Date: Jan 30, 2013 4:59 PM
Author: Virgil
Subject: Re: Matheology � 203

In article 
<9acbd97c-c579-4937-b417-b19eda8b5409@n2g2000yqg.googlegroups.com>,
 WM <mueckenh@rz.fh-augsburg.de> 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
> position.

That is due to WM's perpetually confusing the name of or pointer to an 
object with the object being named or pointed to.
--