Intuition

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.

This time we continued Derek So’s discussion of phenomenology, its recent developments and relations to linear logic and embodied cognition.

Main Readings:

• Tieszen, R. Mathematical Intuition: Phenomenology and Mathematical Knowledge. Dodrecht-Boston-London: Kluwer Academic Publishers.

Additional Readings:

• Zahavi, D. Husserl’s Phenomenology, Stanford Univ. Press, pp. 14-26.

• A fragment on categorial intuition by Jan Gronwald.

In relation to the first chapter of “Mathematical Intuition” by Richard Tiszen, we discussed some notions of Husserl’s phenomenology that pertain to the categorial intuition.

Derek So introduced us to some basic concepts of Husserl’s phenomenology. We focused on intentionality, synthetic and eidetic intuition. Then briefly discussed the different conceptions of intuition in more contemporary phenomenology.

Main Readings:

• Tieszen, R. Mathematical Intuition: Phenomenology and Mathematical Knowledge. Dodrecht-Boston-London: Kluwer Academic Publishers. SUBCHAPTER 2. OF CH. 2, “INTENTIONALITY AND INTUITION”, pp. 21-25.

We partially discussed the 1st chapter from “Mathematical Intuition” by Richard Tiszen.

Main Readings

• Tieszen, R. Mathematical Intuition: Phenomenology and Mathematical Knowledge. Dodrecht-Boston-London: Kluwer Academic Publishers.