Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas 137 | Justin Clarke-Doane on Mathematics, Morality, Objectivity, and Reality
Mar 8, 2021
Justin Clarke-Doane, an Associate Professor of Philosophy at Columbia University, explores the unexpected relationship between mathematics and morality. He argues that both fields grapple with objectivity and reality, despite their apparent differences. The discussion dives into the complexities of moral objectivity, the nature of mathematical truths, and intriguing concepts like the mathematical multiverse. By examining the philosophical links between ethical reasoning and mathematical principles, Clarke-Doane reveals surprising parallels that challenge conventional wisdom in both domains.
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Surprising Similarities
- Morality and mathematics seem disparate, but share surprising similarities regarding realism.
- Exploring their philosophical foundations reveals unexpected connections.
Mathematical Realism
- Mathematical realism asserts statements have truth values independent of human convention.
- The twin primes conjecture exemplifies this, being likely true but unproven.
Truth vs. Expression
- Distinguish a sentence's truth under interpretation from the truth of what it expresses.
- "One plus one is two" can be a logical truth or about numbers, depending on the context.
