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Disquotationalism, Minimalism, and the Finite Minimal Theory

Published online by Cambridge University Press:  01 January 2020

Jay Newhard
Jay Newhard*
Affiliation:
University of Oklahoma, Norman, OK73019, USA
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Extract

Recently, Paul Horwich has developed the minimalist theory of truth, according to which the truth predicate does not express a Substantive property, though it may be used as a grammatical expedient. Minimalism shares these Claims with Quine's disquotationalism; it differs from disquotationalism primarily in holding that truth-bearers are propositions, rather than sentences. Despite potential ontological worries, allowing that propositions bear truth gives Horwich a prima facie response to several important objections to disquotationalism. In section I of this paper, disquotationalism is given a careful exegesis, in which seven known objections are traced to the disquotational Schema, and two new objections are raised. A version of disquotationalism which avoids two of the seven known objections is recommended. In section II, an examination of minimalism shows that it faces eight of the nine objections facing disquotationalism, plus a new objection.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 34 , Issue 1 , March 2004 , pp. 61 - 86
Copyright
Copyright © The Authors 2004

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References

1 Ramsey, F.P. ‘Facts and Propositions’ Proceedings of the Aristotelian Society, supplemental volume 7 (1927) 153–171,CrossRefGoogle Scholar at 157

2 Other prominent disquotationalists include Field, Hartry Leeds, Stephen and Williams, Michael. See Field, Hartry ‘The Deflationary Conception of Truth’ in Fact, Science and Morality: Essays on A.J. Ayer's Language, Truth and Logic, Macdonald, Graham and Wright, Crispin eds. (New York: Basil Blackwell 1986) 55–117;Google Scholar Leeds, Stephen ‘Theories of Reference and Truth,’ Erkenntnis 13 (1978) 111-29,CrossRefGoogle Scholar and ‘Truth, Correspondence, and Success,’ Philosophical Studies 79 (1995) 1-36; and Williams, Michael ‘Do We (Epistemologists) Need a Theory of Truth?’ Philosophical Topics 14 (1986) 223-42,CrossRefGoogle Scholar and ‘Epistemological Realism and the Basis of Scepticism,’ Mind 97 (1988) 415-39. The discussion here focuses on Quine's version of the disquotational theory.

3 Quine, W.V. Philosophy of Logic, 2nd ed. (Cambridge, MA: Harvard University Press 1986), 11.Google Scholar ‘The disappearance theory’ is Sellars’ name for the redundancy theory.

Also, it should be clear that Quine views use of the Operator ‘it is true that’ as equally indirectious, though it does not result in talk about language. In what follows, the truth Operator will not be discussed explicitly, except where it raises separate issues.

4 Ibid. Cf. also the following passage in Quine, W.V. Quiddities: An Intermittenüy Philosophical Dictionary (Cambridge, MA: The Belknap Press of the Harvard University Press 1987), 214:Google Scholar

The attribution of truth to a Statement is equated to the Statement itself. This has been called the disappearance theory of truth, but unjustly; the quotation marks are not to be taken lightly. What can justly be said is that the adjective “true” is dispensable when attributed to sentences that are explicitly before us. Where it is not thus dispensable is in saying that all or some sentences of such and such a specified form are or are not true, or that someone's Statement unavailable for quotation was or was not true, or that the libel laws do not apply to true Statements, or that you will teil the truth, the whole truth, and nothing but the truth, so help you God…. It is there that the truth predicate is not to be lightly dismissed. If ‘dispensable’ is read as ‘eliminable,’ then Quine is making quite a concession regarding cases where the sentences of which truth is predicated do not appear explicitly. It is charitable to read ‘dispensable’ as ‘dispensable as a metalinguistic abbreviatory device’; that is, some such device is useful and even pragmatically required in ordinary discourse.

5 ‘s’ … ‘sn’ are substitutional variables.

