Monday 18:0019:30, Room 221 (Múzeum krt. 4/i)
What is logic? What
makes the rules of logic "correct"? What makes a mathematical
statement "true"? Mathematical truth vs the truth in physics.
The formalist philosophy of mathematics vs. mathematical platonism, etc.
Physicalism in general. The physicalist philosophy of mathematics.
Introduction to the first order predicate
logic: language, axioms, derivation rules, proof, etc. Interpretation
and model. Metatheory.
Examples for first order axiomatic systems: group theory, Euclidean geometry (Tarski axioms), Peano arithmetic, set theory.
Gödel's numbering. Representation of
metatheoretic sentences in the object theory. Gödel's first
incompleteness theorem (with proof). Gödel's second incompleteness
theorem (with proof).
The usual interpretation of the theorems
and their philosophical relevance. Related similar topics: halting
problem and computability, self reference and endophysics.
Criticism of the usual interpretations from a formalist/physicalist point of view.
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The lecture slides will be available in a pdf file.
Suggested readings

K.
Gödel: On formally undecidable propositions of principia
mathematica and related systems,
Oliver and Boyd, Edinburgh,
1962.

E. Nagel
and J. R. Newman: Gödel's
Proof, New York Univ. Press, 1958.

A
matematika filozófiája a 21.század küszöbén. Válogatott tanulmányok,
Szerk.
Csaba
Ferenc,
Osiris, Bp. 2003

L.
E. Szabó: Formal Systems as Physical Objects: A Physicalist Account of
Mathematical Truth, International Studies in the Philosophy of Science,
17 (2003) 117. (preprint: PDF)
 Mathematical facts in a physicalist ontology, Parallel Processing Letters, 22 (2012) 1240009 (12 pages), DOI: 10.1142/S0129626412400099 [preprint]

J. N.
Crossley, et al., What is
Mathematical Logic?, Dover Publications, New York, 1990.
 A. G. Hamilton: Logic
for
mathematicians,
Cambridge Univ. Press, 1988