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Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/892
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Ole Thomassen Hjortland PhD thesis.PDF1.85 MBAdobe PDFView/Open
Title: The structure of logical consequence : proof-theoretic conceptions
Authors: Hjortland, Ole T.
Supervisors: Read, Stephen
Wright, Crispin
Shapiro, Stewart
Keywords: Proof-theory
Logical constants
Harmony
Substructural logic
Issue Date: 25-Jun-2010
Abstract: The model-theoretic analysis of the concept of logical consequence has come under heavy criticism in the last couple of decades. The present work looks at an alternative approach to logical consequence where the notion of inference takes center stage. Formally, the model-theoretic framework is exchanged for a proof-theoretic framework. It is argued that contrary to the traditional view, proof-theoretic semantics is not revisionary, and should rather be seen as a formal semantics that can supplement model-theory. Specifically, there are formal resources to provide a proof-theoretic semantics for both intuitionistic and classical logic. We develop a new perspective on proof-theoretic harmony for logical constants which incorporates elements from the substructural era of proof-theory. We show that there is a semantic lacuna in the traditional accounts of harmony. A new theory of how inference rules determine the semantic content of logical constants is developed. The theory weds proof-theoretic and model-theoretic semantics by showing how proof-theoretic rules can induce truth-conditional clauses in Boolean and many-valued settings. It is argued that such a new approach to how rules determine meaning will ultimately assist our understanding of the apriori nature of logic.
URI: http://hdl.handle.net/10023/892
Type: Thesis
Publisher: University of St Andrews
Appears in Collections:Philosophy Theses



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