David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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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Matthias Neuber (2012). Invariance, Structure, Measurement – Eino Kaila and the History of Logical Empiricism. Theoria 78 (4):358-383.
Leo Corry (1993). Kuhnian Issues, Scientific Revolutions and the History of Mathematics. Studies in History and Philosophy of Science Part A 24 (1):95-117.
E. Roy Weintraub & Philip Mirowski (1994). The Pure and the Applied: Bourbakism Comes to Mathematical Economics. Science in Context 7 (2).
David Aubin (1997). The Withering Immortality of Nicolas Bourbaki: A Cultural Connector at the Confluence of Mathematics, Structuralism, and the Oulipo in France. Science in Context 10 (2).
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