Re: RM formalism supporting partial information

From: Cimode <cimode_at_hotmail.com>
Date: Sat, 17 Nov 2007 14:47:43 -0800 (PST)
Message-ID: <805105c9-2019-42a3-b9fe-e171fcaba326_at_w73g2000hsf.googlegroups.com>


On 16 nov, 18:40, Marshall <marshall.spi..._at_gmail.com> wrote:
> On Nov 15, 10:13 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>
>
>
> > Marshall wrote:
> > > On Nov 14, 9:12 pm, David BL <davi..._at_iinet.net.au> wrote:
>
> > >>On Nov 15, 10:01 am, Marshall <marshall.spi..._at_gmail.com> wrote:
>
> > >>>On Nov 14, 2:21 pm, David BL <davi..._at_iinet.net.au> wrote:
>
> > >>>>On Nov 15, 1:20 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>
> > >>>>>paul c wrote:
>
> > >>>>>>David BL wrote:
> > >>>>>>...
>
> > >>>>>>>http://www.members.iinet.net.au/~davidbl/MVattributes.doc
>
> > >>>>>>>This is still a work in progress.
>
> > >>>>>>>I welcome any comments.
>
> > >>>>>By the second paragraph, the document entered into the realm of
> > >>>>>nonsense, and I stopped reading.
>
> > >>>>An attribute has a name and a domain. How is that nonsense?
>
> > >>>You didn't say an attribute *has* a name and a domain. You said
> > >>>an attribute *is* a name and a domain. So you can have two
> > >>>different attributes with the same name.
>
> > >>I said an attribute *consists* of a name and a domain. That is
> > >>compatible with saying an attribute has (and only has) a name and a
> > >>domain. I assume you're not making some philosophical point about
> > >>the sum being greater than the parts; IMO distinguishing between
> > >>"has" and "is" is splitting hairs. In natural language at that!
>
> > >>Seeing as you're likely to try to interpret mathematical structures in
> > >>terms of words like "has" and "is", I must point out that
> > >>mathematical structures do not exclusively own their "parts". For
> > >>example the point (10,15) in R^2 doesn't exclusively own the integers
> > >>10,15 (ie they can be used for other things!). Similarly an attribute
> > >>doesn't exclusively own it name or its domain. In keeping with the
> > >>spirit of mathematical formalism I didn't say that an attribute has a
> > >>domain-name - instead it has a domain. Formally that only means
> > >>there exists a mapping D from attribute x to domain D(x).
>
> > >>You cannot state that all attributes have different names. That would
> > >>be nonsensical because universal quantification is only meaningful
> > >>with respect to some defined set over which it quantifies. At the
> > >>point of definition of "attribute" there is no such set to quantify
> > >>over. I find it curious that you appear to allow a mathematical
> > >>realism philosophy to invade mathematical definitions.
>
> > >>In the document I (correctly) said nothing about unique names until
> > >>defining a relation.
>
> > > You attribute a bunch of positions here to me, but none of them
> > > are things that I actually think or things that I actually said.
>
> > While I have used the term many times in the past, and I am sure I will
> > use it many times in the future, seeing this discussion has impressed
> > upon me how unimportant "attribute" is as a concept.
>
> > The important concepts are tuples, propositions, predicates etc.
>
> For myself, I have found less and less use for the concept
> of tuple over time. I try as much as possible to do everything
> with just relations. Relations as sets-of-propositions, relations
> as predicates, cardinality-1 relations instead of tuples, etc.
> In fact I am going so far as to attempt the idea of a theory with
> relations as the only primitive. (And possibly also including
> scalars.)
Tuples are nothing but elements of a set that went through some kind of constraining process to constitute a relation as opposed to elements that are drawn from raw domains with no potential restriction applied on their acceptance as a part of the body of a specific relation. IMHO, the main purpose and/or usefulness of such construct is to establis such difference.

Hope that makes sense...

>
> Not 100% clear if the idea can be carried out all the way, but
> it's promising so far.
>
> Marshall
Received on Sat Nov 17 2007 - 23:47:43 CET

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