6 Quine, Philosophy of Logic, 2nd ed., 12

7 Alternately, a disquotationalist may understand a sentence such as ‘Everything Tolstoy said is true’ as a conjunction of the form: [fi Tolstoy said ‘ s1’ then s1 is true, and if Tolstoy said ‘s2’ then s2 is true, and … and if Tolstoy said ‘sn’ then sn is truel; and a sentence such as ‘Something Tolstoy said is true’ as the concomitant disjunction. This version of disquotationalism avoids the meaninglessness objection (see below), but incurs an additional objection which Quine's version does not, namely, that ‘Everything Tolstoy said is true’ is analyzed as an infinite conjunction, though intuitively it is finite, as Quine's version analyzes it. Although this version of disquotationalism is somewhat popular, it otherwise faces the same objections as Quine's version of disquotationalism, and so is not discussed separately.

8 Alternatively, a truth theorist may argue that the truth predicate has different roles, or uses, each calling for its own theory. This is the approach taken by Brandom, Robert ‘From Truth to Semantics: A Path through Making it Explicit,’ in Philosophical Issues 8: Truth, Villanueva, Enrique ed. (Atascadero, CA: Ridgeview Publishing Company 1997) 141-54.Google Scholar The possible theories stemming from this point multiply copiously, and I cannot hope to survey them here. Note also that these theories need not be disquotational in whole or part. I thank an anonymous referee for emphasizing the importance of this approach.

9 In places it may appear as though Quine argues only for the weaker claim that sentences and their truth predications are logically equivalent; for example, that ‘“Snow is white” is true’ and ‘Snow is white’ are logically equivalent, which is to say that ‘“Snow is white” is true if and only if snow is white’ is a tautology. (See Quine, Philosophy of Logic, 2nd ed., 12.Google Scholar) However, sentences obviously different in meaning can be logically equivalent in extensional contexts; for example, ‘Triangles have three sides’ and ‘Squares have four sides’ are logically equivalent in extensional contexts. Quine is committed not only to the weaker thesis that sentences and their truth predications are logically equivalent, but also to the stronger thesis that they are equivalent in meaning.

10 The following remark should emphasize this point: for those already inclined to accept the redundancy of the truth predicate based on the cases where truth is predicated of a quoted sentence, then the appeal in the algorithm to D, though circular, is perhaps not objectionable. However, Quine must argue against the intuition that a sentence in which truth is predicated of a quoted sentence does not say the same thing as the unquoted sentence. For example, Russell registers this intuition:

Consider, again, what it is we mean when we judge. At first sight, we seem to mean that a certain proposition is true; but “p is true” is not the same proposition as p, and therefore cannot be what we mean. And the complex “p's truth” may be assumed just as p may: as assumed, it is not a judgment. Thus, when we af f irm p, we are concerned only with p, and in no way with truth. (Bertrand Russell, ‘Meinong's Theory of Complexes and Assumptions (III)’ Mind 13 (1904) 509-24 at511)

In other words, though D, taken as a meaning equivalence, may strike some philosophers as intuitive, there are strong grounds for the intuition that D is false, taken as a meaning equivalence. Therefore, an appeal to D in the course of the algorithm is circular and objectionable.

11 This point is made by McGrath, Matthew ‘Weak Deflationism,’ Mind 106 (1997) 69–98CrossRefGoogle Scholar at 71, n.l, and in Between Deflationism & Correspondence Theory (New York: Garland 2000), 26, n.l; and also by Devitt, Michael ‘Minimalist Truth: A Critical Notice of Paul Horwich's Truth,’ Mind & Language 6 (1991) 273-83CrossRefGoogle Scholar at 276. Hartry Field seems to have this point in mind when he suggests that truth for Horwich is a logical predicate; see Hartry Field, ‘Critical Notice: Horwich's, Paul Truth,’ Philosophy of Science 59 (1992) 321-30.Google Scholar This point also underlies Anil Gupta's discussion in §IV of ‘A Critique of Deflationism’ Philosophical Topics 21 (1993) 57-81, though he does not make it.

