Philosophy of mathematics, which might seem like some boutique academic specialty, has played a remarkable role in the history of Western thought. To Plato, for example, mathematics provided the very model of knowledge, of truth apprehended with certainty not by the senses but by the mind. St. Augustine learned that lesson from the neo-Platonists of his day, which allowed him to take a crucial step toward his religious conversion, for it made intelligible the possibility of a non-material god. “How is pure mathematics possible?”—the famous question at the heart of the Critique of Pure Reason—was Kant’s way of asking in an aphorism what the world must be like if it can be described by mathematical physics. Mathematics raises, in an acute way, the question of how (or whether) we can bridge the gap between our knowledge and the objects of our knowledge.

The mathematician and...


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