Inferentialism and the categoricity problem: reply to Raatikainen
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.