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History of logic
From Frege to Gödel

2017 Fall semester
Tue 14:00 -- 15:30
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


Classical first-order logic, elements of set theory


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


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.
 Students are expected to give one presentation during the semester. Above the quality of the presentation, the mark will be influenced by your activity at the classes, too.
19th September
26th September
10th October
17th October
        Peano (by Lars Stepan Laichter)
        Dedekind (by  Luis Murillo)
24th October
        Burali-Forti (by Zalán Molnár)
        Cantor (by Áron Dombrovszki)     Note:  The definition of the sequence of alephs on p. 3
                                                                                is wrong (taken from Wikipedia.). On pp. 8-9
                                                                                 you find the correct one.
7th November
        Frege's deduction of the paradox (by András Máté)
14th November
        Quine on Frege's way out (by László Mátyás)
        Zermelo's first proof of the well-ordering theorem (by Zalán Molnár)
 21st November
        Zermelo's second proof (by Luis Murillo)
        Fraenkel's proof of the independence of the axiom of choice (by Áron Dombrovszki)