositions (which could be dispelled by a paratactic theory as the one Künne (2003, p. 329) sketches). Rather, it concerns the particularly transparent character of these descriptive names, for propositions i.e. the fact that we know everything there is to know about their referent once we understand them at all. It follows that we do not know what is denoted by ‘the proposition that p’ unless we understand the proposition that p, and understanding this requires understanding under what conditions it is true. To understand Mod, then, we have to deploy an understanding of ‘…is true’, and hence Mod is, as a definition of the truth-predicate , epistemically circular.Footnote 6

The problem in a nutshell is the following: to understand why propositions are the kind of things that can play the double role they play in Mod —and be quantified over both by quantification into singular term and into sentence position—we have to understand them as the kind of things that are bearers of truth; it is the truth-predicate that provides the ‘bridge’ between their ‘nominal’ and their ‘sentential’ role. To understand Mod, we need to understand the hybrid form of quantification it deploys, and hence the hybrid nature of the things quantified over, which is due to their essential evaluability for truth .

It is not clear, however, that Künne needs to be worried about this kind of circularity. As he makes very clear (2003, p. 13, 16, 118, 338), he does not aim to propose an eliminative (‘dismantling’), but just a ‘connecting’ (explanatory) account of truth, and does not aim to explain the concept of truth without using it. The intertwining of his theories of propositions and of truth, however, makes him vulnerable to another worry that more directly threatens Künne’s project.

In his recent work (2010), Kevin Mulligan has raised a novel objection to the modest account, and indeed all accounts of truth, which take the truth-predicate ‘…is true’ as their definiendum. Mulligan distinguishes the truth-predicate ‘…is true’ (which takes a singular term to make a sentence) from the truth-connective ‘it is true that …’ (which takes a sentence to make a sentence) and asks which one wears the trousers, answering that the connective, not the predicate is fundamental . He thus criticises the contention of Künne (2003, pp. 350–351) that his account of the predicate equally applies to the connective, which the latter interprets as also containing a predication of the truth-predicate, the ‘it’ in ‘it is true that…’ functioning cataphorically, by providing the thing referred to by the subsequent noun phrase ‘that p’ (cf. also Horwich 1998, p. 16, n. and Künne 2013, p.161) .

Though it is not entirely clear this has been realised by its participants, I think there is more at stake in this dispute than the relative priority of the truth-predicate or truth-connective. Mulligan’s point, if sound, undercuts Künne ’s explication of ‘proposition’, as the word one comes to understand by ‘learning to accept, as a conceptual matter of course, any inference from (a substitution-instance of) schema [B 1 ] via [B 2 ] to the corresponding instance of [B 3 ], and vice versa’ (Künne 2003, p. 251), where such substitution instances may be the found in the following transformations:

B 1 :

A believes that it rains

B 2 :

That it rains is the content of A’s belief

B 3 :

The proposition that it rains is the content of A’s belief

Contrary to most critics, who have found the introduction, in the step from B 2 to B 3 , of ‘proposition’ problematic, Mulligan ’s argument targets the step from B 1 to B 2 . Why think, a Mulligan-inspired question goes, that B 1 asserts a relation between a believer and some content, made more explicit in B 2 ? Why not take ‘x believes that p’ to be a hybrid connective or ‘prenective’ (Künne 2003, p. 68), a member of a class of expressions that ‘are as it were predicate s at one end and connectives at the other’ (Prior 1971, p. 19) ? This is not just a question about syntax: If ‘that it rains’ is not an isolable component of B 1 , nothing is predicated of it, and it cannot truly be said to be the content of A’s belief (B 2 ). If there are no such things as contents of beliefs, then Künne’s modest account does not get off the ground, Mod either containing an empty singular term or being guilty of illicit reification .

