MATHEMATICAL DIAGRAMS AND THEIR FOUNDATIONS

Abstract

In the last few decades there has been a revival of interest in diagrams in
mathematics. But the revival, at least at its origin, has been motivated by adherence
to the view that the method of mathematics is the axiomatic method, and specifically
by the attempt to fit diagrams into the axiomatic method, translating particular
diagrams into statements and inference rules of a formal system. This approach does
not deal with diagrams qua diagrams, and is incapable of accounting for the role
diagrams play as means of discovery and understanding. Alternatively, this paper
purports to show that the view that the method of mathematics is the analytic method
is capable of dealing with diagrams qua diagrams, and of accounting for such role.