Sources of contemporary nominalism in the philososphy of mathematics
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Dec 7, 2006
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Abstract
Nominalism is one of the most important positions in the contemporary philosophy of mathematics. The goal of this article is to point out various factors that have effected the rapid development of nominalism. In particular, the figures of the Polish precursors of nominalism are presented, that is, Lesniewski, Kotarbinski and Tarski. Consequently, the article of Quine and Goodman entitled 'Steps Toward a Constructive Nominalism' is discussed. The article became the ideological declaration of nominalism and initiated reconstructionist tendencies within it. The presentation is concluded with the attempt of the modal interpretation of mathematics according to Putnam. This interpretation inspired the nominalists to enrich the existing logical apparatus with new methods and tools that are more efficient in the implementation of the strategy indicated by Quine and Godman.
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Frąckowiak–Ciesielska, A. (2006). Sources of contemporary nominalism in the philososphy of mathematics. Philosophical Problems in Science (Zagadnienia Filozoficzne W Nauce), (39), 92–114. Retrieved from https://zfn.edu.pl/index.php/zfn/article/view/298
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References
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Burdman Feferman A. and Feferman S., 2004, Alfred Tarski: Life and Logic, Cambridge University Press.
Burgess J.P. and Rosen G., 1997, A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics, Oxford.
Chihara C., 1990, Constructibility and Mathematical Existence, New York: Oxford University Press.
Davis Ch., 1975, An Investigation Concerning of Hilbert–Sierpinski Logical Form of the Axiom of Choice, Notre Dame Journal of Formal Logic XVI/2, 145–184.
Dąmbska, I., 1948, Czterdzieści lat filozofii we Lwowie, w: Pięćdziesiąt lat filozofii w Polsce, Przegląd Filozoficzny XLIV, 14–25.
Field H., 1980, Science without Numbers: A Defence of Nominalism, Basil Blackwell, Oxford. Goodman N. and Quine W.V., 1947, Steps Toward a Constructive Nominalism, The Journal of Symbolic Logic 12, 105–122.
Hellman G., 1989, Mathematics Without Numbers, Oxford: Clarendon Press.
Kotarbiński T., 1929, Elementy teorii poznania, logiki formalnej i metodologii nauk, Ossolineum, Lwów (wydanie II, Warszawa 1961).
Kotarbiński T., 1958, Wybór pism, t. II, PWN, Warszawa.
Küng G., 1967, Ontology and the Logistic Analysis of Language, Reidel, Dordrecht.
Lejewski Cz., 1958, On Implicational Definitions, Studia Logica VIII, 189–205.
Leśniewski S., 1927, O podstawach matematyki, Przegląd Filozoficzny XXX, 164–206.
Leśniewski S., 1930, O podstawach matematyki (c.d.), Przegląd Filozoficzny XXXIII, 77–105.
Leśniewski S., 1931, O podstawach matematyki (c.d.), Przegląd Filozoficzny XXXIV, 142–170.
Luschei E.C., 1962, The Logical Systems of Leśniewski, Studies in Logic and Foundations of Mathematics, North — Holland Publishing Company, Amsterdam.
Mancosu P., 2005, Harvard 1940–1941: Tarski, Carnap and Quine on a Finitistic Language of Mathematics for Science, w: History and Philosophy of Logic 26, 327–357.
Mostowski A., 1967, Tarski Alfred, w: The Encyclopedia of Philosophy VIII, ed. P. Edwards, New York, 77–81.
Murawski R., 2001, Filozofia matematyki. Zarys dziejów, Wydawnictwo Naukowe PWN, Warszawa.
Murawski R. and Woleński J., 2008, Tarski and His Polish Predecessors (on Truth), w: New Essays on Tarski and Philosophy, ed. D. Patterson, Oxford University Press, Oxford , 21–43.
Putnam H., 1967, Mathematics Without Foundations, The Journal of Philosophy 64, 5–22.
Simons P., 1982, On Understanding Lesniewski, History and Philosophy of Logic 3, 165–191.
Simons P., 1993, Nominalism in Poland, w: Polish Scientific Philosophy: The Lvov–Warsow School, Poznan Studies in the Sciences and the Humanities, vol. 28, Rodopi, Amsterdam, 207–231.
Słupecki J., 1955, S. Leśniewski’s Calculus of Names, Studia Logica III, 7–71.
Suppes P., 1988, Philosophical Implications of Tarski’s Work, Journal of Symbolic Logic 53, 80–91.
Woleński J., 1984, Reizm a ontologia Leśniewskiego, Studia Filozoficzne 5, 37–41.
Woleński J., 1986, Reism and Leśniewski’s Ontology, w: History and Philosophy of Logic 7, 167–176.
Woleński J., 1985, Filozoficzna Szkoła Lwowsko–Warszawska, PWN, Warszawa.
Woleński J., 1989, Logic and Philosophy in Lvov–Warsaw School, Kluwer Academic Publishers.
Woleński J., 2000, Czy Leśniewski był filozofem?, Filozofia Nauki 3–4, 57–68.