By undermining the need for propositions, Mulligan’s criticism undercuts Künne ’s argument for his modest account of truth . In the case of truth-attributions, we have an intermediate step:

T 1 :

It rains

T ′ 1 :

It is true that it rains

T 2 :

That it rains is true

T 3 :

The proposition that it rains is true

While Mulligan agrees with Künne (and Bolzano ) that the step from T 1 to T ′ 1 and the concomitant ‘introduction’ of that-clauses is unproblematic, he thinks that the one from T ′ 1 to T 2 , and its ontological commitment, can be resisted. As we have seen, Künne (2003, p. 351) holds that the first ‘it’ in T ′ 1 is a cataphoric pronoun, as ‘he’ is in ‘he was wise, the man who drank the hemlock’ and that T ′ 1 and T 2 are ‘stylistic variants’ of each other (2003, p. 351; 2010b, p. 597). Against this, Mulligan (2010, p. 567, 569) claims that:

M 1 :

It is true that it rains because it rains

M 2 :

That it rains is true because it is true that it rains

M 3 :

The proposition that it rains is true because that it rains is true

While M 1 is accepted by all sides (and Künne (2010b, p. 59), with some qualifications, agrees with M 3 ), M 2 is contentious. Mulligan (2010, p. 569) gives three arguments for M 2 : (i) that its left-hand side is more complex than its right-hand side, (ii) that it mentions something more problematic and (iii) that nominalisations are secondary with respect to what they are nominalisations of. In support of (i) he claims that the ‘it’ in ‘it is true that …’ is a dummy term, an expletive pronoun like the ‘it’ in ‘it’s a long way to Tokyo’, that cannot be used in identity statements such as ‘it = that it rains’ (2010, pp. 572–573). To some extent, Künne concedes this point (2011, p. 202, 206). More important, in my view, are (ii) and (iii). The cryptic remark (iii), in this context, is best understood as a preference for less, rather than more, ontological commitments, while (ii) highlights the crucial issue: the alleged difference, between T ′ 1 and T 2 , in ontological commitment. If really ‘it is true that’ is semantically unbreakable, and does not predicate of anything the property of being true, then the step to T 2 introduces a new, and potentially problematic, ontological commitment. Even though Mulligan defends the unbreakability of ‘it is true that …’ at some length,Footnote 7 and Künne presents several arguments against this claim,Footnote 8 Mulligan’s real concern, if I interpret him right, is with the ontological, not the logical form of T 1 , i.e. with the question whether it commits us to truthbearer s. If it does not, then neither does T 2 , in virtue of M 2 (nor does T 3, in virtue of M 3 ).

Boghossian (2010, p. 558) raises a similar worry in the following form: even granting that the step from B 1 to B 2 is analytic, why should we think of it as a ‘means of grasping the notion of a proposition’ rather than as an ‘implicit definition of a technical notion—“the content of”—’? In reply, Künne (2010b, pp. 589–590) points out that the reasons usually advanced against the substitutivity salva congruitate of ‘that p’ and ‘the proposition that p’ do not apply in the context of B 1 and dismisses them as ‘quirks of grammar ’. The worry, however, was not about the expansion of ‘that p’ to ‘the proposition that p’, but about the introduction of ‘that p’ in the first place. Applying Mulligan’s point to B 1 , we do not get B 2 , but rather ‘A’s belief is that it rains’ which is said to express not an identity , but rather some sort of specification à la Pryor (2007) and that ‘that p’ is a ‘less than fully fledged name’ (2010b, pp. 573–574). If ‘is that’ in ‘A’s belief is that it rains’ does not stand for ‘ = the proposition that …’ but rather for ‘has the content: …’ (Pryor 2007, p. 234), then B 1 cannot be said to introduce us to the concept of a proposition.

According to Mulligan’s alternative picture—and contrary to Frege, Bolzano and the contemporary orthodoxy— belief is not conceived of as a propositional attitude: to believe that p is not to stand in a relation to the referent of ‘that p’.Footnote 9 Rather, ‘believes that …’ is a predicate -forming operator which, combined with a sentence, ascribes a property of having a belief of a certain kindFootnote 10 or rather describing such a property.Footnote 11 This does not mean we are home and dry, however. To capture the internal structure of such belief-properties, and to explain the validity of inferences like ‘a believes that p; b believes that p; hence, there is something they both believe’, some sort of quantification into predicate-position will have to be introduced: if it is interpreted substitutionally, it makes beliefs language dependent and individuates them too finely,Footnote 12 if it is interpreted objectually, it reintroduces objects of belief and it is not clear how it can be interpreted in neither of these ways.

