Changes of language in the development of mathematics

Philosophia Mathematica 8 (1):47-83 (2000)
Abstract The nature of changes in mathematics was discussed recently in Revolutions in Mathematics. The discussion was dominated by historical and sociological arguments. An obstacle to a philosophical analysis of this question lies in a discrepancy between our approach to formulas and to pictures. While formulas are understood as constituents of mathematical theories, pictures are viewed only as heuristic tools. Our idea is to consider the pictures contained in mathematical text, as expressions of a specific language. Thus we get formulas and pictures into one linguistic framework, and so we are able to analyse their interplay in the course of history.
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