| Thread Links | Date Links | ||||
|---|---|---|---|---|---|
| Thread Prev | Thread Next | Thread Index | Date Prev | Date Next | Date Index |
John,
. Thanks for your response. It gives me more to chew over.
. Further comments interspersed below, prefaced "GH> ".
Cheers Graham Horn
National Data Standards Unit
Australian Institute of Health and Welfare
================================================
Phone: 02.6244.1094
Fax: 02.6244.1199
Email: Graham.Horn@aihw.gov.au
Knowledgebase: www.aihw.gov.au/knowledgebase/
-----Original Message-----
From: John F. Sowa [mailto:sowa@bestweb.net]
Sent: Thursday, 3 January 2002 2:43
To: Horn, Graham
Cc: standard-upper-ontology@ieee.org
Subject: Re: "Abstract" and "dimensionality" - Re: SUMO axiomatization
Graham,
Your note raises many interrelated issues, which have to be sorted out in any kind of standards document.
> "Horn, Graham" wrote:
> I have had considerable problems with trying
> to tie down the nature of pure structure, theory, etc. I tried to
> apply the term "concept" to this, but was ruled out of order on the
> basis that a concept had to have been conceived by someone, and by
> implication, at a given point in time. The latest draft of
> ISO/IEC 111793 accordingly defines "Concept" as
>
> "a unit of thought constituted through abstraction based on
> characteristics common to a set of objects".
This was a hot topic in the late 19th century, when people like Peirce and Frege were trying to get rid of "psychologism" in logic. Frege was only half successful, since he continued to use words like "Gedanke" (thought) and "Urteil" (judgment). Peirce completely eliminated that terminology by using the terminology of the medieval scholastics, who were much more modern. He adopted the word "proposition" (from the Latin "propositio"), and drew a clear distinction between the proposition as content and its use in a thought, a judgment, an assertion, etc.
> I fear the same attitude may be taken to "Abstract",
> since someone had to perform the (mental) task of "drawing away" the
> pattern or structure from the original observation or thought.
Finding good terminology that is both precise, easy to remember, and free of misleading connotations is always difficult. Whitehead used the term "eternal object" for the entities in my category Abstract because they are all independent of time. However, that led many people to think that they were somehow located in a kind of Platonic heaven and had some sort of spiritual connotations.
GH> I was just following the traditional pattern of depending on etymology for elucidating word meanings. The reason for such a practice is that it follows the logical facilitation of maximising scientific rigour of analysability and repeatability.
I would like to identify all abstract entities with mathematical structures, since they are of the same nature.
GH> I like this line of approach, but am a bit concerned that it may not be selfevident to many lay people. I certainly accept the slight extrapolation that geometry is a subset of mathematics.
(That doesn't solve the problem, because then you have to face the question about what mathematical entities actually *are*. Working mathematicians don't worry about that issue, since they all accept a kind of Platonic view that such things really exist in a mathematical heaven. The mathematician Erdos was fond of saying that God had all of them written down in a big book.)
GH> I guess I'd take the point of view that there are such things as patterns, structures, order (in the entropic sense), and hence geometry and mathematics. I guess my own view runs out of definition when one tries to get to the kernels of meaning behind words like order, arrangement, system, etc. We have observed and developed a pattern of fundamentals of "logic" that allows us to develop more complex conceptual structures. To me, mathematics is a subset of logic - however one that does not restrict itself to binary options.
My solution was to adopt the term "abstract", which is less frightening to most people than "mathematical structure". However, I insisted that the choice of terminology is irrelevant to the formalism. I said that you should think of that category as having the name "A". The word "Abstract" consists of 7 meaningless letters concatenated to "A", which make it easier to remember.
GH> Yes, however many would see "ab" and "stract" as being two Latin derived word parts.
> Personally, I feel there is something in the nature of
> pure structure or pattern that can exist independently of whether it
> exists in physical reality, and also independently of whether any
> intelligent being has conceived of or observed it.
