Paradoxes and vicious circles in logic
BMA-LOTD-333, BBN-FIL-300, BMI-LOTD-333E, BMA-FILD-401
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.
Literature: 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 Presentations:
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