Mathematical structuralism and its basic assumptions
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Jun 2, 2009
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Abstract
The notion of a structure is one of fundamental notions in mathematics: we speak of geometrical, topological, probabilistic, differential etc. structures. This notion is also important in the philosophical discussion concerning ontology for mathematics. In the last decades, the stance of mathematical structuralism attracts more and more attention. In this article the author discusses the motivations which lie behind mathematical structuralism and briefly present Shapiro's 'ante rem' structuralism.
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Wójtowicz, K. (2009). Mathematical structuralism and its basic assumptions. Philosophical Problems in Science (Zagadnienia Filozoficzne W Nauce), (44), 40–60. Retrieved from https://zfn.edu.pl/index.php/zfn/article/view/211
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References
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Bondecka-Krzykowska I., [2007] Matematyka w ujęciu strukturalnym, Wydawnictwa Naukowe UAM, Poznań.
Brink C., Revitzky I., [2002] “Three Dual Ontologies”, Journal of Philosophical Logic 13, 543–568.
Chihara C., [2004] A Structural Account of Mathematics, Oxford University Press, Oxford.
Descartes R., [1958] Prawidła kierowania umysłem; poszukiwanie prawdy przez światło przyrodzone rozumu, PWN, Warszawa.
Heller M., Mączka J., [2004] „Strukturalizm w filozofii matematyki”, Kwartalnik Filozoficzny XXXII (2), 5–22.
Hellman G., [1989] Mathematics without Numbers, Clarendon Press, Oxford.
Parsons C., [1990] “The Structuralist View of Mathematical Objects”, Synthese 84, 303–346; [pol. tłum.:] „Strukturalizm o obiektach matematyki”, [w:] Współczesna filozofia matematyki, [red.:] Murawski R., PWN, Warszawa 2002, 359–376
Quine W.V.O., [1998] Od bodźca do nauki, [tłum.:] Stanosz B., Alatheia, Warszawa.
Resnik M.D., [1981] “Mathematics as a Science of Patterns: Ontology”, Nous 15, 529–550.
Resnik M.D., [1996] “Structural Relativity”, Philosophia Mathematica 4, 83–99.
Resnik M.D., [1998] Mathematics as a Science of Patterns, Oxford University Press, Oxford.
Shapiro S., [1996] “Space, Number and Structure: A Tale of Two Debates”, Philosophia Mathematica 3 (4), 148–173.
Shapiro S., [1997] Philosophy of Mathematics. Structure and Ontology, Oxford University Press, New York, Oxford.