The Battle of Realities: Mathematics and Morality

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This chapter engages in a philosophical exploration of the nature of reality concerning mathematical entities and their existence. It contrasts mathematical realism with anti-realism while intertwining discussions on moral realism, suggesting that moral truths have substantial ties to human experience. Through various philosophical concepts, the chapter questions the correlations and distinctions between mathematics, physics, and ethical frameworks, indicating the complexities involved in understanding existence and objectivity.

On a spectrum of philosophical topics, one might be tempted to put mathematics and morality on opposite ends. Math is one of the most pristine and rigorously-developed areas of human thought, while morality is notoriously contentious and resistant to consensus. But the more you dig into the depths, the more alike these two fields appear to be. Justin Clarke-Doane argues that they are very much alike indeed, especially when it comes to questions of “reality” and “objectivity” — but that they aren’t quite exactly analogous. We get a little bit into the weeds, but this is a case where close attention will pay off.

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Justin Clarke-Doane received his Ph.D. in philosophy from New York University. He is currently Associate Professor of philosophy at Columbia University, as well as an Honorary Research Fellow at the University of Birmingham and Adjunct Research Associate at Monash University. His book Morality and Mathematics was published in 2020.

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