Séminaire PHILMATH (IHPST, SND)
Lundi 16 mars 2015, Institut d’Histoire et de Philosophie des Sciences et des Techniques : 13, rue du Four, 75006 PARIS, Salle de conférence, 18 heures – 20 heures (6:00 pm – 8:00 pm).
Charles Parsons (Harvard University)
The talk will revisit two conceptions of intuition that occur in earlier writings of mine, particularly my 2008 book Mathematical Thought and its Objects. The first, more widespread in philosophical literature, might be called « rational intuition. » It is not intrinsically spatio-temporal. Gödel is its main proponent in philosophy of mathematics. Some remarks will be made about the appearance of this conception in general epistemological literature, where the focus is on the use of « intuitions » in philosophy.
The second is a conception of intuition in arithmetic, distantly derived from Kant’s but more closely inspired by Brouwer and especially Hilbert. A modified version will be presented, designed to meet objections by Felix Mühlhölzer. If time permits we will examine the question whether the revised conception allows intuitive knowledge of arithmetic short of exponentiation.