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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