Radical Interpretation and Logical Pluralism

Abstract

I examine Quine’s and Davidson’s arguments to the effect that classical logic is the one and only correct logic. This conclusion is drawn from their views on radical translation and interpretation, respectively. I focus on the latter, but I first address, independently, Quine’s argument to the effect that the ‘deviant’ logician, who departs from classical logic, is merely changing the subject. Regarding logical pluralism, the question is whether there is more than one correct logic. I argue that bivalence may be subject matter dependent, but that distribution and the law of excluded middle can probably not be dropped whilst maintaining the standard meanings of the connectives. In discussing the ramifications of the indeterminacy of interpretation, I ask whether it forces Davidsonian interpreters to adopt Dummett’s epistemic conception of truth vis-à-vis their interpretations. And, if so, does this cohere with their attributing a nonepistemic notion of truth to their interpretees? This would be a form of logical pluralism. In addition, I discuss Davidson’s arguments against conceptual schemes. Schemes incommensurable with our own could be construed as wholesale deviant logics, or so I argue. And, if so, their possibility would yield, in turn, the possibility of a radical logical pluralism. I also address Davidson’s application of Tarski’s definition of truth.

Appendix: Fitch’s Paradox

Davidson’s requirement that speech and thought be interpretable (his version of the manifestation principle) might fall afoul of a version of Fitch’s paradox of knowability [for Fitch’s paradox, see Brogaard and Salerno (2013), and the references therein; see also Wright (1987), pp. 309–316]. On Davidson’s view, it must be possible for anything I mean by my utterances, or any propositional attitude that I have (including knowledge), to be known by an interpreter.

Let:

• ‘K*p’ abbreviate ‘I know that p’

• ‘Kp’ abbreviate ‘some interpreter of me knows that p’

• ‘P’ abbreviate ‘it is possible that’

I’ll assume that the following are theorems for all propositions p, q:

• (1) Kp → p

• (2) K*p → p

I’ll also assume:

• (3) ‘K(p&q)’ and ‘(Kp&Kq)’ are intersubstitutable salva veritate in both extensional and knowledge contexts, as are ‘K*(p&q)’ and ‘(K*p&K*q)’ (so that, for example, ‘KK*(p&q)’ is true if and only if ‘K(K*p&K*q)’ is also).

and

• (4) If a proposition entails a contradiction, then it is not possible that the proposition be true.

According to Davidson, then,

• (5) For any proposition p: K*p → PKK*p

But he presumably allows that not all my states of knowledge are known to interpreters. [Davidson’s triangulation argument (see Davidson 2001c), I assume, merely purports to show that I have propositional attitudes only if some of them are known to interpreters of me, as opposed to purporting to show that all of my propositional attitude states are known to interpreters of me.] Furthermore, I know this. That is, there are propositions that I know to be true, and also know that no interpreter knows that I know to be true—I have at least some private knowledge that I know to be private.

Thus:

There is a proposition p such that: K*p&K*~KK*p.

Let q be such a proposition, so

• (6) K*q&K*~KK*q

By (3) and (6) we get:

• (7) K*(q&~KK*q)

(5) (substituting ‘q&~KK*q’ for ‘p’) yields:

• (8) K*(q&~KK*q) → PKK*(q&~KK*q)

Applying modus ponens to (7) and (8) yields:

• (9) PKK*(q&~KK*q)

But (9) is not true. ‘KK*(q&~KK*q)’ entails a contradiction (applying (3) to KK*(q&~KK*q) gives KK*q&KK*~KK*q, from whence we get KK*q&~KK*q by applying (1) and (2) to the right conjunct), and thus, by (4), ‘PKK*(q&~KK*q)’ is not true.

Hence we must abandon (5).