12 Gupta, ‘A Critique of Deflationism,’ 69-70

13 Note that Tarski was well aware of these problems; for these and other reasons, Tarski worked with formalized languages, for which problems of ambiguity and context-sensitivity do not arise. Detailed discussion of these problems is given by David, Marian Correspondence and Disquotation: An Essay on the Nature of Truth (New York: Oxford University Press 1994)Google Scholar § 5.8.

14 Problems arising from sentences of foreign languages are discussed by David, Correspondence and Disquotation: An Essay on the Nature of Truth, § 5.6. David's preference is to put the problem in terms of idiolects, but like considerations give rise to analogous problems of truth relativized to an idiolect, or to a language.

Also note that, again, Tarski is well aware of these problems. Tarski observes that ‘[the] same expression can, in one language, be a true Statement, in another a false one or a meaningless expression.’ Thus, ‘[there] will be no question at all here of giving a Single general definition of the term [i.e., the truth predicate]. The problem which interests us will be split into a series of separate problems each relating to a Single language’ (Tarski, Alfred ‘The Concept of Truth in Formalized Languages,’ in Tarski, Alfred Logic, Semantics, Mathematics: Papersfrom 1923 to 1938, 2nd ed. [Indianapolis: Hackett 1983] 152–278,Google Scholar at 153).

15 See footnote 14.

16 For the same reasons, Tarski's Schema T is not a disquotational Schema.

17 Marian David considers the following version of the disquotational Schema to be ‘the deflationist's main attempt’ at a deflationary theory of truth:

D’ x is a true sentence if and only if for some p, x is identical to ‘p’ and p D’ has several advantages over D. First, x ranges over descriptions and proper names of sentences, as well as quotation names. Second, x may be universally and existentially quantified over. Third, David points out that D’ is in the form of an explicit definition from which the property of truth may be specified. However, unless D’ is read as a mutual entailment, it is not strictly speaking in the form of an explicit definition; reasons are given below (§ III) for the implausibility of reading DN as a mutual entailment which apply to D’ mutatis mutandis. Also, the property truth cannot be specified from D’, since ‘p’ is a substitutional variable. Tarski considers and rejects D’ on the grounds that the definiens is of questionable significance; David, who reports Tarski's verdict, concludes that the semi-technical apparatus is essential to D’. Because the truth predicate is syncategorematic and does not express a property on the disquotational theory, these problems are not especially bothersome. For David's discussion, see Correspondence and Disquotation: An Essay on the Nature of Truth, § 4.3. For Tarski's discussion, see ‘The Concept of Truth in Formalized Languages’ 159ff. For further development of this theory, see Christopher S., Hill ‘The Marriage of Heaven and Hell: Reconciling Deflationary Semantics with Correspondence Intuitions’ Phüosophical Studies 104 (2001) 291–321.Google Scholar

The difference between D’ and DN is slight: D’ relates ‘x’ and ‘p’ through the clause ‘x is identical to “p”’, whereas DN is supplemented with the clause that N denotes S.

18 Alternately, it might be held that the truth predicate as it occurs in instances of M1 does not contribute its semantic content to the proposition expressed by sentences containing it. Frege was driven to this view at one point. (See Frege, Gottlob ‘My Basic Logical Insights’ in Frege, Gottlob Gottlob Frege: Posthumous Writings (Chicago: The University of Chicago Press 1979)Google Scholar 251-2 at 251.) However, not only is this move ad hoc, but it also renders Mt ill-formed on both the right and left sides.

19 The context of instantiation may coincidentally provide the correct semantic information for the context-sensitive terms, though such coincidences are expected to be rare, and because fortuitous, inappropriate.

20 Horwich, Truth, 2nd ed. (Oxford: Clarendon Press 1998)

21 Horwich, Truth, 2nd ed., 2-3

22 Horwich, Truth, 2nd ed., 18. Also, see footnote 26.

23 Horwich, Truth, 2nd ed., 18, n.3.

24 This, despite Horwich's explicit rejection of substitutional quantification; see Horwich, Truth, 2nd ed., 25f. I discuss later in this section whether it is necessary to restrict the domain of ‘p’ to sentences of English.

