Is Second-Order Logic Set Theory in Sheep Clothing?

Online
Debates

Tibo will give a short presentation supporting the (in)famous Quine thesis that SOL is in reality ST, followed by a debate. The rules will be uploaded in due time.

Slides used during the presentation are available here (link now unfortunately broken).

Suggested Bibliography (They are freely accessible from your UvA student account)

  • Quine W.V.O., Philosophy of Logic (2nd Edition), Chapter 5: ‘The Scope of Logic’, Harvard University Press, 1986. [PDF accessible from the UvA Library]

  • Boolos,G.S., On Second-Order Logic, The Journal of Philosophy, Vol.72, No.16, pp. 509-527, 1975, URL=<https://www.jstor.org/stable/2025179 >. [Boolos’ paper against Quine’s Thesis]

  • Resnik M.D., Second-Order Logic Still Wild, The Journal of Philosophy, Vol.85, No.2, pp.75-87, 1988, URL=<https://www.jstor.org/stable/2026993 >. [Resnik’s response to Boolos]

  • Väänänen, Jouko, “Second-order and Higher-order Logic”, The Stanford Encyclopedia of Philosophy (Fall 2020 Edition), Edward N. Zalta (ed.), URL=https://plato.stanford.edu/archives/fall2020/entries/logic-higher-order/.

  • Van Benthem J., Doets K. (1983) Higher-Order Logic. In: Gabbay D., Guenthner F. (eds) Handbook of Philosophical Logic. Synthese Library (Studies in Epistemology, Logic, Methodology, and Philosophy of Science), vol 164. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7066-3_4