A quasi-deflationary solution to the problems of mixed inferences and mixed compounds

ABSTRACT

Truth pluralism is the view that there is more than one truth property. The strong version of it (i.e. strong pluralism) further contends that no truth property is shared by all true propositions. In this paper, I help strong pluralism solve two pressing problems concerning mixed discourse: the problem of mixed inferences (PI) and the problem of mixed compounds (PC). According to PI, strong pluralism is incompatible with the truth-preservation notion of validity; according to PC, strong pluralists cannot find any appropriate truth property for mixed compound propositions, whose atomic constituents are from different domains of discourse. I argue that the strong pluralist is motivated to take the truth predicate in truth-involving universal statements to be deflationary to avoid the two pressing problems. Such a move entails that the truth predicate in the platitude of validity (V) does not denote any substantive truth property. Instead, it is merely an expressive device to help people generalize instances of (V) to (V). Analogous stories hold for the truth predicate in the platitudes of compound (e.g. conjunction). The upshot is that, the strong pluralist can solve PI and PC by further conceding that mixed compounds are true/false in a deflationary way.

KEYWORDS:

• Truth pluralism
• equivalence schema
• minimalism
• the problem of mixed inferences
• the problem of mixed compounds

Acknowledgement

An earlier version of this paper was presented at the 1st Beijing International Graduate Conference in Analytic Philosophy. Thanks to the audiences in this conference and to Jeremy Wyatt, Maciek Czerkawski, and Haodong Lyu for helpful comments and discussions on the earlier drafts. Thanks also to the editors and two anonymous referees for this journal. Special thanks to Dilip Ninan for his support and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 In this paper, I assume the primary truth-bearers are propositions without committing to this assumption. Also, by ‘correspondence theories of truth’ I mean various correspondence monisms, which take truth to universally consist in one specific correspondence relation (e.g., isomorphism). But see, for example, Sher (2013) for correspondence pluralism, which takes the correspondence relations to vary across domains.

2 Following Horwich (1998), I use ‘<p>’ as an abbreviation of ‘the proposition that p’.

3 In this paper, a truth property is said to be substantive if and only if it has some hidden nature that is not revealed by our grasp of the concept of truth. See Lynch (2009, 116) for this characterization of substantivity.

4 See Horwich (1998).

5 “A statement is superassertible just in case it is, or can be, warranted and some warrant for it would survive arbitrarily close scrutiny of its pedigree and arbitrarily extensive increments to or other forms of improvement of our information” (Wright 1992, 48).

6 Pedersen and Wright (2013) defines truth pluralism to be a substantivism, which takes truth to be everywhere substantive. My definition here is more liberal than theirs, for it allows some (but not all) truth predicates to be deflationary. This definition is more commonly assumed. See Tappolet (2000, 209), Cotnoir (2013, 1), Pedersen and Wright (2018, 1), Strollo (2022, 155) for examples. 

7 See, for examples, Wright (1992, 38), Lynch (2009, 76–78).

8 Wright (1992), Cotnoir (2013), Kim and Pedersen (2018), Ferrari et al. (2020) have defended (SP).

9 See Pedersen and Wright (2018) for a comprehensive introduction to the problems for strong pluralism.

10 See Tappolet (1997).

11 This way of presenting the problem of mixed inferences is widely adopted. See Lynch (2009, 59), Edwards (2018, 132–133) for examples. 

12 See Williamson (1994) and Tappolet (2000).

13 By ‘truth-involving universal statements’ I mean the statements in which there is at least one truth predicate being predicated of truth-bearer(s) that are universally quantified over (e.g., every proposition is true).

14 For examples, see Armour-Garb, Stoljar, and Woodbridge (2022), Horwich (1998), and Soames (1999, 247) for this point. And paradoxical instances of (ES) are those instances that will generate paradoxes and thus may not be true, let alone necessarily true a priori. For example, the instance ‘<this statement is false> is true if and only if this statement is false’ will generate liar paradox. In this paper, I set aside the issue concerning paradoxical instances of (ES). Treatment of those paradoxical instances should be addressed elsewhere.

15 Whether we are permitted to do sentential quantifications in natural languages is controversial (see Künne (2003)). But at least we cannot express (S-truth-free) in natural languages (see Schindler and Schlöder (2022)).

16 Actually, we cannot assert every instance of (S-truth-free-schema) in real life, since it has infinitely many instances.

17 The minimalist explanation I have illustrated is reconstructed from Horwich (1998).

18 Truth is conceptually deflationary iff it plays no substantive explanatory role in our conceptual scheme. More on this later.

19 See Gupta (1993), Soames (1999), and Armour-Garb (2010) for detailed elaborations on GP.

20 See Armour-Garb (2010) for a negative answer. But see Oms (2019) for a positive answer.

21 One may reject (D) on the ground that people may refuse to accept paradoxical instances of (ES). But since in this paper I set aside the issue caused by paradoxical instances of (ES), this objection should not bother us here. 

