Re: Columns without names
Date: 19 Sep 2006 17:41:56 -0700
Message-ID: <1158712915.941408.151050_at_d34g2000cwd.googlegroups.com>
JOG wrote:
> vc wrote:
> > JOG wrote:
> > > vc wrote:
> > [...]
> > > > Is it the same thingy as the predicate
> > > > defining some set ? If yes, why not say so ?
> > >
> > > No not exactly. The intension of a set of tuples may be viewed as a
> > > predicate such as P(id, name, age) combined with constraints, but in
> > > that format it can be difficult to encode as one logical statement. So
> > > given a data collection as a whole is a hotch potch of different
> > > asserted statements, I've been consdering viewing a proposition, x, as
> > > a relationship between attributes and values, so you could say
> > > something like:
> > >
> > > S = { x: Ea Name(x, a) & Eb Age(x,b) }
> > > (E representing the existential operater 'there exists' here)
> > >
> > > but also combine it with a constraint that age must be more than 18
> > > say...
> > >
> > > S = { x: Ea [ Name(x, a) ] & Eb [ Age(x,b) & b>18 ]}
> > >
> > > Don't get me wrong, I'm just exploring this stuff. It doesn't affect
> > > the RM in any way as far as I can see, it's just offers me a
> > > mathematically pleasing way of writing the makeup of a relation down.
> >
> > So what would be an "set intension" example which is not a predicate ?
> > The above clearly does not qualify.
>
> S = { x : x = x^2)
>
> 0 and 1.
>
> But I gather your point. The reason I use a different terminology is
> because in RM the use of the term predicate, traditionally refers to an
> atomic form such as P(a,b..c) and not a compound predicate.
That is quite a piece of news. Wherefrom did you get such a notion ?
Anyway, since you sort of admit that there is no example that would demonstrate alleged difference between an intension (as used in the mathematical context) and the predicate, the question remains: why use homebrewn terminlogy for something that already has clear and familiar to everybody appelation?
>> > that would use such bizzare terminology in preference to commonly
> >
> >
> > >
> > > > The "set intension"
> > > > expression is hard, if not impossible, to find in any decent
> > > > predicate logic/math book that one might be familiar with.
> > >
> > > Quite the opposite vc. The concept of intension is one of the basic
> > > grounding blocks of set theory, and will be detailed in any beginners
> > > set theory text book in the first couple of chapters. Its a bog
> > > standard way of defining sets.
> >
> > Could you kindly supply a mathematical set theory textbook reference
> > accepted FOL language ?
>
> bizarre? formal you mean. http://mathworld.wolfram.com/Intension.html
To that, there can be many objections, like Wolfram can be many things but he is neither a logician, nor a set theorist; his book is not a standard textbook, etc. More importantly, note that he uses the bare word "intension" without any "set" qualifier and for a good reason, not every "intension" (or more traditionally predicate) has an extension (or more traditionally defines a set). In this capacity, "intension" is just a synonym of "predicate" which begs the question why bother with introducing non-traditional terminology except for trying to sound important.
You may want to check more mainstream textbooks like Enderton's, Halmos', or Jech's that treat this kind of stuff very well without resorting to esoterica like "set intension". Received on Wed Sep 20 2006 - 02:41:56 CEST