Gödel, Turing, and the Freedom of Will

1. To give an introduction to the basic concepts of formal logic and mathematics, in particular those which are essential for Gödel's incompleteness theorems.

2. To present the proof of Gödel's incompleteness theorems.

3. To give an introduction to the theory of Turing machines and the problem of computability, and to prove the halting theorem.

4. To discuss the usual interpretations of Gödel's theorems and the halting theorem, with special emphasis on the problem of self-reference and self-knowledge. In this context, we discuss the compatibilist thesis that the subjective experience of free will is due to the objective fact that the brain, even if it is as deterministic as a Turing machine, cannot predict its own future states.

Grading criteria, specific requirements:

Oral exam from the material of the lectures. Video records and the slides of the lectures will be available.

Reading:

• J. N. Crossley, et al., What is Mathematical Logic?, Dover Publications, New York, 1990.

• A. Grünbaum:  Free Will and Laws of Human Behaviour, in: New Readings in Philosophical Analysis, H. Feigl, W. Sellars and K. Lehrer (eds.), Appleton-Century-Crofts
  (1972).
•   L.  E. Szabó: Meaning, Truth, and Physics, In G. Hofer-Szabó, L. Wroński  (eds.),   Making it Formally Explicit, European Studies in Philosophy of Science 6. (Springer International Publishing, 2017) DOI 10.1007/978-3-319-55486-0_9. (Preprint: //philsci-archive.pitt.edu/14769/)

Suggested further reading:

•  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.
•     Mathematical facts in a physicalist ontology, Parallel Processing Letters, 22 (2012) 1240009 (12 pages), DOI: 10.1142/S0129626412400099 [preprint]
•     A. G. Hamilton: Logic for mathematicians, Cambridge Univ. Press, 1988
•     K. R. Popper: The Open Universe - An Argument for Indeterminism, Hutchinson, London (1988).
•  D. MacKay: Freedom of action in a mechanical universe, Cambridge University Press, Cambridge (1967).