Notes on the First Chapter of Das Kontinuum : Intension, Extension and Arithmetism.

Notes on the First Chapter of Das Kontinuum : Intension, Extension and Arithmetism. Philosophia Scientiae, 13 (cahier 1) :155–176, 2009.

journals.openedition.org/philosophiascientiae/308?lang=en

In The Continuum, Hermann Weyl gives new bases to the notions of set and function. With them, he constructs mathematics close to physics and solves the continuum problem. Those new notions are so unusual with respect to Set Theory that they are often misunderstood.
We propose to explain the meaning of Weyl’s reform of those notions. We first make a synthesis of his main epistemological thesis, and then propose a comparative approach to stress the distance between the mathematical and logical principles of The Continuum and those of Set Theory. Our discussion will be centred on the distinction between intension and extension, and on the place Weyl gives to natural numbers for the foundations of analysis.