Bulletin of Symbolic Logic

Foundations and applications: axiomatization and education

F. William Lawvere

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Foundations and Applications depend ultimately for their existence on each other. The main links between them are education and the axiomatic method. Those links can be strengthened with the help of a categorical method which was concentrated forty years ago by Cartier, Grothendieck, Isbell, Kan, and Yoneda. I extended that method to extract some essential features of the category of categories in 1965, and I apply it here in section 3 to sketch a similar foundation within the smooth categories which provide the setting for the mathematics of change. The possibility that other methods may be needed to clarify a contradiction introduced by Cantor, now embedded in mathematical practice, is discussed in section 5.

Article information

Bull. Symbolic Logic Volume 09, Issue 2 (2003), 213-224.

First available in Project Euclid: 11 May 2003

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Lawvere, F. William. Foundations and applications: axiomatization and education. Bull. Symbolic Logic 09 (2003), no. 2, 213--224. doi:10.2178/bsl/1052669290. http://projecteuclid.org/euclid.bsl/1052669290.

Export citation