Re: Cantor's circular "proof" that evens = integers

Jesse F. Hughes wrote:

Phil <toob-headman@xxxxxxxxxxxxx> writes:


Notice that instead of using the entire set of axioms to determine how
many numbers exist, you used just one axiom. Since the characteristics
of the natural numbers are determined by the ENTIRE set of axioms, you
CANNOT use just ONE axiom to determine some characteristic; that is an
error of logic and reasoning.


Sorry, Phil, but this is just nonsense. If we can prove that
something follows from a single axiom, then it follows from a set of
axioms that include the single axiom.

Jesse, I'm fairly certain that it is your claim that is actually nonsense. See if this sounds correct: If axiom A LIMITS, or RESTRICTS, axiom B, then a conclusion drawn from axiom B by itself may or may not be compatible with the conclusions that can be drawn from the combination of axioms A and B.

Well, what do you think?

Phil
.

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