🚀 go-pugleaf

Randall,

>I do not agree with Zeleny that quantification involves ontological
>commitment to the domain over which one is quantifying as a completed
>totality.  It merely involves commitment to each of the objects in the
>domain.  I'll admit that I am committed to an ontology including all
>of the quantification ranges, since there is only one, the universe,
>which is in fact an object!  But this involves taking unfair advantage
>of my NF advocacy; even from a ZFC standpoint, it can be observed that
>quantification ranges are not necessarily objects; they can be
>non-reified predicates, and they can be "referred to" using
>syntactical means.

I hope I don't have to ask for the longer reply!

But, I don't understand how using unreified predicates instead of
objects helps avoid set theoretic paradoxes. Grelling's paradox
uses only a predicate, and (unless I'm very confused) does not
require reification.

You said earlier that the REAL trick is denying Separation.
That seemed promising. Can I follow up a bit?

I can talk about everything all at once. But everything all at
once is not a completed totality. Check.

I can restrict my quantifiers, too. I suppose that denying Separation
means that there are some ways I cannot restrict them. For example,
I CAN say something like, "Everything blue is also square." May
I also say, meaningfully, "Every quantifier that has another
quantifier in its range commits its employer to abstract objects"?

(I am not at all interested, right now, in whether I can say that
TRULY, only MEANINGFULLY.)

Can I meaningfully say, "Some quantifiers have themselves in their range."?

I won't insult you by leading you down such an obvious path. You can
see better than I can where this is going.

Where do you get off? (Is the problem inherent in speaking of a "range"?
I will be surprised if it is.)

Jamie