Date: Jun 3, 2013 11:01 PM
Author: ross.finlayson@gmail.com
Subject: Re: LOGIC & MATHEMATICS

On Jun 3, 3:15 pm, Shmuel (Seymour J.) Metz
<spamt...@library.lspace.org.invalid> wrote:
> In <dknqt.14105$Ju6....@newsfe22.iad>, on 06/01/2013
>    at 08:13 AM, Nam Nguyen <namducngu...@shaw.ca> said:
>

> >Agree. Mathematics is just a language,
>
> So far, so good.
>

> >a description, of physics,
>
> No, any more than English is a description of Physics. Mathematics is
> a language that is not about Physics, even if physicists find it
> useful. In fact, part of its utility is its generality.
>
> --
> Shmuel (Seymour J.) Metz, SysProg and JOAT  <http://patriot.net/~shmuel>
>
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It's so that mathematics is a tool for the sciences, and that only
what we can express in natural language is in our (or the, or a)
language of mathematics. What is beyond natural language is beyond
what we can construct as a symbolic language. (It's fair to say that
there are infinitely complex objects of the mathematical universe, in
terms of their notation in symbolic language, obviously with a natural
read-out).

Then, the point as above was that true _features_ and _effects_ in the
numbers, would be directly evidenced in physical effect, where the
objects of physics behave according to mathematical laws (as they do,
whatever they are, else there would not be causality, generally, which
there is).

Then, for the plainly logical, with geometry and mathematics and
category as to theories of geometry, numbers, and here sets: then the
total reduction and as well the implications of a reduction that is
total may well be seen as truly fundamental, for each of those and
then all else they describe. Then, the reduction or reductio may well
have that there are structural features, instead of a lack thereof, in
reducing to the origin and reducing to the universe, and necessarily
addressing the duality or generally plurality, of implication, of the
the most basic principles in symmetry and conservation: here of
theories, theoretical-theoretical.

From an axiomless system of natural deduction, here as simply logical
and as the only theory without non-logical axioms, a unique logical
and uniquely logical theory, there is the void: and all.

Then, for application, for continuum mechanics: there is an entire
field of mathematics yet to be discovered, in the polydimensional, for
the natural in the uniform, and the continuous, and the discrete. The
continuous/discrete distinction, and where it's resolved, has much
more in it, for the discovery of features in numbers, as it has been
so ignored, then as to where it's a or the primary subject of research
in mathematics of the infinitesimals: and infinity.

Regards,

Ross Finlayson