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Physicalist Philosophy of Mathematics

lecture course
Monday 16:15 - 17:45   Room 221  (Múzeum krt. 4/i.)
(The course will  be given in English, except if all students speak Hungarian. The exam can be taken in English or Hungarian.)

If physicalism is true, everything is physical. In other words, everything supervenes on, or is necessitated by, the physical. Accordingly, if there are logical/mathematical facts, they must be necessitated by the physical facts of the world. In this lecture course I will sketch the first steps of a physicalist philosophy of mathematics; that is, how physicalism can account for logical and mathematical facts.

We will proceed as follows. First we will clarify what logical/mathematical facts actually are. Then, we will discuss how these facts can be accommodated in the physicalist ontology.

This might sound like immanent realism (as in Mill, Armstrong, Kitcher, or Maddy), according to which the mathematical concepts and propositions reflect some fundamental features of the physical world. Although, in my final conclusion I will claim that mathematical and logical truths do have contingent content in a sophisticated sense, and they are about some peculiar part of the physical world, I reject the idea, as this thesis is usually understood, that mathematics is about the physical world in general. In fact, I reject the idea that mathematics is about anything. In contrast, the view I am proposing here will be based on the strongest formalist approach to mathematics.

Suggested readings:
  • L. E. Szabó: Formal Systems as Physical Objects: A Physicalist Account of Mathematical Truth, International Studies in the Philosophy of Science, 17 (2003) pp. 117 – 125 (preprint: PDF)
  • L. E. Szabó: How can physics account for mathematical truth? http://philsci-archive.pitt.edu/archive/00005338/
  • 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
  • E. Szabó László: Filozofikus bevezetés a matematikai logikába, egyetemi előadásjegyzet, ELTE 2007.  [PDF]
  • J. N. Crossley, et al., What is Mathematical Logic?, Dover Publications, New York, 1990.
  • A. G. Hamilton: Logic for mathematicians, Cambridge Univ. Press, 1988
  • K. Gödel: On formally undecidable propositions of principia mathematica and related systems, Oliver and Boyd, Edinburgh, 1962.

Credit requirements
  • oral exam from the material of the lectures
  • PhD students, in addition, must write a 10 page course paper in English, arguing against  the main theses I am proposing in the lecture course



David Hilbert

Kurt Gödel

Múzeum krt. 4. i épület