Philosophy of mathematics  a physicalist account
(Fizikalista matematikafilozófia)
lecture
course
Friday 14:00 
15:30 Room 221 (Múzeum
krt. 4/i.)
(This semester
the course will be
given in English.
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: Mathematical facts in a
physicalist ontology, Parallel Processing Letters, 22 (2012) 1240009 (12
pages), DOI: 10.1142/S0129626412400099 [preprint]
 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



