SP107 F1.15

This time our classmates, Matteo and Josje, will presenet Panu Raatikainen’s Conceptions of truth in intuitionism.

We often summarize the intuitionist notion of truth as “truth as provability”, which marks a fundamental difference with the classical logicians. But in doing so, we overlook the fact that there are multiple competing conceptions of truth within intuitionism itself. Raatikainen presents a systematic overview of these different accounts, ranging from actualist to possibilist, and ultimately offers a critique of each, putting in question about the coherence of the intuitionist framework as a whole.

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.