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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References found in this work BETA
Wolfgang Stegmüller (1979). The Structuralist View of Theories: A Possible Analogue of the Bourbaki Programme in Physical Science. Springer-Verlag.
Michael D. Resnik (1981). Mathematics as a Science of Patterns: Ontology and Reference. Noûs 15 (4):529-550.
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Citations of this work BETA
Till Düppe & E. Roy Weintraub (2014). Siting the New Economic Science: The Cowles Commission's Activity Analysis Conference of June 1949. Science in Context 27 (3):453-483.
Jean-Pierre Marquis (1995). Category Theory and the Foundations of Mathematics: Philosophical Excavations. Synthese 103 (3):421 - 447.
E. Roy Weintraub & Philip Mirowski (1994). The Pure and the Applied: Bourbakism Comes to Mathematical Economics. Science in Context 7 (2).
A. R. D. Mathias (2001). The Strength of Mac Lane Set Theory. Annals of Pure and Applied Logic 110 (1-3):107-234.
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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