Re: Columns without names
From: paul c <toledobythesea_at_oohay.ac>
Date: Wed, 20 Sep 2006 21:59:40 GMT
Message-ID: <gRiQg.3463$R63.307_at_pd7urf1no>
>
> In the mathematical context, a predicate extension is a collection of
> things in some universe for which the predicate holds. In other words,
> a predicate can be interpreted as a mathematical relation in some
> domain of interpretation, or one can say that a predicate defines a
> relation in some domain. The '<' predicate in the {1,2,3} domain
> defines the {(1,2), (1,3), (2,3)} relation which is the predicate
> extension.
>
> - a predicate
>
> It depend on your favorite set theory. In some, R = {x | not( x in x)}
> does not exist, in others it does.
> ...
Date: Wed, 20 Sep 2006 21:59:40 GMT
Message-ID: <gRiQg.3463$R63.307_at_pd7urf1no>
vc wrote:
> JOG wrote:
>> While I have your attention perhaps you might also clarify a >> distinction that I previously had: >> >> I was under the impression that - given that the extension of a >> predicate is the set of true propositions that can be formed by >> substituting a term for each of its free variables
>
> In the mathematical context, a predicate extension is a collection of
> things in some universe for which the predicate holds. In other words,
> a predicate can be interpreted as a mathematical relation in some
> domain of interpretation, or one can say that a predicate defines a
> relation in some domain. The '<' predicate in the {1,2,3} domain
> defines the {(1,2), (1,3), (2,3)} relation which is the predicate
> extension.
>
> - a predicate
>> /always/ has an extension.
>
> It depend on your favorite set theory. In some, R = {x | not( x in x)}
> does not exist, in others it does.
> ...
I'm having a hard time seeing this - in what set theory would R = {x | not( x in x)} exist?
thanks,
p
Received on Wed Sep 20 2006 - 23:59:40 CEST