[FOM] R: R: constructivism and physics
Alasdair Urquhart
urquhart at cs.toronto.edu
Fri Feb 10 10:28:38 EST 2006
Antonino Drago commented:
> For your curiosity, there exist also examples of physical notions which can
> be defined by means of infinitesimal, but not by rigorous calculus.
> An instance is the notion of reversible process in thermodynamics: a process
> composed by states of equilibium; i.e here the state is defined by an exact
> number which moreover has to express its belonging to a series (process):
> this notion is exactly that of an infintesimal. No definition is possble in
> rigorous calculus, because either you have a process of limit, i.e a series
> of distinct approximations, or you have the final number only, not both.
I don't see why this is inexpressible in rigorous calculus. For example,
in Giovanni Gallavotti's "Statistical Mechanics: A short treatise"
(Springer 1999), the notion of a reversible system is explained on
pp. 283-284 in terms of a reversible flow, that is to say, there is
a certain volume preserving smooth map representing time reversal
defined on the phase space of the system. All of this is perfectly
rigorous and expressible using the normal concepts of classical
calculus.
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