Paradoxes and vicious circles in logic


  András Máté
2014 Spring semester
Friday 14:00-15::30
 Múzeum krt. 4/i/-107

The central topic of the course is the  Liar Paradox, i.e. the property of the sentence 'This sentence is false' that in the case the demonstrative 'this' denotes the sentence itself, we cannot assign attribute the sentence a truth value - neither the True nor the False - without running into a contradiction. The paradox was discovered probably by Eubulides of Megara in the 4. century b.C. and widely  discussed in the late antiquity and in Scholastic  logic,  but forgotten in the early modern era.  The 19th and 20th century  beholds a curious revival of the paradox. Trains of thought very similar to the Liar (and partly inspired by the Liar) lead to the paradoxes of  Naive Set theory but to important theorems in settheory and logic (Cantor, Gödel, Tarski) as well.  Till the sixties-seventies logicians kept self-reference  - as the suspected cause of the paradoxes - apart from formalized languages. But  computer science, natural language semantics and some areas within mathematics demanded some systematic and formal treatment of circularity.

We shall  study two of  such  formal treatments of circular/self -referential  phenomena: the waybreaking essay by Saul Kripke from 1975 which uses standard set  theory and a moderate generalization of Tarski's method to define truth for a series of larger and larger languages, and the book of Barwise andEtchemendy that uses Peter Aczel's theory  of Non-Well-Founded Sets  and Barwise's Situation Semantics.

The Barwise-Etchemendy-book contains many excercises. Students are  expected to solve a relevant part of them either at the classes or by homework.


Kripke, S.: Outline of a Theory of Truth - Journal of Philosophy, 72(1975), 690-716.

Barwise – Etchemendy: The liar. An essay on truth and circularity. Oxford, 1987

Barwise-Moos: Vicious Circles. On the Mathematics of Non-Wellfounded Phenomena CSLI Publications, Stanford, 1996