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Logos and Máthēma

Studies in the Philosophy of Mathematics and History of Logic


Roman Murawski

The volume contains twenty essays devoted to the philosophy of mathematics and the history of logic. They have been divided into four parts: general philosophical problems of mathematics, Hilbert’s program vs. the incompleteness phenomenon, philosophy of mathematics in Poland, mathematical logic in Poland. Among considered problems are: epistemology of mathematics, the meaning of the axiomatic method, existence of mathematical objects, distinction between proof and truth, undefinability of truth, Gödel’s theorems and computer science, philosophy of mathematics in Polish mathematical and logical schools, beginnings of mathematical logic in Poland, contribution of Polish logicians to recursion theory.


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Editorial Note 327


Editorial Note Mathematical Knowledge. In: I. Niiniluoto, M. Sintonen and J. Woleński (eds.), Handbook of Epistemology, pp. 571–606 (2004). Dordrecht-Boston-London: Kluwer Academic Publishers. c© 2004 Kluwer Academic Publishers. Reprinted with kind permission of Springer Science and Business Media. On the Power and Weaknesses of the Axiomatic Method – published (in Polish) under the title: O potędze i słabościach metody aksjomatycznej i ich konsekwencjach dla filozofii matematyki. In: S. Ziemiański SJ (red.), Philosophia vitam alere. pp. 455–465. Kraków: Ignatianum – WAM (2005). Translated and published with the permission of the publisher. Remarks on the Mathematical Universe – published under the title: Did Leibniz and Newton Discover or Create the Calculus?, Fundamenta Informaticae 81 (2007), 249–256. c© 2007 Polish Mathematical Society. Reprinted with kind permission of Zarząd Główny Polskiego Towarzystwa Matematycznego. Structuralism and Category Theory in the Contemporary Philosophy of Mathematics. Logique et Analyse 204 (2008), 365–373 (published as a joint paper with I. Bondecka-Krzykowska). Reprinted with kind permission of the editor of the journal Logique et Analyse. Hilbert’s Program: Incompleteness Theorems vs. Partial Realizations. In: J. Woleński (ed.), Phi- losophical Logic in Poland, pp. 103–127 (1994). Dordrecht–Boston–London: Kluwer Academic Publishers. c© 1994 Kluwer Academic Publishers. Reprinted with kind permission of Springer Science and Business Media. On the Distinction Proof-Truth in Mathematics. In: Ga¨rdenfors P. et al. (eds.), In the Scope of Logic, Methodology and Philosophy of Science, pp. 287–303 (2002). Dordrecht–Boston–London: Kluwer Academic Publishers....

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