On 7/29/2010 10:25 PM, Jason Resch wrote:
On Thu, Jul 29, 2010 at 10:55 PM, Mark Buda <her...@acm.org
<mailto: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.
William S. Cooper wrote a book to show the contrary. Why should I
credence your bald assertion?
Belief in the existence of numbers also helps explain the unreasonable
effectiveness of math, and the fine tuning of the universe to support
life.
If numbers are derived from biology and physics that also explains their
effectiveness. Whether the universe if fine-tuned is very doubtful (see
Vic Stengers new book on the subject) but even if it is I don't see how
the existence of numbers explains it.
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,
Actually not on any nomological reading of "could".
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?
On the contrary, I'd say numbers and other logical constructs can be
more (but not completely) comprehended than the elements of physical
models. That's why explaining other things in terms of numbers is
attractive.
Brent
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