Re: Columns without names

From: JOG <jog_at_cs.nott.ac.uk>
Date: 19 Sep 2006 18:24:32 -0700
Message-ID: <1158715472.693077.237350@e3g2000cwe.googlegroups.com>

vc wrote:
> 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 ?

Codds use of the term in his early papers.

>

> 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?

Because I believed it to be standard terminology from the set theory literature that I have encountered. I am genuinely suprised to see that you are telling me it is so esoteric and that you feel so strongly about it.

> > > > > 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
> > > that would use such bizzare terminology in preference to commonly
> > > 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.

Sure, it was the first thing an internet search threw up.

> More importantly, note that he uses
> the bare word "intension" without any "set" qualifier

Quoting the page - "intension: A definition of a set by mentioning a defining property." seems to clearly refer directly to a 'set' to me.

> reason, not every "intension" (or more traditionally predicate) has
> an extension (or more traditionally defines a set).

While correct, I do not see the relevance of this to the discussion at hand.

> 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.

As previously mentioned this was not the intention. I have no agenda and nothing to sell.

>

> 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".

I believe I first picked up the terminology originally in "Set Theory and Its Philosophy: A Critical Introduction" by Michael Potter. While I appreciate your advice on terminology, perhaps that this is a book worth reading too.

I take on board your objections of course, but a google search "set intension" will show you that the terminology is far from as obtuse as you suggest. Received on Tue Sep 19 2006 - 20:24:32 CDT