Brent Meeker <meeke...@dslextreme.com> writes:
> On 8/1/2010 3:42 PM, Quentin Anciaux wrote:
>
> The only problem is if numbers were a human invention... other
> humans could come with a prime number that is even and not
> 2... There would exists a biggest number, 1+1=2 could be false
> somewhere sometime (even by following the rules that makes 1+1=2
> true always)...
>
> They can and do. In modulo two arithmetic 1+1=0. You can invent all
> kinds of number systems or other logics and axiomatic systems.

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No. You can define your terms, and you can use your terms, but you can't
redefine your terms while you're using them and end up with a valid
argument. When Quentin says 1+1=2 always, he has a meaning behind those
symbols. He's talking about the idea in his mind underlying the
utterance "1+1=2" being true always. You can't take a different idea
that happens to be expressed using the same symbols and then assert that
that has any bearing on the truth of Quentin's original idea.
You could do that if he were writing a formal mathematical proof,
because then you would be explicitly bound by the same
symbol-manipulating rules he is.
So what you said above is perfectly true, but doesn't make your case
that numbers are a human invention. The symbols and words we use to talk
about numbers are a human invention. Not the numbers.
--
Mark Buda <her...@acm.org>
I get my monkeys for nothing and my chimps for free.
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