Marian David observes similarly that ‘it does not make sense’ for values of p to be propositions; see David, Marian ‘Minimalism and the Facts about Truth,’ in What Is Truth?: Current Issues in Theoretical Philosophy, Volume 1, Schantz, Richard ed. (Berlin: Walter de Gruyter 2002) 161-75,Google Scholar at nn.27 and 28. I thank an anonymous referee for calling my attention to this passage.

25 Horwich, Truth, 2nd ed., 19Google Scholar

26 Horwichpresents E as: ‘<p> is true iff p! For Horwich, instances of E are expressions, and corresponding instances of E* (i.e., E* instantiated for the same value of p) are the propositions expressed by those instances of E. Thus, for E to be related to E* in this way, the quotation marks Horwich presents in Schema E must be dropped.

27 See Horwich, Truth, 2nd ed., 23,Google Scholar n.7. This requirement was first noted by Gupta, Anil; see his ‘Minimalism,’ Philosophical Perspectives 7, Tomberlin, James E. ed. (Atascad ero, CA: Ridgeview 1993) 359-69.Google Scholar The requirement may be met by changing the informal principle to read, ‘For any proposition x….’ However, a supplementary axiom needs to be added to properly restrict Horwich's formal Statement of the axioms constituting MT:

(x) (x is an axiom of MT ↔ (∃y) (x = E*(y)))

28 Vann McGee argues that if our only guidance in collecting the axioms of the minimal theory is that the axioms are to be those belonging to the maximal consistent set of instances of E*, our guidance will be too weak to form such a set, because there are too many, and we are given no further guidance to choose among them. See McGee, Vann ‘Maximal Consistent Sets of Instances of Tarski's Schema (T)’ Journal of Philosophical Logic 21 (1992) 235-41.CrossRefGoogle Scholar thank an anonymous referee for recalling this article to my attention.

In addition, there are an infinite number of instances of E* whose paradoxicality depends on empirical circumstances, so that excluding the paradoxical instances of E* is not as straightforward or as minor as it may appear at first blush.

29 Horwich writes that ‘[the] Single respect in which the minimal theory can seem unattractive is its infinite, list-like character’ (Horwich, Truth, 2nd ed., 107Google Scholar).

30 Kaplan, David ‘Dthat,’ in Syntax and Semantics, volume 9, Cole, Peter ed. (New York: Academic Press 1978) 221-53.Google Scholar

31 Where V is an objectual variable, ‘dthat()’ cannot operate on V since V is not an expression. Therefore, ‘p’ is a substitutional variable, since both readings of ‘< >’ have this result.

32 The angled brackets may also be read as an Operator taking an expression ‘p’ as its argument and returning the proposition denoted by ‘p’, if there is one. On this reading, E is well-formed for names, descriptions, and demonstratives of propositions, but ill-formed for sentences expressing propositions. No problems are avoided by reading the angled brackets in E as a functor and the additional angled brackets in E* as an Operator, or vice versa.

33 Horwich recognizes the problem, but does not adopt a solution. Cf. Horwich, Truth, 2nd ed., 39. Notice also the examples he gives of ‘what Oscar thinks’ and ‘Einstein's principle’ in the passage cited by n.21.

34 Horwich, Truth, 2nd ed., 38

35 The confusion is explicit in the PostScript: ‘the minimalist thesis is that the meaning of “true” is constituted by our disposition to accept those instances of the truth Schemata that we can formulate’ (Horwich, Truth, 2nd ed., 128;Google Scholar Horwich's italics).

36 Horwich, Truth, 2nd ed., 3Google Scholar

37 Horwich, Truth, 2nd ed., 2Google Scholar

38 Gupta, Anil ‘A Critique of Deflationism’ Philosophical Topics 21 (1993) 57–81CrossRefGoogle Scholar

39 Sosa, Ernest ‘The Truth of Modest Realism’ Philosophical Issues 3: Science and Knowledge, Villanueva, Enrique ed. (Atascadero, CA: Ridgeview 1993) 177-95Google Scholar at 188. See also Sosa, Ernest ‘Epistemology, Realism, and Truth’ Philosophical Perspectives 7: Language and Logic, Tomberlin, James E. ed. (Atascadero, CA: Ridgeview 1993) 1–16.Google Scholar

40 Sosa, ‘The Truth of Modest Realism’ 188Google Scholar

41 This is the reading of‘()’ which is needed for FMT to capture Sosa's Statement of the finite minimal theory. Also, it accords with his use of‘()’ throughout his discussion of the finite minimal theory.

