Date: Jan 30, 2013 4:59 PM
Subject: Re: Matheology � 203
WM <email@example.com> wrote:
> On 30 Jan., 12:53, fom <fomJ...@nyms.net> wrote:
> > On 1/30/2013 5:29 AM, WM wrote:
> > > On 30 Jan., 12:02, fom <fomJ...@nyms.net> wrote:
> > >> As for those "logical considerations," I mean that
> > >> one can develop a hierarchy of definitions that
> > >> depend on actual infinity. To say that mathematics
> > >> is "logical" is to concede to such a framework. I
> > >> do not believe that mathematics is logical at all.
> > > That is a very surprising statement. Why do you think so?
> > In his papers on algebraic logic, Paul Halmos made
> > the observation that logicians are concerned with
> > provability while mathematicians are concerned more
> > with falsifiability.
> Same is true for physicists. But I had the impression that
> mathematicians are more concerned with proving. I, as a physicist, am
> more concerned with showing counter examples.
> > It is also the exact question discussed by Aristotle
> > when speaking of the relation between definitions and
> > identity in Topics.
> > Logical identity, in the modern parlance, is ontological
> > "self-identity" arising from a combination of Russell's
> > description theory and Wittgenstein's rejection of
> > Leibniz' principle of identity of indiscernibles.
> Well in mathematics we can ask whether in a = a the right a can be the
> same as the left a, because both can be distinguished by their
That is due to WM's perpetually confusing the name of or pointer to an
object with the object being named or pointed to.