Re: Skolem's Paradox and why is math the way it is?

From: KRamsay (kramsay_at_aol.com)
Date: 10/02/04 

Date: 02 Oct 2004 06:48:56 GMT

In article <39d6e584.0409300712.3dfef8c@posting.google.com>,
troubled6man@yahoo.com (J.E.) writes:
[...]
|The axioms don't put anything into a line, the whole point is that the
|axioms don't generate ALL the points on the line, only a countable
|number of them. Consistently one can add more axioms to have more
|numbers on the line, that's what the diagonal arguement says, but if
|one doesn't add more axioms, then you only have a countable number of
|points that the original ZF(C) axioms talk about directly. And sadly,
|even after adding more axioms you still only have a countable number.
|
|> Are second order logic and "countable" models of the "uncountable" not
|> slippery slopes? (They are.)
|
|I don't see how it is a slippery slope to be clear what you are
|tlaking about and what you are not.

Then avoid such unclarities as "set that the ZFC axioms talk
about". If you actually plan to go anywhere with this, it'll be
really important not to use phrases like that without defining
what you mean by it.

It's not a phrase that is ordinarily used. I can come up with
various things that you *might* mean by it; I just don't know
which you have in mind, if you actually have a specific one
in mind after all.

Keith Ramsay

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