Invitation
Will Stafford
In Defence of Proof-Theoretic Semantics
Proof-theoretic validity offers a justification for the logical laws. However, it has recently been shown that proof-theoretic validity does not offer a semantics for intuitionistic logic, but rather it provides a semantics for intermediate logics which isn’t harmonious. But baked into the philosophical justification for proof-theoretic validity is the idea that it results in a logic with harmonious rules. I show that the lack of harmony stems from the treatment of atomic sentences, not from the treatment of logical connectives. I propose a modification to proof-theoretic validity that will remove the undue impact of atomic formulas. And I show that the logic justified by the new definition is intuitionistic logic. Hence this modification saves proof-theoretic validity from the above objection.
Invitation pdf
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