


Ferenc
Csatári

Department of Logic, Institute of Philosohy
Eötvös University, Budapest 

Az egytől
az omegáig  fejezetek a
számfogalom történetéből
(From
'1' to 'omega'  selected
topics from the history of arithmetic)

Röviden áttekintjük
a számok (számkörök) történetének egyegy fontosabb fejezetét.
Megállapítjuk, hogy egyáltalán nem triviális, mi az, amit számnak
tekintünk; a matematika mai számfogalma (és tőle nyilván nem
függetlenül hétköznapi számfogalmunk) hosszú, verítékes történeti
fejlődés eredménye.
Ezután megvizsgálhatjuk, bíre mindez valamilyen tanulsággal – s ha
igen, milyennel – a matematikai objektumok státuszával
kapcsolatos esetleges elkötelezettségeinkre nézve.


Balázs Gyenis

Department of History and Philosophy of Science University of Pittsburgh


Exact descriptions and wellposedness

When
thinking about "what is physically possible" it is a standard attitude
in philosophy of science to follow the cookbook: take your favorite
fundamental physical theory, extract the laws of nature, and claim that
all mathematical models which are compatible with these laws represent
physically possible worlds. And so we end up with Norton's Dome, Plato
machines, time traveling spacetimes and so on. Until these examples are
ruled out by a similar recipe based on a more fundamental theory we
should regard them as representing real possibilities inferred from our
best theories, or so we are told. One might argue that
following this cookbook favors mathematical possibilities too much;
models need to meet additional criteria as well in order to qualify as
representing the physically possible. The difficulty is in, of course,
finding such additional criteria. In the talk I'm planning to take a
look at a candidate (wellposedness) and construct an argument for it.
The argument is based on interpreting exact correspondence between
mathematical statedescriptions and physical states; in general we are
going to worry about what is the relationship between pieces of
mathematics and physical systems which they are supposed to describe.
This is supposed to be a general philosophy talk so I will keep the
technology at the bare minimum. Also, it is very much a work in
progress, so I'm looking forward to the discussion, both technical and
philosophical.



