Philosophia Mathematica 8 (1):47-83 (2000)

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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DOI 10.1093/philmat/8.1.47
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References found in this work BETA

Mathematical Thought From Ancient to Modern Times.M. Kline - 1978 - British Journal for the Philosophy of Science 29 (1):68-87.
Begriffsschrift.Gottlob Frege - 1967 - In Jean Van Heijenoort (ed.), From Frege to Gödel. Cambridge: Harvard University Press. pp. 1-83.
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Citations of this work BETA

Informational Realism and World 3.Donald Gillies - 2010 - Knowledge, Technology & Policy 23 (1-2):7-24.
On Classification of Scientific Revolutions.Ladislav Kvasz - 1999 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 30 (2):201-232.
Kant's Philosophy of Geometry--On the Road to a Final Assessment.L. Kvasz - 2011 - Philosophia Mathematica 19 (2):139-166.
Bayesianism and Language Change.Jon Williamson - 2003 - Journal of Logic, Language and Information 12 (1):53-97.

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