Mancosu - Philosophy of Mathematical Practice (Oxford, 2008).pdf

what structuralism achieves 367But they would have come singly, one after another, and without our being ableto perceive their common bond. (Poincaré, 1908, p.380)Each language has its own deep results and must be spoken for its ownsake, but each can also take specific results and general analogies from theother. Structuralism has aided and not eliminated such languages. Categoricalconcepts make an easy format for each one, and give uniform tools for relatingformats, so they facilitate ever new interactions in substance. Before she wentto university Emmy Noether was certified as a language teacher (Tollmien,1990, p.155).Acknowledgments. Thanks to John Mayberry for many conversations onaxiomatics and structure, and to John Cobb, Fraser MacBride, Michael Resnik,and Jamie Tappenden and students in his seminar especially Michael Docherty,for comments that have improved this paper.BibliographyAwodey, Steven(2004), ‘An answer to G. Hellman’s question: ‘‘Does category theoryprovide a framework for mathematical structuralism?’’ ’, Philosophia Mathematica, 12,54–64.Benacerraf, Paul(1965), ‘What numbers could not be’, Philosophical Review, 74,47–73.Bourbaki, N.(1939), Théorie des Ensembles, Fascicules de résultats (Paris: Hermann).Carter, Jessica (2004), ‘Ontology and mathematical practice’, Philosophia Mathematica,12, 244–267.(2005), ‘Individuation of objects: a problem for structuralism?’, Synthese, 143,291–307.Chihara,Charles(2004), A Structural Account of Mathematics (Oxford: Oxford UniversityPress).Conway, John and Smith, Derek (2003), On Quaternions and Octonians (Natick, MA:A. K. Peters).Corfield, David (2003), Towards a Philosophy of Real Mathematics (Cambridge: CambridgeUniversity Press).Cornell, Gary, Silverman, Joseph, and Stevens, Glenn (eds.) (1997), Modular Formsand Fermat’s Last Theorem (New-York: Springer-Verlag).Dedekind, Richard (1888), Was sind und was sollen die Zahlen? (Braunschweig: Vieweg).Reprinted in Essays on the Theory of Numbers (New York: Dover Reprints, 1963).Eilenberg, Samuel and Steenrod,Norman(1945), ‘Axiomatic approach to homologytheory’, Proceedings of the National Academy of Science, 31, 117–120.