Physico-formalist philosophy of mathematics
(Fiziko-formalista
matematikafilozófia)
lecture course
Monday 16:00 - 17:30
Room 221 (Múzeum krt. 4/i.)
First
lecture: 14 September
This semester
the course will be given in English.
(The exam can be taken in English or
Hungarian.)
Codes:
FLN-350
BBN-FIL-402
BMA-FILD-402
BMA-LOTD-361
BMI-LOTD-361E
XXXN9526
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.
Records and the slides of the lectures will be available.
Credit requirements:
- oral exam from the material of the lectures
- PhD students, in addition, must write a 5-10
page critical essay (in English) in connection
with the main theses I am proposing in the
lecture course
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Records
and slides
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LÁSZLÓ E. SZABÓ
