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Foundations and Applications: Axiomatization and Education

Published online by Cambridge University Press:  15 January 2014

F. William Lawvere
F. William Lawvere*
Affiliation:
Mathematics Department, Suny at Buffalo, 244 Mathematics Building, Buffalo, Ny 14260-2900, USA.E-mail:[email protected]
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Abstract

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.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 9 , Issue 2 , June 2003 , pp. 213 - 224
Copyright
Copyright © Association for Symbolic Logic 2003

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References

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