Expressing Validity: Towards a Self-Sufficient Inferentialism

In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2019. London: College Publications (forthcoming)

Authors
Ulf Hlobil
Concordia University
Abstract
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.
Keywords inferentialism  naive validity  v-Curry paradox  non-transitive consequence  substructural logic
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