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@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 - 16:59:40 CDT