Proof theoretic criteria for logical constancy

Shortt, Julian (2023) Proof theoretic criteria for logical constancy. PhD thesis, University of Glasgow.

Abstract

Logic concerns inference, and some inferences can be distinguished from others by their holding as a matter of logic itself, rather than say empirical factors. These inferences are known as logical consequences and have a special status due to the strong level of confidence they inspire. Given this importance, this dissertation investigates a method of separating the logical from the non-logical. The method used is based on proof theory, and builds on the work of Prawitz, Dummett and Read. Requirements for logicality are developed based on a literature review of common philosophical use of the term, with the key factors being formality, and the absolute generality / topic neutrality of interpretations of logical constants. These requirements are used to generate natural deduction criteria for logical constancy, resulting in the classification of certain predicates, truth functional propositional operators, first order quantifiers, second order quantifiers in sound and complete formal systems using Henkin semantics, and modal operators from the systems K and S5 as logical constants. Semantic tableaux proof systems are also investigated, resulting in the production of semantic tableaux-based criteria for logicality.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: B Philosophy. Psychology. Religion > BC Logic
• Colleges/Schools: College of Arts & Humanities > School of Humanities > Philosophy
• Supervisor's Name: Rieger, Dr. Adam
• Date of Award: 2023
• Depositing User: Theses Team
• Unique ID: glathesis:2023-83920
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 08 Nov 2023 09:00
• Last Modified: 08 Nov 2023 09:03
• Thesis DOI: 10.5525/gla.thesis.83920
• URI: https://theses.gla.ac.uk/id/eprint/83920