Re: Galileo's Paradox

In article <457e2364$1@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

MoeBlee wrote:
Tony Orlow wrote:
The point is, omega cannot coexist with NSA.

You just want to ignorantly say that over and over and over.

Non-standard analysis is done in classical mathematical logic and with
Z set theory (and, as far as I know, you can't do it without choice,
whether with ultrafilters or otherwise).

And Z set theory is SUBtheory of IST. Every theorem of set theory is a
theorem of IST, incuding the existence of infinite ordinals.

There is NO contradiction between the existence of a non-standard
system of numbers and the existence of omega. Omega doesn't happen to
be a member of the non-standard system, but that doesn't entail that
there is a contradiction. Look, for that matter, omega isn't a member
of the STANDARD reals.

Of course it's not a standard real. Is it an infinite number? I guess
it's not an infinite "nonstandard" number, and there are no infinite
"standard" numbers. It's a limit ordinal number. It just doesn't mean
anything to me, or satisfy any intuitions, or seem the least bit
sensible, whereas Robinson makes sense and comes to all the right
conclusions. I kind of like that. :)

Those conclusions are no more "right" than those of standard analysis,
and none of them could exist without standard set theory as a basis.
.

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