Inferentialism and the categoricity problem: reply to Raatikainen
Julien Murzi, Ole Thomassen Hjortland · Analysis · 2009
It is sometimes held that rules of inference determine the meaning of the logical constants: the meaning of, say, conjunction is fully determined by either its introduction or its elimination rules, or both; similarly for the other connectives. In a recent paper, Panu Raatikainen argues that this view – call it logical inferentialism – is undermined by some ‘very little known’ considerations by Carnap (1943) to the effect that ‘in a definite sense, it is not true that the standard rules of inference’ themselves suffice to ‘determine the meanings of [the] logical constants’ (Raatikainen 2000: 283). In a nutshell, Carnap showed that the rules allow for non-normal interpretations of negation and disjunction. Raatikainen concludes that ‘no ordinary formalization of logic … is sufficient to “fully formalize” all the essential properties of the logical constants’ (2000: 283). We suggest that this is a mistake. Pace Raatikainen, intuitionists like Dummett and Prawitz need not worry about Carnap's problem. And although bilateral solutions for classical inferentialists – as proposed by Timothy Smiley and Ian Rumfitt – seem inadequate, it is not excluded that the classical inferentialists may be in a position to address the problem too.