On Nov 27, 3:54 am, Bruno Marchal <[EMAIL PROTECTED]> wrote:

>
> > Besides which, mathematics and physics are dealing with quite
> > different distinctions.  It is a 'type error' it try to reduce or
> > identity one with the other.
>
> I don't see why.

Physics deals with symmetries, forces and fields.
Mathematics deals with data types, relations and sets/categories.

The mathemtical entities are informational.  The physical properties
are geometric.  Geometric properties cannot be derived from
informational properties.



>
>
>
> > Mathematics deals with logical properties,
>
> I guess you mean "mathematical properties". Since the filure of
> logicism, we know that math is not really related to logic in any way.
> It just happens that a big part of logic appears to be a branch of
> mathemetics, among many other branches.

I would classify logic as part of applied math - logic is a
description of informational systems from the point of view of
observers inside time and space.

>
> > physics deals with spatial
> > (geometric) properties.  Although geometry is thought of as math, it
> > is actually a branch of physics,
>
> Actually I do think so. but physics, with comp, has to be the science
> of what the observer can observe, and the observer is a mathematical
> object, and observation is a mathematical object too (with comp).


>
> > since in addition to pure logical
> > axioms, all geometry involves 'extra' assumptions or axioms which are
> > actually *physical* in nature (not purely mathematical) .
>
> Here I disagree (so I agree with your preceding post where you agree
> that we agree a lot but for not always for identical reasons).
> Arithmetic too need extra (non logical) axioms, and it is a matter of
> taste (eventually) to put them in the branch of physics or math.
>
> Bruno
>

I don't think it's a matter of taste.  I think geoemtry is clearly
physics, arithmetic is clearly pure math.  See above.  Geometry is
about fields, arithmetic (in the most general sense) is about
categories/sets.


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