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

On 2007-05-15, in sci.logic, george wrote:
On May 14, 3:13 pm, Aatu Koskensilta <aatu.koskensi...@xxxxxxxxx>
wrote:
In the ordinary sense people know very well what 'cumulative hierarchy'
means,

In their and your ignorant opinion.
If they can't explain or defend it, what good is it?

It's very easy to explain it; you'll find such explanations in any number of
textbooks. As to defending it, it's not clear what there's to defend.

what it means for a statement P to be true in V_alpha, and so on.

Rational human beings do not talk about "truth" in any of these
contexts anyhow.

Sure they do. It's a perfectly ordinary mathematical notion, and there's
nothing more dubious in talking about a set theoretic statement P being true
in V_alpha than there is in any talk about sets. Again you'll find the
details in any decent textbook.

Isn't *L*_alpha a HELL of a lot more meaningful
in this context anyhow?

There is no relevant distinction between L_alpha and V_alpha here.

You must have in mind some special form of knowledge

No, dumbass: YOU do, and not only do you have it in mind,
you claim to have it in YOUR mind -- or at least you concede that
THEY do -- I definitely recall your once being as bemused about
all this as I am, back when you when you were a smaller fish
and the group was a bigger pond.

Indeed I was once bemused. Happily, I was cured, in the course of learning a
lot of mathematics, thinking about these issues, and discussing them with
intelligent people, over the last ten years or so.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.

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