Chapter

How We Got Here

Stewart Shapiro

in Philosophy of Mathematics

Published in print October 2000 | ISBN: 9780195139303
Published online November 2003 | e-ISBN: 9780199833658 | DOI: http://dx.doi.org/10.1093/0195139305.003.0006
 How We Got Here

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This chapter sketches the historical development, within mathematics, of the idea that mathematics is the science of structure. We begin with the complex transition from geometry as the study of physical or perceived space to geometry as the study of freestanding structures. Of particular note is the debate between Poincaré and Russell, and the debate between Frege and Hilbert. Hilbert's work on geometry is the culmination of the programme to banish anything like Kantian intuition, in favour of implicit definitions. Another crucial event was Dedekind's work in arithmetic and real analysis. The Bourbaki school is also briefly investigated.

Keywords: Bourbaki; Dedekind; Frege; geometry; Hilbert; intuition; Kant; Poincaré; Russell; structure

Chapter.  19757 words. 

Subjects: Philosophy of Mathematics and Logic

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