Re: Are open formulae really needed?

From: reader (not_at_a.b.c.dINVALID)
Date: 02/04/05 

Date: Fri, 04 Feb 2005 20:04:35 GMT

george wrote:
> 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.
>

    Thank you for clarifying this point.

    My introduction to predicate language came via Prolog,
in which, by convention, constants are alphanumeric identifiers
that start with a lowercase letter and variables are alphanumeric
identifiers that start with an uppercase letter. Variables are assumed
to be universally quantified, and Prolog processors
typically issue a warning whenever a variable that occurs only
once in a clause is detected. 

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