Stafford, Will2025-05-232025-05-232024-11-07https://hdl.handle.net/2097/45046Several recent results bring into focus the superintuitionistic nature of most notions of proof-theoretic validity, but little work has been done evaluating the consequences of these results. Proof-theoretic validity claims to offer a formal explication of how inferences follow from the definitions of logic connectives (which are defined by their introduction rules). This paper explores whether the new results undermine this claim. It is argued that, while the formal results are worrying, superintuitionistic inferences are valid because the treatments of atomic formulas are insufficiently general, and a resolution to this issue is proposed.enThis Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).http://rightsstatements.org/vocab/InC/1.0/https://authorservices.taylorandfrancis.com/research-impact/sharing-versions-of-journal-articles/Proof-theoretic validityProof-theoretic semanticsIntuitionistic logicProof-theoretic SemanticsText