Physicalist Philosophy of
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.
- 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
mathematical truth? http://philsci-archive.pitt.edu/archive/00005338/
- E. Nagel and J. R. Newman: Gödel's
Proof, New York Univ. Press, 1958
filozófiája a 21.század küszöbén.
Válogatott tanulmányok, Szerk. Csaba Ferenc,
Osiris, Bp. 2003
- E. Szabó László: Filozofikus
bevezetés a matematikai logikába, egyetemi előadásjegyzet, ELTE
- J. N.
Crossley, et al., What is
Mathematical Logic?, Dover Publications, New York, 1990.
- A. G. Hamilton: Logic
Cambridge Univ. Press, 1988
Gödel: On formally undecidable propositions of principia
mathematica and related systems,
Oliver and Boyd, Edinburgh,
- oral exam from the material of the lectures
- PhD students, in addition, must write a 10 page
course paper in English, arguing against
proposing in the lecture course