Re: Can We Quantify over Everything?

On May 22, 7:28 pm, george <gree...@xxxxxxxxxx> wrote:
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 seem to think that (1) is a proposition, since you consider it
tautologous and hence (I assume) true. You might then only object that
I have not clearly defined what 'being about' is.

I achieve this in a reasonable way (IMHO) later in my post and the
paradoxes is reproduced.

As for your opinion that no single proposition can really quantify,
well I don't understand your point. I would say that:

'all horses are mammals'

does quantify by itself.

For all I know Aristotle would say it quantifies universally. Excuse
me if I misunderstand you.

And finally, the only principled way I can figure out to escape the
paradox is that no proposition can quantify over itself even if single
propositions can quantify. That's why I said that the paradox suggests
it.

Regards



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