Re: Columns without names
From: paul c <toledobythesea_at_oohay.ac>
Date: Thu, 21 Sep 2006 00:32:29 GMT
Message-ID: <x4lQg.4562$R63.2298_at_pd7urf1no>
>>> JOG wrote:
>>>> While I have your attention perhaps you might also clarify a
>>>> distinction that I previously had:
>>>>
>>>> I was under the impression that - given that the extension of a
>>>> predicate is the set of true propositions that can be formed by
>>>> substituting a term for each of its free variables
>>> In the mathematical context, a predicate extension is a collection of
>>> things in some universe for which the predicate holds. In other words,
>>> a predicate can be interpreted as a mathematical relation in some
>>> domain of interpretation, or one can say that a predicate defines a
>>> relation in some domain. The '<' predicate in the {1,2,3} domain
>>> defines the {(1,2), (1,3), (2,3)} relation which is the predicate
>>> extension.
>>>
>>> - a predicate
>>>> /always/ has an extension.
>>> It depend on your favorite set theory. In some, R = {x | not( x in x)}
>>> does not exist, in others it does.
>>> ...
Date: Thu, 21 Sep 2006 00:32:29 GMT
Message-ID: <x4lQg.4562$R63.2298_at_pd7urf1no>
vc wrote:
> paul c wrote: >> 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?
>
> NBG.
>
>> thanks,
>> p
>
thanks for that. now i'll try to figure out what NBG stands for. maybe the plonk is slowing me down. if it's obvious to everybody else, then the joke's on me.
p Received on Thu Sep 21 2006 - 02:32:29 CEST