Sets and set theoretic foundations

The event is taking part on the Tuesday, Oct 29th 2019 at 15.30
Theme/s: Pure and Applied Colloquia, Pure Maths
Location of Event: 306 Alan Turing
This event is a: Public Seminar

Many philosophers of mathematics claim mathematics requires a foundation of axiomatic set theory which is almost invariably Zermelo-Fraenkel set theory with the axiom of choice. In contemporary mathematical practice elementary set properties are an essential part of ordinary mathematical thought and language, and can be understood by reflecting on the pre-axiomatic concept of a set. Importantly elementary set properties (or representations thereof) suffice for most proofs in classical mathematics. In this talk I will use examples from topology and functional analysis to illustrate the difference between elementary set properties and the foundational role of axiomatic set theory. Given this difference I will argue that interest in the foundational role of axiomatic set theory is frequently motivated by philosophical problems about the epistemology and ontology of mathematics rather than by a concern to make sense of contemporary mathematical practice. Category theory deserves more philosophical attention than it has previously had since it offers a perspective on mathematical structures and mappings which is far more closely aligned with actual practice.

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External Speakers

Mark Addis, Open University