Re: MV Keys

jason.glumidge_at_gmail.com wrote:
> vc wrote:
> > Brian Selzer wrote:
> > [...]
> > > "x is 2" is a sentence; "y is 3" is a sentence.
> > > "x is 2 and y is 3" is also a sentence.
> >
> > You are confused. "x is 2" is not a sentence in the contex of FOL.
> > It's a predicate with a free variable which will become a sentence if
> > you substitute a constant for x.
>
> I am a bit confused too then :(
>
> "There is a person whose age is 45" is a valid sentence, and that looks
> identical to "x is 2" to me.

How come ? The former is a sentence where the free variable is bound by the existential quantifier:

E (x in X)(x = 2)

whose truth depends on whether the set/domain X contains 2.

The latter admits two reading: 'x' is a variable and 'x = 2' is an open formula in FOL in which case, by itself, it does not tell anything; x is a constant, in which case 'x=2' becomes a sentence whose truth or falsity depends on what 'x' is in a given context.

>"There is a whatever" I read implicitly
> and x is a column-name just as 'age' is (not a variable). So overall
> it reads as "There is an item whose attribute 'x' is of value '2'".
>
> That is a valid sentence even if it is a bit abstract, no?

A formula with a free variable(s) is never interpreted as having implicit existential quantification (although sometimes as having universal). Of course, one is free to use one's private language but it's hardly productive. Received on Wed Mar 08 2006 - 18:00:20 CET