Revitalizing Logical Conventionalism Jared Warren November 12, 2014 Abstract Logical conventionalism was the most popular philosophical theory of logic amongst scientifically-minded mid-twentieth century philosophers, but today the theory is thought to face insuperable difficulties and is almost universally rejected. This paper aims to revitalize logical con- ventionalism. I start by clarifying the nature of the conventionalist thesis (section 1), then I develop a novel version of logical inferentialism in detail (section 2)andshowthatthis,unrestricted,versionofinferentialismen- tails logical conventionalism (section 3). I follow by defending the theory arrived at from the two most influential counterarguments—the problem of tonk and what I call the “proposition making” argument against truth by convention (section 4). I close with a brief conclusion (section 5). By presenting, arguing for, and defending a conventionalist theory of logic, I hope to make it plausible that, pace widespread opinion, logical conven- tionalism remains a viable theory in contemporary philosophy. Keywords: Conventionalism, Inferentialism, Philosophy of Logic, Logical Plu- ralism Conventionalism was the philosophical theory of logic favored by the logical positivists and other scientifically minded mid-twentieth century philosophers.1 Statements of the conventionalist doctrine took a variety of forms: “logical truths are true by convention”, “logical truths are true in virtue of meaning”, “logic is analytic”, “logic is true by definition”, “logical claims are instructions for the use of language”, “logical axioms are linguistic rules”, etc. But these formulations aren’t obviously equivalent or even compatible with each other—how can logical 1Defenses of logical conventionalism include Ayer (1946), Carnap (1934), Hahn (1933), Hempel (1945), Malcolm (1940), Nagel (1944), Reichenbach (1951), and (arguably) Wittgen- stein (1974). 1 1 WHAT IS LOGICAL CONVENTIONALISM? 2 claims be true while also being rules or instructions? The common thread among conventionalist accounts was that logic can be explained by appeal to linguistic meaning and linguistic meaning itself can be explained in terms of human decisions and behavioral regularities. The goal was a theory of logic that didn’t appeal to spooky mental abilities or mysterious metaphysical facts. Today logical conventionalism is almost universally rejected.2 It is rejected because: (i) the general account of necessity and the a priori of which it was part is thought to have collapsed; (ii) Quine and others influentially criticized the view on its own terms; and (iii) developments of conventionalism rarely went beyond the slogan phase.3 Against this consensus, I think that conventionalism about logic can be salvaged and that the folkloric objections commonly cited against it can be answered. After clearly formulating the key conventionalist thesis, I’ll argue for conventionalism by presenting and endorsing a novel form of logical inferentialism—unrestricted logical inferentialism—and arguing that logical conventionalism follows directly from this theory. In addition, I’ll discuss and rebut two very widely accepted arguments against conventionalism. 1 What is Logical Conventionalism? As already noted, slogan formulations of logical conventionalism come in a va- riety of forms. What is common to conventionalist or linguistic theories of logic is that human language use somehow accounts for logical truth and entailment. Before explaining how conventionalism should be understood (and will be un- derstood here), two implausible versions of the view—sometimes endorsed by conventionalists themselves—must be set aside. (i) The first implausible version of the view holds that logical claims somehow express facts about our use of logical words like “not”, “and”, and “if”. In A.J. Ayer’s Language, Truth, & Logic he gives a slogan statement of conventionalism that might suggest this reading when he says of logical truths: They simply record our determination to use words in a certain fashion.4 2Post-positivist defenses of logical conventionalism are offered in Giannoni (1971) and Syverson (2003). 3See Kripke (1980) and Kaplan (1989) for criticisms of the general linguistic theory of necessity and the apriori; see Quine (1936), (1951), and (1960a) for some of his criticisms of logical conventionalism in particular and analyticity in general. 4Ayer (1946), page 84. Ayer’s conventionalism is applied to all necessary and apriori truths, not just those of logic. 1 WHAT IS LOGICAL CONVENTIONALISM? 