, Volume 186, Issue 1, pp 371-386

And so on . . . : reasoning with infinite diagrams

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Abstract

This paper presents examples of infinite diagrams (as well as infinite limits of finite diagrams) whose use is more or less essential for understanding and accepting various proofs in higher mathematics. The significance of these is discussed with respect to the thesis that every proof can be formalized, and a “pre” form of this thesis that every proof can be presented in everyday statements-only form.

This paper is based in part on a lecture delivered to the Workshop on Diagrams in Mathematics, Paris, October 9, 2008. Slides for that talk and another one on the same topic for the Logic Seminar, Stanford, February 24, 2009 are available at http://math.stanford.edu/~feferman/papers/Infinite_Diagrams.pdf. I wish to thank Jeremy Avigad, Michael Beeson, Hourya Benis, Philippe de Rouilhan, Wilfrid Hodges, and Natarajan Shankar as well as the two referees for their comments on a draft of this article. I wish also to thank Ulrik Buchholtz for preparing the LaTeX version of this article.