Yes, indeed. The usual term for it is mathematics.
GH> True.
> By way of explanation, I would suggest that both
> Newton's law of gravity and Kepler's laws of planetary motion are not
> precisely accurate, and so do not exist in physical reality, but are
> rather mere approximations of physical reality. Yet, I would suggest
> that they are both timeless and without location or mass
> ("zerodimensional" in the physical sense), and hence existed
> infinitely before either Newton or Kepler were born, and will continue
> to do so after all records and other traces of them have been
> obliterated.
GH> overnight I also realised that far simpler examples are the traditional geometric structures, such as a square or a sphere. No-one has ever seen real ones - only some approximations. I'm sure that the pattern of a square and a sphere existed before there were sentient beings.
And that is exactly what mathematics is.
GH> Agreed
> The problem is I don't know what term I can use to
> apply to such pure structures or patterns that one can abstract or
> conceive.
I agree that there is no word that is immediately recognizable to everybody and which is free from all misleading connotations. That is why the "official" name of my category, which I usually write as "Abstract", is really "A".
GH> I'll think about this. At least this approach fits in with the concepts of abstract and concrete nouns as defined in formal English Grammar.
> Neither does "information" cover this. One can observe
> and document the spread of information, whether be it physical, such
> as through the spread of genes, etc., or purely conceptual, such as
> with nemes, by means of, say, semaphore communication.
I once considered the word "Information" for category A, but it also had too many misleading connotations.
GH> You too, huh?
> The reason I ask this question is that there are times
> when I wish to consider these "zerodimensional" patterns
> structures.
Certainly.
> Incidentally, t have a related problem about the
> nature of "dimensionality". I wish to apply the term beyond the
> traditional physics scope of mass, length and time, into far more
> abstract areas. This is because it can be extremely useful in
> information management and information based sciences to apply to a
> far broader range of concepts. Statisticians psychologists and
> pharmacists do this when they are looking to ascertain which factors
> are relevant, and which irrelevant, for particular avenues of research
> and endeavour. The concept of "dimensionality", along with others like
> "mutual exclusivity" or "orthogonality" also come into play here, and
> can greatly facilitate conceptual design and analysis.
In my previous note, I used the term "dimension" for what the letter t happened to represent. That was another misleading use. I should have just used the word "parameter" for t.
GH> A convenience of applying the term "dimension" is that it allows the application of attributes like it allows the application of attributes like "orthogonality".
GH> Also, one can regard the focus of my interest here as conceptually extending (or further "abstracting") the paradigm of geometry to beyond the issue of shape. So, one can abstract "orthogonality" similarly to the concept of logical independence.
GH> However, I guess one could argue that all I am doing is applying a geometrical metaphor to the field of logic. Not withstanding this, I still think it has great usefulness, as allowing one to geometrically model otherwise abstract notions vastly facilitates their analysis. Other different kinds of examples are data and process modelling.
> Can anyone suggest a rigorous definition that covers
> this broader scope?
As I said, mathematics is the subject that characterizes all possible entities in category A, and every entity in category A is of the same nature as the mathematical structures.
That is why Plato posted the sign above his Academy:
ageometretos medeis eisito
(Let no one ignorant of geometry enter here.)
In the _Republic_, Plato elaborated on that idea: "The knowledge at which geometry aims is knowledge of the eternal, and not of anything perishing and transient." That is the justification for Whitehead's term "eternal object".
GH> I think this validates what I have just said about geometrical metaphors.
To avoid all those confusing connotations, I would prefer to use the term "mathematical structure", but that just adds further confusion for those people who are not mathematicians. So my only other suggestion is to use the term "Category A". That is to be distinguished from "Category P", where the letter P can be concatenated with the 7 meaningless letters "hysical".
GH> Of course, this has the same etymological problems as "Abstract".
John Sowa