Azamat (01)
Yes
As you say, observation, experiment and reasoning, induction and
deduction I also concur that any connection with validation or
verification, are pillars for accuracy of any scientific theory?
Thanks. (02)
Ravi (03)
(Dr. Ravi Sharma) Senior Enterprise Architect (04)
Vangent, Inc. Technology Excellence Center (TEC) (05)
8618 Westwood Center Drive, Suite 310, Vienna VA 22182
(o) 703-827-0638, (c) 313-204-1740 www.vangent.com (06)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Azamat
Sent: Friday, February 29, 2008 5:41 AM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Search engine for the ontology (07)
----- Original Message -----
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Thursday, February 28, 2008 5:00 PM
Subject: Re: [ontolog-forum] Search engine for the ontology (08)
> AA> The universality of mathematics had been accepted since Euclid
> > and Nicomachus, who put quantity with its key species, multitude
> > and magnitude, as its subject matter.
>
> The *idea* of universality would go back farther, at least
> to Pythagoras. But he spent many years studying in Egypt and
> later in Babylon. There is no clear record of what any of
> those mathematicians believed, not even Pythagoras. But in any
> case, the idea of universality is a *goal* that has *never*
> been achieved in any closed, finished accomplishment. (09)
That's correct. Such nontrivial ideas, the world has a mathematical
structure, ''all is number'' and everything can be reduced to numerical
relationships, come from his school. The reason why i put forward Euclid
is
rather simple: the axiomatic paradigm was first established by his
geometry.
The axiomatic method suggests that a genuine scientific theory is a body
of
original constructs: meaningful concepts and fundamental statements
(axioms, definitions, rules, laws). The meanings of other concepts are
defined from the primitive ones as well as the truths of subordinate
statements are deducted from a fundamental set of axiomatic truths. (010)
> AA> While Descartes, Whitehead, Russell extended the mathematical
> > universe by introducing order and relation. Its universality
> > implies a single axiomatic foundation regardless your practicing
> > mathematicians disregarding the mathematical foundation.
>
> That is the fundamental flaw in the argument. Mathematics does
> not have and never has had anything that could remotely resemble
> "a single axiomatic foundation". (011)
It had, remember logicism, which can be replaced by ontologism, covering
the
axiomatic set theory and the category theory. (012)
That was a goal that had been
> proposed by Hilbert and pursued vigorously during the early
> 20th century. But it had been criticized by many professional
> mathematicians, even before Goedel. Afterwards, the goal seems
> hopeless -- and *useless* even if it were possible.
>
> Practicing mathematicians -- people who actually solve problems
> that other people pay somebody to solve -- dismiss the study
> of foundations as *irrelevant*. For any given problem, they
> *never* start from axioms. Instead, they have a large toolkit
> of methods and techniques, which is constantly being enlarged
> by new methods all the time. For any particular problem, they
> start with informal intuitions, and only *after* they have found
> a solution do they state it in a closed form with a small set
> of problem-specific axioms. The axioms always come at the *end*,
> not the beginning of any mathematical research. And they are
> *always* problem specific, not universal. (013)
The axiomatic system basing on basic concepts and axioms and deduction,
in
no way excludes induction. Induction, either as an intuitive
generalization
ofyour experiences or an inference from experimental data, is the
initial
source of axioms in empirical sciences and theoretical sciences as
ontology. (014)
All great scientific minds followed Euclid' axiomatic approach trying to (015)
establish a singel foundation in their field of knowledge. Leaving its
validity, take logicism, promoted by Frege, Russell and Whitehead, that
all
of mathematics, its key principles, can be derived from the logical
principles. (016)
Extend a bit this approach and you may come to a more ground-breaking
statement, all of science, its basic principles, postulates and
assumptions,
can be derived from the ontological principles.
>
> JFS>> The state of physics is much worse. See _The Road to Reality_
> >> by Roger Penrose, for a very good overview.
>
> AA> Here you need a great conceptual design, uniform ontological
> > design, single conceptual framing, a consistent and comprehensive
> > top ontology.
>
> Such an exercise would be worth writing a book, and I congratulate
> you on doing so. (017)
Thanks. It has citing of your works, and could be interesting reading
for
you. Also for all who are interested in objective, i hope, analysis of
the
SUO ontologies and the semantic web foundations. It also proposes how to (018)
construct N-relational ontology, natural language ontology model, and
how we
can build the Digital Aristotle, or the Virtual Aristotle Machine (VAM). (019)
> But we had both come to the same conclusion: *all* understanding and
> problem solving is *always* task specific. (020)
Only at the initial stage, it is case-specific. At the final stage, you
come
to generalizations. How the scientific method works: stating a problem,
collecting of data, formulating a hypothesis or law or rule, testing it
by
deductions, proving a consistency with other hypotheses, establishing a
theory as a deductive-hypothetical system. Scientific understanding is
not
only accurate and exact but systematic also. Intelligence implies
general
knowingness. (021)
Real science, not immature practical quasi-sciences, as politics,
economics,
jurisprudence, is the sum of universal knowledge organized as the
material
axiomatic system. Note the difference, not as the formal axiomatic
syntactic
system with inherent inconsistency and incompleteness, but as the
material
axiomatic semantic system. (022)
> 'I am just opposed to the idea that there must be exactly one or
exactly
> two foundations or exactly N foundations. (023)
Right. Actually they are four. Any scientific theory (ST) involves
several
foundations:
1. the factual laws and hypotheses (F);
2. the logical assumptions and principles (L);
3. he mathematical postulates and laws (M);
4. the semantic rules and formulas (S).
But there is always one and single background: ontological classes and
axioms (O). Or, the structure of science founds on a single ontological
foundation and four conceptual pillars, as in the formula:
ST = {O; F, L, M, S} .
The science means knowledge and certainty, not opinion and judgment. Its (024)
principles are facts, definitions, axioms, hypotheses and unifying
models
and theories. It's object is not the measurable and sensible but the
substantial and necessary, the abstract and universal, the universal
laws of
reality. To reach this high aim, the science is using three techniques:
observation, experiment and reasoning, induction and deduction.
An enterprise not corresponding to the standard axiomatic structure of a (025)
scientific theory, as practical sciences of ethics, politics, economics, (026)
history, etc., is not strictly scientific. (027)
azamat abdoullaev
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