2022 - 2023

2022 - 2023 (University of Siena - docenza a contratto)

           Department of Social, Political and Cognitive Sciences

• Logic and cognition - Wittgenstein on the foundations of mathematics: the course concerns Wittgenstein's Cambridge 1939 lectures on the foundations of mathematics, an ideal field for applying the more general theories that, in his post-tractarian phase, Wittgenstein developed about such crucial topics as the idea that meaning is determined by use, the transparency and epistemic power of proofs, linguistic games, and the rules that the latter involve. These topics are in turn fundamental to some recent approaches in the philosophy of language, of logic and of science.

Bibliography

• L. Wittgenstein, Lectures on the foundations of mathematics. Cambridge 1939, edited by C. Diamond, Chicago University Press, 1976 (lectures I - XVII)

• P. Frascolla, Philosophy of mathematics, in H.J. Glock and J. Hyman (ed), A companion to Wittgenstein, J. Wiley & Sons, 2016, pp. 268-288

• P. Frascolla, Wittgenstein's philosophy of mathematics, Routledge, 1994 (chapters 2, 3)

• A. Kenny, Wittgenstein, Wiley-Blackwell, 2005 (chapters 4, 8, 9)

Further optional readings

• J. Floyd, "Surveyability" in Hilbert, Wittgenstein and Turing, in Philosophies, 8, 6, 2023

• P. Frascolla, On the size of infinite sets: some Wittgensteinian themes, in L. Belotti, L. Gili, E. Moriconi and C. Marletti (ed), Essays in Honour of Mauro Mariani and Carlo Marletti, ETS, pp. 139-152

• M. Marion, Wittgenstein, finitism and the foundations of mathematics, Oxford University Press, 2008

• G. Sundholm, The general form of the operation in Wittgenstein's Tractatus, in Grazer Philosophische Studien 42, 1992