Nicolas Bourbaki and the concept of mathematical structure

Synthese 92 (3):315 - 348 (1992)
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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DOI 10.1007/BF00414286
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References found in this work BETA
Stewart Shapiro (1983). Mathematics and Reality. Philosophy of Science 50 (4):523-548.

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A. R. D. Mathias (2001). The Strength of Mac Lane Set Theory. Annals of Pure and Applied Logic 110 (1-3):107-234.

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