Re: Columns without names

From: vc <boston103_at_hotmail.com>
Date: 19 Sep 2006 18:46:11 -0700
Message-ID: <1158716771.116979.80420@m73g2000cwd.googlegroups.com>

JOG wrote:
> 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.

Care to provide a reference ? Even so, that is not standard mathematical usage.

>


> >

> > 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.

>

I do not have any particular feeling wrt the usage, just a bit curious as to what may cause one to use obscure jargon when simpler language is readily available.

> > > > > > 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.

I never implied you did, others may, though.

>


> >

> > 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.

That's where the problem appears to be. A philosopher's take on math, eh ? Nothing wrong with that mind you, but it might be just a bit more productive to move in a slightly different fashion -- from mastering math notions (and vocabulary) toward purportedly broder philosophical viewpoint, not vice versa.

>While

> I appreciate your advice on terminology, perhaps that this is a book
> worth reading too.

It very well may be.

>

> 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.

I just repeated your googling exercise ("set intension") and discovered, no surprise here, that none of the links is even remotely related to mathematical logic or set theory. Besides, the search produced whopping three pages which means that the term *is* obscure even in fields other than logic/set theory (I imagine philosophers or AI folks might be the culprits). Received on Tue Sep 19 2006 - 20:46:11 CDT