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Wesley Wrigley

Wesley Wrigley

Department: Philosophy

Supervisor: Dr Tim Button

College: Sidney Sussex

AHRC Subject Area: Philosophy

Title of Thesis: Axiomatization and Incompleteness in Arithmetic and Set Theory


I read the Philosophy Tripos at King’s College, here in Cambridge (2010-2013), before moving to Wadham College, Oxford for the BPhil in Philosophy (2013-2015). I’m now back in Cambridge for a PhD in Philosophy, this time at Sidney Sussex.

My dissertation is a systematic account of the philosophical significance of Gödel’s Incompleteness Theorems. These theorems show (amongst other things) that no consistent arithmetical theory can prove all arithmetical truths. Since the incompleteness theorems were proved in 1931, various philosophers and mathematicians have credited them with a bewildering array of philosophical implications. They have been thought to show that the human mind cannot be modelled as a digital computer, that numbers are self-sufficient objects independent of our mathematical activity, and that 'mathematical intuition' or 'rational insight' is a legitimate source of arithmetical knowledge. Within mathematics itself, the Incompleteness Theorems birthed a major research paradigm that continues to this day, the Large Cardinals Program. I argue that paying proper philosophical attention to certain computational properties of axiomatic theories of arithmetic is the key to understanding both the implications of Gödel’s theorems, and the epistemological foundations of the Large Cardinals Program.

Other academic interests

Philosophy of Language, Logic and Mathematics

History of Analytic Philosophy

Logic and Set Theory