History of logic From Frege to Gödel
2017 Fall semester Tue 14:00 -- 15:30 i/226 First class: 19th September The
period covered in this lecture is rather short but it is a golden age
of logic: full of original ideas and great discoveries. The title
refers to the excellent collection of source texts by Jean van
Heijenoort. We will study some of the most important papers in this
collection
(plus the papers of Ramsey and Tarski below on the list of readings) -
some of them will be a topic of my lectures, others will be presented
by students Prerequisites: Classical first-order logic, elements of set theory
Topics:
1. Frege's logical achievements
2. Paradoxes in set theory
3. Well-ordering and the axiom of choice 4. Type-theoretical logic as a way out from the paradoxes 5. The Löweinheim-Skolem theorem
6. Intuitionism and formalism 7. The incompleteness of arithmetic 8. The undefinability of truth Literature: Heijenoort, J. van(ed.), From Frege to Gödel. A Source Book in Mathematical_Logic 1879-1931 Gabbay-Woods(eds.), Handbook of the History of Logic Vol. 4. The Rise of Modern Logic from Leibniz to Frege. Elsevier, 2004 Vol. 5. Logic from Russell to Church. Elsevier, 2009 Tarski, A., 'The concept of truth in formalized languages', in: A. Tarski, Logic, semantics, metamathematics. Papers from 1923 to 1938 . Clarendon Press, 1986. Ramsey, F.P., 'The Foundations of Mathematics',, in: F.P. Ramsey (ed. D.H. Mellor) Foundations. Essays in Philosophy, Logic, Mathematics and Economics. Routledge & Kegan Paul, 1978. |