Logic Supergroup — Online Colloquium, April 9, 2021
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Will Stafford (Czech Academy of Sciences) – Proof-Theoretic Validity for Intuitionistic Logic
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 aren’t harmonious. This is worrying as 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 could remove the undue impact of atomic formulas sentences.
