Re: Platonism
From: patty (pattyNO_at_SPAMicyberspace.net)
Date: 12/06/04
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Date: Sun, 05 Dec 2004 23:26:57 GMT
robert j. kolker wrote:
>
>
> patty wrote:
>
>>
>> I don't know if its totally accurate to say that mathematics is not
>> empirical. Once you make a construction, you subject it to tests. If
>> the tests fail, you reject the construction. What is your criteria
>> for being empirical ?
>
>
> Measurement and observation vs formal deduction. Essentially all
> mathematical proofs are tautologies. The same is not true for
> empirically true statements.
>
> It is empirically true that the washington monument is 555 +- 1 foot
> high. No logical contradiction would be entialed if it were only 500
> feet high. An empirically true statement just so happens to be true. A
> logically true statement is necessarily true.
>
> Bob Kolker
Oh, your drawing that distinction. How do you determine that it
applies? What do you do to determine that one construction is analytic
and another is synthetic? Take for example "x^n+y^n=z^n". We can
substitute integral values for x,y, z and n, and (with the with the
exception of n=2) can not find an integral solution to the equation.
Pretty soon you conjecture that "there are no such solutions". I can
examine many animal species and determine that every one i look at which
has a heart also has kidneys. Pretty soon i conjecture that "all
animals with a heart also have kidneys". What is the big difference?
Aren't you just talking about proofs that have already been tested ?
patty
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