18min chapter

Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas cover image

137 | Justin Clarke-Doane on Mathematics, Morality, Objectivity, and Reality

Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas

CHAPTER

Exploring Logic and Mathematical Truths

This chapter explores the distinctions between first order and second order logic, particularly focusing on the philosophical debates surrounding their implications. It delves into the nature of mathematical truths, discussing concepts such as quantifiers and the complexities of axiomatic systems in geometry and arithmetic. The conversation invites listeners to rethink foundational mathematical concepts and their philosophical underpinnings, particularly in light of Gödel's incompleteness theorems.

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