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Re: [ontolog-forum] FW: Next steps in using ontologies as standards

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Patrick Cassidy" <pat@xxxxxxxxx>
Date: Sat, 10 Jan 2009 02:06:15 -0500
Message-id: <05ca01c972f1$effcd9a0$cff68ce0$@com>


   Good example, thanks. 

   In cases like that my suggestion would be that all 3 of those concepts would be included, since the result would only increase the size of the FO, but not include anything objectionable to any of the participants (unless they disagreed with F=ma)  Of course, this specific case is actually an instance of a ‘Theory’ (incompatible with Einstein) that would have to be encoded as an assertion  inside a Theory rather than as an axiom of the FO itself.   But it is a good example, point well taken.




Patrick Cassidy



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From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Matthew West
Sent: Saturday, January 10, 2009 1:55 AM
To: '[ontolog-forum] '
Subject: Re: [ontolog-forum] FW: Next steps in using ontologies as standards


Dear PatC,


Just to pick up on this point, which I think I understand.


[PH] > By using the word "the"  here, you beg the central question: whether there is a *single* set of primitives out of which all other meanings can be formed. 

Ah so.  This is an objection I hadn’t gleaned from the earlier notes.   Interesting point.  I thought the main objection was about the finite number of primitives, not their identity.   I confess it has been an assumption of mine that, from the point of view of a “primitive” concept being indivisible into smaller primitive concepts (crudely analogous to an atom, in its role as a component of molecules), that a finite inventory of such primitive-atoms (if such exists) would be unique.  I have never seen this point raised, and it may be significant, but right now I can’t think of any way a set of indivisible primitives could be anything but unique.  Limited imagination, perhaps.

   Now I have noticed that there are mathematical objects that have very non-intuitive properties, and perhaps a mathematician can provide some examples of how a set of primitive concepts (not divisible into component primitive concepts) might be able to be formulated in more than one way.  I am genuinely curious about this suggestion.


[MW] There are two ways (at least) that one concept can be defined in terms of another: relationally, and by intersection (strictly a special sort of relational definition I suppose).


Definition by intersection works for example when you take, say, blue things, and cars, and derive the intersection blue cars. Quite straightforward.


An example of a relational definition is:  f = ma


The characteristic of this kind of definition is that of the 3 objects, any two can be taken as primitive and the third derived from them. (I recall Chris Menzel making this point recently).


This is where the problem lies for you. Any time you want to define something except by intersection, you have the option to choose your primitives (and it is questionable whether you should  not retain all as primitives anyway).




Matthew West                            

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