Intellectica 2009/1, n° 51

The Mathematical Continuum. New Conceptions, New Challenges

Jean Petitot

A Transcendental View on the Continuum: Woodin’s Conditional Platonism

Abstract: One of the main difficulty concerning the nature of the continuum is to do justice, inside the set theoretical Cantorian framework, to the classical conception (from Aristotle to Thom, via Kant, Peirce, Brentano, Husserl and Weyl) according to which the continuum is a non-compositional, cohesive, primitive, and intuitive datum. This paper investigates such possibilities, from Gödel to Woodin, of modelling inside a ZFC-universe the transcendence of the intuitive continuum w.r.t. its symbolic determination.

Key words: Constructive universe, Continuum, Gödel, Forcing, Kant, Large cardinals, Ω-logic, Projective hierarchy, V = L, Woodin, 0#.