Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas
282 | Joel David Hamkins on Puzzles of Reality and Infinity
Jul 15, 2024
Joel David Hamkins, the John Cardinal O'Hara Professor of Logic at Notre Dame, navigates the perplexing world of infinity and mathematical truths. He discusses the evolution of mathematical thought, from Cantor’s groundbreaking work to Gödel's Incompleteness Theorems. The conversation dives into the concept of the mathematical multiverse and how different axioms shape our understanding of reality. Hamkins also addresses the Continuum Hypothesis and its implications, highlighting the philosophical challenges posed by infinity in mathematics.
01:18:23
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Quick takeaways
- Infinity in mathematics leads to counterintuitive results and challenges clarity.
- Gödel's incompleteness theorem raises deep philosophical questions about provability and axioms.
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