Re: Can We Quantify over Everything?
 From: george <greeneg@xxxxxxxxxx>
 Date: 22 May 2007 06:53:24 0700
On May 20, 3:15 pm, LauLuna <laureanol...@xxxxxxxx> wrote:
The aboutness paradox seems to show
that no proposition can quantify over itself.
No, it doesn't. At best it would seem to show, correctly,
that no proposition can quantify over EVERYthing.
Quantifying is, in any sense, something that it would
be hard to allege that any SINGLE proposition does AT
ALL. The way quantification WORKS in contexts where it
is REASONABLY defined entails that WHOLE REALMS
of propositions, ALL, JOINTLY, quantify over some other
realm in THE SAME manner. To speak of any one of the
individual propositions quantifying over anything at all is
basically ungrammatical.
Let me briefly expound the paradox.
Nobody here is stopping you, but the point is, your
attempt fails.
Consider
(1) all propositions not about themselves are propositions
If (1) quantifies over (1),
Well, whether 1 quantifies over 1 (or not) DEPENDS on whether
1 is (or is not) a proposition. IF IT IS, then OF COURSE it
quantifies
over itself. It is also clearly tautologous. It is NOT, however,
clearly
ABOUT itself. Nor is it clearly NOT about itself, for that matter.
That, however, simply has nothing to do with whether it is a
proposition.
then (1) is about (1) iff (1) is not about (1).
That simply does not follow.
You have 3 SEPARATE questions to answer about 1.
1. Is 1 a proposition?
2. Does 1 quantify over itself?
3. Is 1 about itself?
There is no paradox unless ALL 8
of the universes this puts us into are paradoxical.
.
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