Re: Are open formulae really needed?

From: george (greeneg_at_cs.unc.edu)
Date: 02/01/05 

Date: 1 Feb 2005 07:45:57 -0800

LordBeotian wrote:
>
> So why the typical approach of logic textbooks
> is based on valutations and
> open formulae as theorems?

I haven't surveyed what's typical;
I only remember what was in the books I
was taught from. And from the viewpoint of
at least one of those books, open formulas are
simply a mirage. There is simply no such thing,
really. The question is arguably not so much
"are open formulae really needed" as "are existential
quantifiers really needed?". The answer to that
question turns out to be "no". Once you have eliminated
them, the only possible use you can have for a variable
(as opposed to a constant) is to identify a place where
you're going to do universal quantification. So you might
as well assume that all the variables are in fact undergoing
that (universal quantification) anyway. And that closes the
formula. Typographically, at that point, you don't need
universal quantifiers either, since ALL variables are
universally quantified by definition.

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