22 For exceptions, see Gamester (2023), where he advocates truth nihilism. And here I (again) assume that proposition is the primary truth bearer.

23 This argument can be seen as a variant of the problem of generalization posed for strong pluralism. Lynch (2001, 726) and Edwards (2018, 133) have briefly addressed that problem.

24 The possibility of saying that truth is metaphysically but not conceptually deflationary is explored and defended by Asay (2013) and Bar-on and Simmons (2013).

25 See, for example, Bar-on and Simmons (2013)’s critique of conceptual deflationism.

26 See Edwards (2018, 89) for this observation. Here I use ‘denotation’ and ‘reference’ interchangeably.

27 See Tarski (1944).

28 (${\mathrm{T}}_{\mathrm{corr}}$) is adopted by object-based correspondence theorists like Glanzberg (2015). See Lynch (2009, 23–24) for this characterization.

29 Cf. Lynch (2009, 138).

30 This definition of truth is standardly attributed to Dewey (1941).

31 Wright (2012, 253) has made this observation.

32 See Sher (2005), David (2009) (2013), Wyatt (2013), and Gamester (2022) for relevant discussions.

33 (2) is justified by the fact that <a is F> has representational semantics iff (TCS) holds for <a is F>. See (TCS) in p.14. 

34 Wyatt (2013) proposes an analogous proposal to determine the truth property of an atomic proposition.

35 It also largely justifies my previous suggestion that the strong pluralist should take the truth predicate in truth-involving universal statements to be deflationary. Under strong pluralism, a large number of truth-involving universal statements (e.g., <everything Socrates asserted is true>) have their instances apt for different semantic accounts. Since no substantive truth predicate can apply to all those instances with different kinds of semantics, the truth predicate in the relevant universal statements can only be deflationary.

36 I have not been explicit in the treatment of the instances where the <p> is an existential/universal proposition. The crux is to identify whether such a proposition is mixed. A universally applicable strategy is to consider the infinite disjunction/conjunction that is materially equivalent to the <p>: <p> is mixed whenever the infinite disjunction/conjunction is mixed. Once we know whether <p> is mixed, we can apply my proposal as usual.

37 Such difficulty has been noted by Dummett (1973, 360–361) and Schroeder (2008, 90–91). But see Podlaskowski (2018)’s proposal to ease the difficulty.

38 Thanks to an anonymous referee for raising this concern.

39 The following presentation of L and $T_L$is adapted from Soames (1984, 403) and Lepore and Ludwig (2005, 43–44).

40 To simplify the presentation, I do not include quantifiers into L and thus avoid introducing variables and the satisfaction relation.

41 See Davidson (1984[1967]), and Tarski (1932) 1983, 187–188)

42 In his later writings (e.g., Davidson (1984, introduction) (1990, ft.20)), Davidson changed his view and thought that we cannot simultaneously define truth in Tarski’s way and use the definition to provide compositional semantics to a natural language. He thought that the concept of truth must be treated as primitive in the truth theory, such that by laying out the structure of the truth theory we can give a compositional meaning theory as wanted. Whether truth-theoretic semantics requires the truth concept to be primitive needs not concern us here, for nothing I have argued in this paper requires strong pluralists to reject primitivism of truth concept. Pluralists of truth property are free to hold primitivism of truth concept if needed, and arguably many have already done so (what I have in mind is the platitude-based approach in truth pluralisms, see Wright (1992) and Lynch (2009)). 

43 See Kölbel (2002, Ch. 5), Lepore and Ludwig (2005, 54), and Lynch (2009, 144). Williams (1999), and Lasersohn (2016, 3) also expressed similar points. Indeed, Kölbel (2002) and Lasersohn (2016) have strived to develop truth-theoretic semantics that can be compatible with a version of truth pluralism, which includes a relativized notion of truth.

44 Some may worry that another commitment of my proposal, namely some complex sentences have “mixed semantics” also threatens the compatibility, perhaps in a more straightforward way. This worry will be dispelled once the potential threats from (A) and (B) are eliminated.

45 The metasemantic pluralism presented here resembles Lynch (2009, 147–148)’s functionalist treatment to denotation. Lynch thinks denotation explains truth in representational domains (where truth is correspondence), while truth explains denotation in non-representational domains (where truth is an anti-realist property).

46 See Dummett (1959), Davidson (1990), and Horwich (1998) for examples. And see Horisk (2008) for a comprehensive literature review.

47 See Horisk (2007). 

48 See Lynch (2009, 111–114) and Gamester (2018) for examples.

49 See Beall (2000); Pedersen (2006); Cotnoir (2013); Ferrari et al. (2020) for other proposals.