[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

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