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Nicolas Bourbaki and the Concept of Mathematical Structure

Leo Corry
Synthese
Vol. 92, No. 3 (Sep., 1992), pp. 315-348
Published by: Springer
Stable URL: http://www.jstor.org/stable/20117057
Page Count: 34
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Nicolas Bourbaki and the Concept of Mathematical Structure
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Abstract

In the present article two possible meanings of the term "mathematical structure" are discussed: a formal and a nonformal one. It is claimed that contemporary mathematics is structural only in the nonformal sense of the term. Bourbaki's definition of "structure" is presented as one among several attempts to elucidate the meaning of that nonformal idea by developing a formal theory which allegedly accounts for it. It is shown that Bourbaki's concept of structure was, from a mathematical point of view, a superfluous undertaking. This is done by analyzing the role played by the concept, in the first place, within Bourbaki's own mathematical output. Likewise, the interaction between Bourbaki's work and the first stages of category theory is analyzed, on the basis of both published texts and personal documents.

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