Wednesday, January 21, 2009 8:48 PM, John wrote:
"For example, the axiom F=ma relates force, mass, and acceleration without
requiring any prior
definition of any of those three terms."
I am in accord with many your sound judgments re. the efficiency of the SW
formal languages. But your interpretation of the fundamental law of
mechanics seems not so convincing. The laws of classical mechanics hardly
ever could be formulated without its fundamental concepts, such as matter,
energy, physical body, quantity, unit, dimension, force, motion, extended
from the top foundation classes as substance, state, change, relationship,
cause, duration, space.
The second law states F = (d/dt)P, that the Change of Motion of a Body is
Propotional (Relation) to the Force (Cause) applied. It took some effort to
define motion as momentum P. No scientific laws, including all the basic
laws of mechanics, classical and quantum, could be constructed without the
firm ontological background added with the mathematical axioms and the real
semantic formulas (designation, denotation and representation rules). (01)
Azamat Abdoullaev (02)
----- Original Message -----
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Wednesday, January 21, 2009 8:48 PM
Subject: Re: [ontolog-forum] Next steps in using ontologies as standards (03)
> Your multiline expansion of my two line simplification of your
> proposal does nothing to address the issues involved:
> PC> I have not suggested creating a terminology by using words
> > as representatives of primitive concepts, and at no time have I
> > *ever* confused words or other terms with the concepts that
> > they label, nor with the logical representations of the concepts
> > that they label. I have suggested creating a common foundation
> > **ontology** that *includes* logical representations of the concepts
> > that are also represented by the Longman defining vocabulary.
> Several points:
> 1. If you have a one-to-one mapping of the Longman words to your
> concepts, you have solved nothing by changing the term 'word'
> to the term 'concept'.
> 2. The Longman definitions are hopelessly vague and frequently false.
> 3. That vagueness is not a problem for human readers because they
> use their background knowledge to compensate for the vagueness.
> But that solution is not possible for a computer system.
> 4. If you replace the Longman definitions with unambiguous formal
> statements, you will get one precise definition of each term
> and thereby lose the option of the multiple microsenses that
> a human reader can use to supplement the vagueness.
> In short, you'll take a dictionary that is useful for humans and
> replace it with a selection of underspecified concepts that are
> of no value for a computer system.
> PC> As Pat Hayes pointed out, all of his time theories can be
> > "expressed by" (Pat Hayes's phrase) axioms containing only
> > three classes, time point, time interval, and duration.
> Yes, indeed. But his axioms (or anybody else's) relate those terms
> without assuming any prior definitions. For example, the axiom F=ma
> relates force, mass, and acceleration without requiring any prior
> definition of any of those three terms.
> But as Pat H said, and I strongly agreed, many of the theories
> that use those terms (Newtonian, relativistic, quantum mechanical,
> etc.) relate them by means of different axioms that are inconsistent
> with one another. The kinds of primitives you have suggested and
> the vague definitions that accompany them are of *ZERO* value for
> helping a professional in any field write axioms.
> PC> ... I have said that a very large number of complex concepts
> > (such as, but not restricted > to, concepts defined by necessary
> > and sufficient conditions) or theories can be represented as
> > combinations of the primitive concepts.
> As I've said before, if you want to find commonalities among theories,
> go look at actual theories. The commonalities will lie in the axioms
> of those theories, not in definitions of so-called primitives.
> PC> What we don't know now, but can discover by the consortium process,
> > is just how large a group of logically consistent ontology elements
> > can be agreed on, whether they are considered "basic" or not.
> The idea of a consortium for writing definitions was tried by the
> Japanese EDR project. They spent billions of yen on that project,
> they produced a dictionary of 410,000 concepts mapped to English and
> Japanese, CSLI has a copy of it, and nobody has found any commercial
> use for it:
> As that web page says, "Japan Electronic Dictionary Research Institute,
> Ltd. disincorporated on March 31, 2002 and completed its liquidation
> in autumn, 2002." It might be useful for research, but they charge
> money for it, and WordNet is free.
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