On 8/8/2011 9:16 PM, Jason Resch wrote:
On Mon, Aug 8, 2011 at 1:56 PM, benjayk
I am getting a bit tired of labouring this point, but honestly
is postulating something that seems nonsensical to me. Why on
earth would I
believe in the truth of something that *can never be known in any way*
(namely, that arithmetics is true without / prior to consciousness)?
Do you think that the 10^10^100th digit of Pi has a certain value even
though we can never know what it is and no one has ever or will ever
(in this universe at least) be conscious of it? If I assert the digit
happens to be 8, would you agree that my assertion must be either true
or false? If so, where does this truth exist?
Note that one cannot say it has an indefinite or value, or that its
value is inconsequential because that level of precision will never
make a difference in any equation we work with. Euler's identity:
e^(Pi * i) + 1 = 0, would be false without each of the infinite digits
of Pi having a definite and certain value. These values that are
unknown to use, but nonetheless must be there.
Mathematical existence isn't a matter of being "there", it's a matter of
satisfying, making true, a certain proposition. So why does the
putative digit of pi have the value it does, because it satisfies
certain propositions which we infer from other propositions we are
pleased to hold hypothetically true as axioms. Existence in the usual
sense never enters into it.
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