Re: AETHER / OR

From: Bill Hobba (bhobba_at_rubbish.net.au)
Date: 12/29/04 

Date: Wed, 29 Dec 2004 23:56:13 GMT

"shevek" <shevek4@yahoo.com> wrote in message
news:1104354811.417428.270520@f14g2000cwb.googlegroups.com...
> robert j. kolker wrote:
> > >
> > >
> > > To me mathematics represents one of the highest levels of truth
> > > possible.
> >
> > Nonsense. Mathematics is about logical inference from axioms (or
> > postulates) not about truth. Truth is a property of a proposition
> that
> > asserts a fact. The best you can say is that it is true that such and
>
> > such is a proof of a theorem.
> >
>
> Well I knew I shouldn't have mentioned that in my defense of 19th
> century physics..
>
> Anyway, what is it about mathematical statements that make them not
> worthy of "propositions that assert facts" ? You can also say it is
> true that such and such a theorem is true. For example, it is true
> that there are infinitely many prime numbers. How is this any less
> true than a statment like most of the mass in material is concentrated
> in atomic nuclei?

I have enjoyed Roberts, Bilges and your discussion on such matters. But as
far as the above is concerned the statements about prime numbers is a
statement of the if so and so is true then such and such follows ie a
statement of logical inference - specifically if the axioms of arithmetic
are true then there are infinitely many primes. However the statement the
mass in a material is concentrated in the nucleus is an observation found to
be true in innumerable cases where it has been investigated. It does not
follow that every atom than has ever existed or will ever exist has this
property - we simply observe it does. Thus its truth is conditional on not
finding such an atom - the validity of the statement concerning primes
depends entirely on the validity of logic which is usually assumed true
without farther support.

The discussion seems to be a long standing one dating back to Plato - do the
equations of physics represent reality or at least describe it (I think most
physicists accept it describes reality but I have heard some go further and
side with me in saying they are reality - but I have also heard the view
that they are simply concepts we use to bring our observations into order
and have nothing to do with reality). I believe they are reality - in fact
I believe they represent a sort of super reality that determines how the
reality we perceive operates ie it is sort of like Plato's 'shadows on the
wall'. Can I prove my position true - well no. I in fact go even further
and say that mathematics is reality - can I prove that true - well no. But
in support I offer as evidence the fact lamented by the great mathematician
Hardy that the most beautiful and seemingly totally useless of mathematics
eventually finds application. My belief accommodates this observation - I
do not know of any other explanation. But unlike a lot of crank rot you see
on this forum I will also point out I have not shown it requires
explanation - it may simply be an interesting observation not telling us
anything deeper at all.

Thanks
Bill

>
> >
> > > If you can prove a theorem to me, so that I understand it,
> > > that is more convincing than your story of an experiment that I
> have
> > > not yet duplicated. But basically I agree with you in terms of the
> > > tools and the ideas (theories).
> >
> > I can prove theorems about things that don't exist, like infinite
> sets.
> > So what? What does this have to do with the -facts- out there in the
> world?
> >
>
> They are facts out there in the world, aren't they? (theorems about
> infinite sets) Sure, they may be next to useless but there is still
> truth in them.
>
>
> > Physics is an empirical science. Mathematics is a handy hammer or
> > screwdriver that physicists use to do their science.
> >
>
> Mathematics is also an empirical science. As a simple experiment, draw
> one circle on your paper, then draw another. Note that there are now
> two circles. This type of experiment is the basis of arithmetic.
> Scientists use all such tools available to them.
>
> CHeers -
>

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