3 One reading of this sees Ayer as claiming that logical truths are equivalent to descriptive truths about how we use certain words. So that the logical truth “either it will rain or it will not rain” is equivalent to something like “we use the words “or” and “not” so that the sentence “either it will rain or it will not rain” is always true”. But can’t be right, since the former sentence expresses an a priori necessary truth, while the latter expresses an a posteriori contingent truth; and anecessarytruthcanbeequivalenttoacontingenttruthonlyintheextremely weak sense of sharing a truth value. There is no way that these two sentences can be equivalent in any deep sense, much less share the same meaning.5 Ayer himself disavows this reading in the introduction to the second edition of his book: It has, indeed, been suggested that my treatment of a priori propo- sitions makes them into a sub-class of empirical propositions. For I sometimes seem to imply that they describe the way in which cer- tain symbols are used, and it is undoubtedly an empirical fact that people use symbols in the ways that they do. This is not, however, the position that I wish to hold. 6 The relationship between logical claims and language use is not one of descrip- tion—no credible version of conventionalism can take logical truths to describe linguistic rules or regularities. (ii) The second implausible conventionalist theory simply identifies logical claims with linguistic rules. Once again, Ayer provides a nice statement—this time in his contribution to a 1936 Analysis symposium: I think that our view must be that what are called a priori propo- sitions do not describe how words are actually used but merely pre- scribe how words are to be used. They make no statement whose truth can be accepted or denied. They merely lay down a rule which can be followed or disobeyed.7 According to this view, logical claims simply are linguistic rules. One odd thing about this view—something Ayer notes—is that rules aren’t the kinds of things that can be true or false, while logical claims and, in particular, logical truths most certainly are. In other words, this version of logical conventionalism faces 5Malcolm (1940) contains a useful discussion of the relationship between logical claims and descriptive linguistic claims. 6Ayer (1946), page 16. 7Ayer (1936), page 20. 1 WHAT IS LOGICAL CONVENTIONALISM? 4 the famous Frege-Geach problem of harmonizing a non-assertoric account of a branch of discourse with the apparent truth-aptness of said branch.8 Aconventionalistcouldbitethebulletandsimplydenythatlogicalclaims are truth-apt, appearances be damned. Ayer isn’t the only person to have found this appealing, Yemina Ben-Menahem’s recent book on conventionalism argues—by drawing on logical conventionalism’s roots in the geometric conven- tionalism of Henri Poincare and David Hilbert—that historical conventionalists shouldn’t be seen as embracing the idea of truth by convention.9 An alternative to this approach allows for logical claims to be true or false in some minimal sense, while adding that, none-the-less, they are used to express commitments to linguistic rules; this follows so-called quasi-realist theories in meta-ethics.10 In fact, Simon Blackburn, the originator of quasi-realism in meta-ethics, has applied quasi-realism to discourse about necessity.11 Some version of this quasi- realist view might be defensible, but it won’t be the type of conventionalism I’ll be arguing for here, and I don’t think it was the kind favored by historical conventionalists. (iii) Every version of logical conventionalism posits a tight relationship be- tween logical claims and linguistic rules, but I think the correct relationship is explanatory:thelinguisticrulesofourlanguageexplainthetruthandnecessity of logical claims in our language. The historical literature on conventional- ism has struggled to formulate this clearly—some of the quotes above illustrate this struggle in action—but from our present vantage point it’s apparent that this is what was meant by the talk of truth “by convention” or “in virtue of meaning”.12But whatever its historical merits, the explanatory reading of con- ventionalism is the philosophically interesting thesis and it’s the one that I’ll be arguing for here: Logical Conventionalism : Logical truths and logical validities in any language are fully explained by the linguistic rules of that lan- 8See Geach (1965) for the problem and the attribution to Frege. 9See Ben-Menahem (2006); see also Coffa (1986) and (1991). 10See Blackburn (1984) and Gibbard (1990). 11In Blackburn (1987). 12For example, it is apparent in Giannoni (1971)’s discussion, though he uses epistemic terminology rather than explanatory terminology while decrying the epistemic terminology’s inadequacy. See also Ayer’s full discussion in the introduction to his (1946) where he rejects both of his earlier formulations in favor of something like the explanatory reading. Ebbs (2011) argues that Carnap never