Paul Benacerraf

For our first session of 2025, we will engage with Robin Jeshion’s Intuiting the Infinite. He defends Charles Parsons’ Kantian appeal to mathematical intuition to address the access problem of Platonism: If mathematical objects are abstract objects, how can we gain knowledge of them?

Jeshion argues that intuition plays a fundamental role in justifying our knowledge of the infinitude of natural numbers, responding to key criticisms about the cogency of arbitrary objects, vague representation, and the role of spatial and temporal structures in mathematical thought.

Our second reading will be Paul Benacerraf’s What Numbers Could Not Be.

For this session we expect attendants to have read in advance:

• Benacerraf, Paul. “What Numbers Could Not Be.” The Philosophical Review 74, no. 1 (1965): 47-73.

The article can be accessed freely by University of Amsterdam students through JSTOR, by logging in with the institution.

During the session, Evan will present the paper, followed by a discussion.