We thus see that Mulligan ’s worry really is about ontological commitment. As I understand it, Mulligan’s point is inscribed into a more general strategy of making good on the Husserlian claim that ‘ground’ and ‘explain’ derive from ‘because’ (Mulligan 2004, p. 391). As Correia (2010, p. 254) stresses, the main motivation for the operationalist view is ‘reasons of ontological neutrality: it should be possible to make claims of grounding and fail to believe in facts’.Footnote 13 Analogously, we may understand Mulligan as urging that we may believe in claims of the forms ‘it is true that p’ and ‘a believes that p’ without believing in truths or objects of beliefs.

Mulligan’s criticism can thus be understood as urging Künne to go back to his earlier self, who claimed (in 1983, p. 121) that the variable in ‘∀p (Otto claims that p & p)’ is what Brentano (1930, p. 76) calls a ‘Fürsatz’, i.e. a pro-sentence, and does not incur an ontological commitment (cf. Künne 2008, p. 390).Footnote 14 Rather, he then said, it is to be understood as quasi-ontic quantification à la Prior (1971, p. 36, 68) and Lejewski (1970, pp. 174–178) . Künne now says that ‘[i]n the years after the publication of (2003) [he] ruefully returned to the view of quantification into sentence-position that [he] had endorsed in (1983): sentential quantification is quantification sui generis—it is not quantification over anything, and it is not substitutional quantification either.’ (2010b, p. 586) But what is it?

An immediate problem, therefore, is how to understand quasi-ontic quantification. Understanding it as substitutionalFootnote 15 makes the ‘modest’ account circular, for reasons clearly explained by Künne (2003, pp. 357–359). So how is to be understood? In 2003 (p. 361, fn. 130), Künne agrees with the complaint of Richard (1996, pp. 438–442) that Prior’s view makes sentential quantification ‘unduly mysterious’.

While Mulligan ’s point legitimately pressures Künne on this point, it also undercuts the very project. Even if we grant the intelligibility of primitive, sui generis ‘quasi-ontic’ quantification, Mulligan’s problem remains: Both B 2 and Tʹ 1 do, as Künne (2010b, p. 587, n. 10) says, start from ‘“something,” namely a premiss containing a “that”-clause’. If the relational construal of ‘believes’ and the predicational construal of ‘it is true’ are undercut, then these sentences do not have quantificational structure at all, quasi-ontic or not. Fortunately for Künne, this broader attack can be answered.

2 The Aristotelian Equivalence and The Relational Nature of Truth

To better understand the central issue in question, and to prepare the grounds for my criticism of Mulligan ’s criticism of Künne , let us briefly review a claim about which they agree, i.e. M 1 above. Nothing, we learned on Tarski’s knees, deserves the name ‘truth-predicate’ if it does not satisfy the T-schema (Tarski 1933) or ‘Aristotelian Equivalence’:

(T):

It is true that p iff p.

The T-schema is a biconditional, and with all biconditionals, we may ask in what direction (if any) goes the relation of explanatory priority (or, equivalently, which side ‘wears the trousers’). This question may be phrased as the one whether

(r2l):

It is true that p because p

or rather

(l2r):

p because it is true that p

is true. As far as I know, it is common ground that if one of them is true at all, it is (r2l), i.e. M 1 .Footnote 16 Some of us want indeed to be able to say things like:

Truth is a matter of reality, which means that if a statement is true, it is because reality renders it true: No sentence is true but reality makes it so… (Quine 1970, pp. 10–11)

It is indeed undeniable that whenever a proposition or an utterance is true, it is true because something in the world is a certain way—something typically external to the proposition or utterance. (Horwich 1998, p. 104)

In the first edition of Truth, Horwich (1990, pp. 111–112) accepted ‘Snow is white’s being true is explained by snow’s being white’, ‘The fact that “snow is white” is true is explained by the fact that snow is white’, and even ‘“ snow is white” is made true by the fact that snow is white’ as ‘trivial reformulations’ of (r2l) and said that the minimal theory could account for it:

In mapping out the relations of explanatory dependence between phenomena, we naturally and properly grant ultimate explanatory priority to such things as basic laws and the initial conditions of the universe. From these facts we deduce, and thereby explain, why for example

(5) Snow is white.

