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Revisiting Quine on Truth by Convention

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Abstract

In “Truth by Convention” W.V. Quine gave an influential argument against logical conventionalism. Even today his argument is often taken to decisively refute logical conventionalism. Here I break Quine’s arguments into two—(i) the super-task argument and (ii) the regress argument—and argue that while these arguments together refute implausible explicit versions of conventionalism, they cannot be successfully mounted against a more plausible implicit version of conventionalism. Unlike some of his modern followers, Quine himself recognized this, but argued that implicit conventionalism was explanatorily idle. Against this I show that pace Quine’s claim that implicit conventionalism has no content beyond the claim that logic is firmly accepted, implicit rules of inference can be used to distinguish the firmly accepted from the conventional. As part of my case, I argue that positing syntactic rules of inference as part of our linguistic competence follows from the same methodology that leads contemporary linguists and cognitive scientists to posit rules of phonology, morphology, and grammar. The upshot of my discussion is a diagnosis of the fallacy in Quine’s master critique of logical conventionalism and a re-opening of possibilities for an attractive conventionalist theory of logic.

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Notes

  1. Logical conventionalism is defended in, for example, Ayer [1], Carnap [8], and Giannoni [30].

  2. Quine [45].

  3. Soames [56], page 265.

  4. Sider [54], page 216.

  5. Benacerraf [3], page 676—I have omitted a footnote referencing Quine [45] in this quote.

  6. Ebbs [24].

  7. See Goldfarb [31] and Ricketts [50]. I disagree with the reading of Carnap offered by these philosophers; a remark made by Hilary Putnam in response to Ricketts is worth quoting: “Ricketts’s Carnap, the Carnap who holds no doctrines but only asks for “clarification,”...is just not the Carnap I knew and loved.” (quoted from Clark and Hale [17], page 281).

  8. For some relevant exegesis, Creath [19] critically discusses the standard view of Quine [45] as breaking fully with Carnapian conventionalism and associated doctrines.

  9. See Warren [60].

  10. For dissenting views see Ebbs [24] and Ben-Menahem [2].

  11. The conventionalist is also going to want to provide a similar explanation of the validity of logical rules like modus ponens—see the discussion of linguistic rules below for more on this.

  12. The “super-task” terminology, in roughly this sense, was introduced in Thomson [57].

  13. Here I accept the standard diagnosis of Zeno’s paradoxes, supported by modern mathematical analysis, Russell [52], pages 182–198 is a canonical discussion.

  14. Carroll [11].

  15. Two early responses to Carroll somewhere in this rough ballpark are Rhees [49] and Thomson [58].

  16. Boghossian [7], page 381.

  17. The founding documents of logical inferentialism are Carnap [8], Gentzen [29], and Wittgenstein [66]; see also Boghossian [7], Dummett [23], Hacking [32], Peacocke [40], and Prawitz [44], for example. A general philosophical account of inferentialism can be found in Warren [61].

  18. This is not actually as straightforward as is sometimes assumed, see Carnap [9].

  19. This will only work in full generality for logics that are semantically complete; for simplicity I am confining my discussion to such logics. I think that an inferentialist/conventionalist approach can be applied to incomplete logics, but discussing this involves tackling obstacles that are irrelevant to an assessment of Quine’s arguments.

  20. If applied to natural languages, we would need to supplement this type of approach with an account of which sentences are truth-apt; Wright [68] spells out a use-based strategy for doing this that would be congenial to implicit conventionalists.

  21. Cf. Field [26], page 388.

  22. Kripke [37] famously argued against dispositionalist accounts of rule-following; for defenses of dispositionalism against Kripke’s arguments see, e.g., the discussions in Forster [28], Horwich [35], and Shogenji [53].

  23. For simplicity I’ll be ignoring the role of patterned coordination by simply assuming that everyone in the community follows the very same inference rules. In practice this might happen only because ordinary speakers defer to logical experts.

  24. Carnap [10] is a rare exception; there Carnap favors a dispositionalist style approach to rules and analyticity in natural language.

  25. My distinction between direct and indirect rules is related to Harman [33]’s psychological notions of immediate implication and immediate inconsistency. Also relevant is Peacocke [40]’s notion of a primitively compelling inference, note however, that my notion of a direct rule is not at all epistemic, it is rather psychological/behavioral.

  26. Lewis [38].

  27. See also Quine’s introduction to Lewis [38].

  28. See Fodor and Lepore [27] for a book length attack on semantic holism.

  29. Blanchette [5], pages 132–133.

  30. This type of response will only apply to valid but derivable rules of inference. Here I have ignored valid but non-derivable rules (see the discussion of the restriction to semantically complete logics above in footnote 19).

  31. See Wittgenstein [65], Dummett [22], and Wright [67].

  32. Quoted from the close of Quine [45]; see also Quine [46] for extended related discussion as well as the quotations below.

  33. In some of Quine’s later discussions, e.g., his [46], a behavioral notion of “obviousness” is playing a similar role; see Creath [20] for relevant critical discussion.

  34. See Berko [4]; my account of the wug test is based on Pinker [42], pages 14–15.

  35. The symbol “\(^{\smallfrown }\)” expresses the concatenation function: so \(``a"^{\smallfrown }``b"=``ab"\).

  36. See Chomsky and Halle [15].

  37. See Chomsky [12] and [14]; Chomsky’s theories of syntax have changed since these initial presentations, see Jackendoff [36] for a partial overview. For an account of the development of linguistics in the twentieth century focusing on the pivotal but often controversial role of Chomsky, see Harris [34].

  38. See Pinker [41] for a popular account of the deliverances of mainstream linguistic theory.

  39. From Chomsky’s [13] review of Skinner [55], quoted from page 59 of Block [6].

  40. Recursive grammatical rules are often taken to be universal amongst human languages, but recently Daniel L. Everett has argued that the language used by the Pirahã people in the Amazon lacks recursion; see Everett [25] for a popular presentation. Everett thinks that the Pirahã are capable of a type of recursive thinking and that recursion in some sense is central to human thought, it is just that he denies that sentence recursion occurs in their language.

  41. This has been challenged, e.g., by McGee [39].

  42. See Rumelhart and McClelland [51]; see also the discussion of connectionism in Churchland [16] for endorsement by a philosopher.

  43. Pinker and Prince [43] is a comprehensive rebuttal to connectionist theories of human language; Pinker [42] contains a popular treatment of arguments against connectionism.

  44. Thanks to a referee for this journal here.

  45. I think that this is true even if the rule-based theory is explanatory in approximating a true, non-rule-based theory.

  46. A classic example is the Wason selection task or Wason card task; see Wason [62, 63] and Wason and Shapiro [64].

  47. See Cosmides and Tooby [18].

  48. See, e.g., Davies et al. [21].

  49. This distinction was introduced by Chomsky in his [14].

  50. Quoted from van Bentham [59].

  51. A full case for both logical and mathematical conventionalism is developed in my book, “Shadows of Syntax”.

  52. Quoted from Quine [47].

  53. Quine [48], page 386.

  54. See Warren [60].

  55. Thanks to several anonymous referees.

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Warren, J. Revisiting Quine on Truth by Convention. J Philos Logic 46, 119–139 (2017). https://doi.org/10.1007/s10992-016-9396-8

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