Strict finitism as a foundation for mathematics

Mawby, Jim (2005) Strict finitism as a foundation for mathematics. PhD thesis, University of Glasgow.

Abstract

The principal focus of this research is a comprehensive defence of the theory of strict finitism as a foundation for mathematics. I have three broad aims in the thesis; firstly, to offer as complete and developed account of the theory of strict finitism as it has been described and discussed in the literature. I detail the commitments and claims of the theory, and discuss the best ways in which to present the theory. Secondly, I consider the main objections to strict finitism, in particular a number of claims that have been made to the effect that strict finitism is, as it stands, incoherent. Many of these claims I reject, but one, which focuses on the problematic notion of vagueness to which the strict finites seems committed, I suggest, calls for some revision or further development of the strict finitist’s position. The third part of this thesis is therefore concerned with such development, and I discuss various options for strict finitism, ranging from the development of a trivalent semantic, to a rejection of the commitment to vagueness in the first instance.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: B Philosophy. Psychology. Religion > B Philosophy (General); Q Science > QA Mathematics
• Colleges/Schools: College of Arts & Humanities > School of Humanities > Philosophy
• Supervisor's Name: Hale, Bob
• Date of Award: 2005
• Depositing User: Elaine Ballantyne
• Unique ID: glathesis:2005-1344
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 30 Nov 2009
• Last Modified: 10 Dec 2012 13:37
• URI: https://theses.gla.ac.uk/id/eprint/1344