And only then, given the minimal theory, do we deduce, and thereby explain, why (6) ‘Snow is white’ is true. (Horwich 1990, p. 111)Footnote 17

Why this falls short of accounting for the ‘“correspondance” intuition ’Footnote 18 has been aptly put by Crispin Wright :

This train of thought, it may well seem, is just beside the point. The challenge was to legitimate the idea of a state of affairs (snow’s being white) being the source of the truth of the sentence ‘snow is white’—the idea of a state of affairs transmitting a truth value, as it were, across a substantial relation, the converse of correspondence. [Horwich’s explanation] is, evidently enough, not to explain why ‘snow is white’ is true in terms of snow’s being white; it is rather (quite a different thing) to explain why ‘snow is white’ is true in terms of the physical laws and initial conditions which also explain snow’s being white. (Wright 1992, pp. 26–27)Footnote 19

While Künne (2003, pp. 156–157) agrees with Wright’s criticism of Horwich , he does not say much about how his own account fares any better. But it does. The general statement of the modest account allows us to locate the explanatory priority on the right-hand side of (T), by privileging the expressing function of the sentential variable over its denoting one. It is because ‘p’ has the meaning it has that it is true iff p.Footnote 20

It is not clear, however, how Mulligan ’s anemic operator -theory can match this. The question is not so much whether one’s account of truth allows us to accept M 1 —it is rather what resources it does provide to explain M 1 . It is here, I think, that we find a reason to side with Künne against Mulligan on the relative priority of the truth-predicate and the truth-connective . If we do not identify, in M 1 , an attribution of the property of truth to some truthbearer, we have no possibility whatsoever to explain its truth. We simply postulate a brute explanatory connection without earning our right to do so. While arguing in favour of M 2 , Mulligan was presupposing that he is, in the same way as Künne, entitled to M 1 . But he is not.

But what is so bad about biting this bullet? Indeed, Mulligan (2004) has recently argued from the absence of an explanation for M 1 to the failure of Husserl ’s account of modification. The latter ‘cannot get off the ground’, he says, because

It is obvious that (The proposition that Sam is sad is true because Sam is sad) because…cannot be completed so as to yield a truth by any sentence referring to the essence of what ‘Sam is sad’ refers to. Similarly, no essential ground of the inference [‘Sam is sad. Therefore, the proposition that Sam is sad is true.’] is forthcoming. (2004, p. 407)

In the light of the foregoing, this criticism can be met: what grounds the truth of M 1 is the essential fact that ‘Sam is sad’ has the meaning it actually has, viz. that Sam is sad. So, even if the T-schema is true because of facts about truth and the nature of truthbearers, this does not yet settle the question of the relation of the explanatory dependence between its left-hand side and right-hand side. Philosophers of a realist persuasion, however, may appeal to other considerations to settle the matter: It is because truth depends on the world, in its broadest sense, that (r2l), but not (l2r), is true—because only in the first, but not the second case what comes after ‘because’ may serve as a truthmaker.

We thus arrive at a double conclusion: Künne is right that an account of truth goes in tandem with an account of truthbearers and right to resist the invitation to do away with this ontological commitment by turning ‘operationalist’. Accepting truthbearers that have their meaning essentially in addition has the advantage that one earns the right to M 1 , i.e. to an explanation of the Aristotelian equivalence. In order to explain M 1 (and not just to assert it), however, one has to go further and accept a real relation, underwriting the explanation of truth : truthmaking. Rather than trying to have truth without truths, as Mulligan would have it, or having truthmaking without truthmakers, as is Künne’s intent, we should be staunch realists about all four of them: truth, truths, truthmakers and truthmaking. As Mackie has said about his version of the ‘modest account’ (cf. n. 14 above):

The word ‘true’ is here eliminated, but truth is not eliminated but displayed: the relation in which it consists is made clear. (1973, p. 52, my emphasis)