Expressing Validity: Towards a Self-Sufficient Inferentialism

In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2019. London: College Publications. pp. 67-82 (2020)
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For semantic inferentialists, the basic semantic concept is validity. An inferentialist theory of meaning should offer an account of the meaning of "valid." If one tries to add a validity predicate to one's object language, however, one runs into problems like the v-Curry paradox. In previous work, I presented a validity predicate for a non-transitive logic that can adequately capture its own meta-inferences. Unfortunately, in that system, one cannot show of any inference that it is invalid. Here I extend the system so that it can capture invalidities.
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