Re: RM formalism supporting partial information
From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Fri, 16 Nov 2007 16:06:47 -0400
Message-ID: <473df7ff$0$5291$9a566e8b_at_news.aliant.net>
>>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.
Date: Fri, 16 Nov 2007 16:06:47 -0400
Message-ID: <473df7ff$0$5291$9a566e8b_at_news.aliant.net>
Marshall 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.) > > Not 100% clear if the idea can be carried out all the way, but > it's promising so far.
I agree with your sentiment; however, I have a nit to pick. Just as a relation is a set of propositions, it is also a set of tuples. There is a sort of duality involved where a tuple is to the algebra as a proposition is to the calculus. Received on Fri Nov 16 2007 - 21:06:47 CET