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The Underdetermination of the Meaning of Logical Words by Rules of Inference
After setting up the framework of logical inferentialism and explaining that view’s relevance for the question of a priori justification, this chapter presents and discusses ‘the underdetermination challenge’ to the view. The challenge consists in arguing that, contrary to logical inferentialism, some logical words are such that no set of formal, recursively enumerable rules of inference can pin down their meaning, in that, for any candidate such set, one can show that the set is adequate also with respect to a meaning different from the intended one. I substantiate the challenge by looking at four broad classes of logical words: 1ary intensional operators, conditionals, variable-binding operators, and congruence predicates. I close by offering a tentative diagnosis of why logical inferentialism is subject to the underdetermination challenge.