42 This is the relation most commonly called ‘entailment’.

43 The notion here called ‘logical entailment’ is sometimes called ‘implication’ or ‘logical implication’. The relation of mutual logical entailment is standardly called ‘logical equivalence’.

44 Sosa has confirmed this by e-mail correspondence.

45 Sosa, ‘The Truth of Modest Realism’ 188Google Scholar

46 Those philosophers, like Peter van Inwagen, who have qualms about the intelligibility of substitutionally quantified expressions may raise a statability objection, but since this is a separate philosophical issue, I do not pursue it here.

47 Indeed, Sosa adopts additional principles giving necessary and sufficient conditions for the truth of an expression; see ‘The Truth of Modest Realism’ 190.

48 For discussion of these and related candidates, see O'Leary-Hawthorne, John and Oppy, Graham ‘Minimalism and Truth’ Noüs 31 (1997) 170-96.Google Scholar

There is one further Option for the finite minimal theory: FMT may be reformulated using the truth Operator in lieu of the truth predicate, yielding the following Schema: x ↔ 〈it is true that x〉. Accordingly, it may be claimed that ‘it is true that’ has semantic features similar to ‘it is not the case that’; sc, it operates on a sentence or proposition and returns a different sentence or proposition, though it does not express a property. Finally, it might be claimed that the truth predicate is a derivative form of the truth Operator, such that the truth predicate, whether occurring as part of the truth Operator or as a grammatical predicate, does not express a property.

Objections may be raised against the claim that ‘is true’ does not express a property. Although it is plausible to claim that Operators do not express properties, ‘is not the case’ presumably does express a property. If so, it is implausible and counterintuitive to claim that ‘is true’ does not express a property. Also, since truth may be predicated of quoted sentences or other denoting expressions, while the truth Operator is well-formed only for sentences, it is prima facie implausible to claim that the truth Operator is primitive and the truth predicate derivative.

49 This is the Option Sosa takes; see ‘The Truth of Modest Realism,’ 191 f.

50 Davidson, Donald ‘The Folly of Trying to Define Truth’ The Journal of Philosophy 93 (1996) 263-78;CrossRefGoogle Scholar McGinn, Colin Logical Properties (Oxford: Clarendon Press 2000) eh. 5;CrossRefGoogle Scholar and Dodd, Julian An Identity Theory of Truth (London: Macmillan 2000).CrossRefGoogle Scholar Ithas also been endorsed by Putnam, Hilary ‘Reference and Understanding’ in Meaning and Use, Margalit, Avishai ed. (Dordrecht, Holland: D. Reidel 1979) 199–217CrossRefGoogle Scholar at 209 f.

51 This is not a definition of an haecceity; rather, it describes a property had by haeeeeities.

52 The prima facie plausibility enjoyed by S is not sufficient support. Note that HX also has some prima facie plausibility, and might even be true; yet its plausibility is not sufficient to justify it.

53 Moore, G.E. Some Main Problems of Philosophy (New York: Macmillan 1953), 261Google Scholar

54 There is no danger of circularity, since FMT is not a definition of the truth predicate.

55 Weakening FMT to a material biconditional yields M1, objected to above. It does not help to suppose that the relation between x and (x is true) is explanation, as Matthew McGrath suggests in Between Deflationism & Correspondence Theory. Since explanation is in general not Symmetrie (even in McGrath's technical sense; see his ‘Weak Deflationism’ 76), explanation cannot be used to derive the axioms of MT. Otherwise, McGrath's principle faces the same objections as Mj.

56 I wish to thank Gary Gates, Matthew McGrath, and Ernest Sosa for helpful discussion and comments, as well as two anonymous referees.