Hey Patrick,
>
You wrote:
> But don't these conventions lead you to statements that are undoubtely
> true or not true WITHIN the system? It seems to me that the axioms,
> rules or 'conventions' are out there somewhere in sort of a Platonic
> world of Ideas perhaps, and although you could say that the choice of
> which axiom you take from this world is rather arbitrary and indeed
> convention, but once you accept these axioms you have no choice but to
> exept the consequences...
--- Try it like this instead:
GRAHAM had said:
The possible exception that I am thinking of are mathematical proofs. Please
tell me if I am wrong (I am no mathematician), but my understanding is that
a mathematical proof is only accepted if it is irrefutable. Pythagoras's
theorem will always be true - no matter what end of the universe you exist
in.
RICK: (new answer):
Pythagoras's theorem is a 'definition' and therefore it's not quite
right to describe it as being "true" or not. For sure, A(sq) + B(sq) =
C(sq) seems to 'apply' to every right triangle no matter what end of the
universe you are in. But that's deceptive from the perspective of 'truth'.
For in reality a 'right triangle' and 'A(sq) +B(sq) = C(sq)' are merely two
different terms for the exact same thing. Saying that, "Pythagoras's
theorem will always be true - no matter what end of the universe you exist
in" is really saying nothing more than "A=A no matter what end of the
universe you exist in."
better?
rick
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