Foundations and applications: axiomatization and education
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.
Permanent link to this document: http://projecteuclid.org/euclid.bsl/1052669290
Mathematical Reviews number (MathSciNet): MR1988967
Digital Object Identifier: doi:10.2178/bsl/1052669290
Zentralblatt MATH identifier: 02133245