On Thu, Jul 29, 2010 at 10:55 PM, Mark Buda <her...@acm.org> wrote:

> Numbers exist not in any physical sense but in the same sense that any
> idea exists - they exist in the sense that minds exist that believe
> logical propositions about them. They exist because minds believe
> logical propositions about them. They are defined and distinguished by
> the logical propositions that minds believe about them.
> There are three worlds: the physical world of elementary particles, the
> mental world of minds, and the imaginary world of ideas. They are
> linked, somehow, by logical relationships, and the apparent flow of time
> in the mental world causes/is caused by changes in these relationships.
> I wouldn't be surprised if the "laws" of physics are changing, slowly,
> incrementally, right under our noses. In fact, I would be delighted,
> because it would explain many things.
The existence of numbers can explain the existence of the physical universe
but the converse is not true, the existence of the physical world can't
explain the existence of numbers.  Belief in the existence of numbers also
helps explain the unreasonable effectiveness of math, and the fine tuning of
the universe to support life.  I think it is a smaller leap to believe
properties of mathematical objects exist than to believe this large and
complex universe exists (when the former implies the latter).

Even small numbers are bigger than our physical universe.  There are an
infinite number of statements one could make about the number 3, some true
and some false, but more statements exist than could ever be enumerated by
any machine or mind in this universe.  Each of these properties of 3 shapes
its essence, but if some of them are not accessible or knowable to us in
this universe it implies if 3 must exist outside and beyond this universe.
 Can 3 really be considered a human invention or idea when it has never been
fully comprehended by any person?


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