Re: Galileo's Paradox

In article <457c12f6@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

David Marcus wrote:
Tony Orlow wrote:

Well, I have been through much of that regarding such specific language
approaches as the T-riffic digital numbers, but that's not necessary for
this purpose. It suffices to say that, if a statement is proved true for
all n greater than some finite k, that that also includes any postulated
infinite values of n, since they are greater than any finite k. I don't
need to construct these numbers. Consider them axiomatically declared.

Then list the axioms for them.


(sigh)

infinite(x) <-> A yeR x>y

This may serve in some sense as a definition, but does not imply that
any such x exists, so it is totally unsatisfactory as an axiom declaring
or requiring such x's existence.

One can equally well say

"x is Santa Claus if and only if ...", but no matter how one fills in
that blank, it doesn't mean any Santa exists.
.

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