A Wittgensteinian philosophy of mathematics
DOI:
https://doi.org/10.12775/LLP.2005.010Keywords
Wittgenstein, Frege, realism, anti-realism, formalism, mathematicsAbstract
Three theses are gleaned from Wittgenstein’s writing. First, extra-mathematical uses of mathematical expressions are not referential uses. Second, the senses of the expressions of pure mathematics are to be found in their uses outside of mathematics. Third, mathematical truth is fixed by mathematical proof. These theses are defended. The philosophy of mathematics defined by the three theses is compared with realism, nominalism and formalism.References
Frege, Gottlob, The Foundations of Arithmetic, second edition, Basil Blackwell & Mott Ltd, 1953. Translated by J. L. Austin.
Hugly, Philip, and Charles Sayward, “Quantifying Over the Reals”, Synthese 101: 53–64, 1994.
Jeffrey, Richard, Formal Logic: Its Scope and Limits, McGraw-Hill, 1967.
Massey, GeraldJ., Understanding Symbolic Logic, Harper and Row, 1970.
Mates, Benson, Elementary Logic, second edition, Oxford University Press, 1972.
Pollock, JohnL., An Introduction to Symbolic Logic, Holt, Rinehart and Winston, Inc, 1969.
Stoll, RobertR., Sets, Logic and Axiomatic Theories, W. H. Freeman and Company, 1961.
Wittgenstein, Ludwig, Tractatus Logico-Philosophicus, Routledge & Kegan Paul, 1922. Introduction by B. Russell.
Wittgenstein, Ludwig, Philosophical Investigations, Macmillian, 1953. Translated by G.E.M. Anscome and R. Rhees.
Wittgenstein, Ludwig, Remarks on the Foundations of Mathematics, Basil Blackwell, 1956. Edited by G.H. von Wright, R. Rhees, G.E.M. Anscome. Translated by G.E.M. Anscome.
Wittgenstein, Ludwig, Notebooks 1914–1916, Basil Blackwell, 1961. Edited by G.H. von Wright and G.E.M. Anscome. Translated by G.E.M. Anscome.
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