Re: The Difference between a Set and an Element

From: G. Frege <nomail@invalid>
Date: Wed, 17 Jan 2007 22:33:48 +0100

On 17 Jan 2007 10:49:03 -0800, "Paul Holbach"
<paulholbachDELETETHENAME@xxxxxxxxxx> wrote:

Now in a 2OL we have the principle of comprehension:
~~~~~~~~~~~~~
EFAx(Fx <-> ...x...),

where "...x..." is a formula in x.

That's the key to the proof (of course).

But it seems that if we want to allow formulas which are not finitely
expressible, we need to employ infinitary logic [...]

_If_ we want to do that. But why _should_ we want to do that?

It's not necessary for the proof.

The concept corresponding to an infinite arbitrary set would be
infinitely disjunctive, and hence not be finitely expressible.

???

F.

--

E-mail: info<at>simple-line<dot>de
.

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