Azamat, (01)
Many thanks. It makes "axioms" background pretty clear and relatable to
previous experience. "Mystery of intellect" requires both neural
processing as well as ability to further process verifiable experiences
to synthesize and analyze to accept as "universal class"? (02)
Similarly "hypotheses", are these not like axioms, as we try to build
models and theories? (03)
In axioms and hypotheses, verification by some science, experiments or
observations (e.g. astrophysics) increases confidence levels of accuracy
or relevance. Is it correct? (04)
Thanks. (05)
Ravi (06)
(Dr. Ravi Sharma) Senior Enterprise Architect (07)
Vangent, Inc. Technology Excellence Center (TEC) (08)
8618 Westwood Center Drive, Suite 310, Vienna VA 22182
(o) 703-827-0638, (c) 313-204-1740 www.vangent.com (09)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Azamat
Sent: Saturday, March 01, 2008 3:51 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Search engine for the ontology (010)
Friday, February 29, 2008 11:29 PM, Ravi wrote:
''does such a powerful concept - axiom - mean a priori proposition based
on
deep insight or experience? How does the
axiomatic process germinate? What process of mind helps it?'' (011)
Ravi, (012)
Many think that axiomatic knowledge is derived by intuitive inductions
(insight, inspiration, immediate apprehension, feeling, gnosis, etc.). (013)
Others believe, by inference (analogy, entailment, corollary),
conjecture,
or synthetic thinking. (014)
Others think that axioms are among a priori knowledge and they must be
reached by manipulating innate categories, cognitive universals, or
universal ontology, brain-wired in the human mind. (015)
But some state that axiomatic, self-evident truths are discovered by
observation and experiment or experience. This is a classic view: ''When (016)
from many notions gained by experience one universal judgment about a
class
of objects is produced'', art and science come into being. (017)
The great mystery of intellect is how it translates individual
constructs
into universal classes. (018)
Knowing the mechanism of transforming sense-perceptions individual
instances, particular observations and specific notions) into general
classes (rules and laws and axioms) opens up the new world of knowledge
systems and intelligent machines. (019)
have a nice weekend,
azamat abdoullaev (020)
----- Original Message -----
From: "Sharma, Ravi" <Ravi.Sharma@xxxxxxxxxxx>
To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Friday, February 29, 2008 11:29 PM
Subject: Re: [ontolog-forum] Search engine for the ontology (021)
> Azamat
> Thanks for clarification, does such a powerful concept - axiom - mean
a
> priori proposition based on deep insight or experience? How does the
> axiomatic process germinate? What process of mind helps it?
> Thanks.
>
> Ravi
>
> (Dr. Ravi Sharma) Senior Enterprise Architect
>
> Vangent, Inc. Technology Excellence Center (TEC)
>
> 8618 Westwood Center Drive, Suite 310, Vienna VA 22182
> (o) 703-827-0638, (c) 313-204-1740 www.vangent.com
>
>
>
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Azamat
> Sent: Thursday, February 28, 2008 4:46 PM
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Search engine for the ontology
>
> On Thursday, February 28, 2008 10:01 AM, Ravi wrote:
>
> Is it not right to state that axioms have roots in metaphysics or
> philosophy and need not address reality as is in the many other
> branches
> of mathematics? What is the a priori basis of universality?
>
> This is both right and correct. All key axioms of fundamental
sciences,
> formal or empirical, have roots in ontology. The foundations of any
> valuable
> scientific theory includes apart the permanent trio, mathematical
> postulates
> and axioms, factual formulas and law statements, semantic formulas and
> rules, the ontological background in the first place.
> It might be a surprise for working mathematicians and logicians, but
all
> key
> logical predicates have been ontological predicates, such as
''exist'',
> ''is
> true'', '' is actual'', '' is false'', ''is identical with'', etc.
>
>>
>> John
>>
>> Most of what you say about physics, I agree with. One has to keep in
>> mind the accuracy to which one is trying to compute. For example Fast
>> movement of matter near black holes is covered by general theory of
>> relativity, while movement of matter in near earth or solar system is
>> covered by special relativity. But ordinary accuracy of projectiles
> and
>> planets is adequate for most purposes using Newton's laws.
>>
>> Physical Sciences admit imperfection to a degree. Bio sciences and
> human
>> behavior are inherently less accurate in the prediction and quantum
>> basis is reaching close to understand mutation and unexpected
behavior
>> of life elements.
>>
>> Social predictability and behavior gauging is beyond my
comprehension.
>> So is the admirable quest of mathematicians and axiom seekers
> necessity,
>> as a prerequisite to understanding?
>>
>> But our readers do not want to acknowledge that mathematics is as old
> as
>> the metaphysics (5000 years +) that gave us numbers and decimals and
>> zero and infinity as I have translated before in this forum. A date
of
>> 600 BC is rather recent. We seem to not go before or parallel to
> Greeks
>> just because these translations have not yet widely reached the West
> but
>> Schopenhauer and Max Muller recognized the concepts originating then
> in
>> Sanskrit.
>>
>> Is it not right to state that axioms have roots in metaphysics or
>> philosophy and need not address reality as is in the many other
> branches
>> of mathematics? What is the a priori basis of universality?
>>
>> Thanks.
>>
>> Ravi
>>
>> (Dr. Ravi Sharma) Senior Enterprise Architect
>>
>> Vangent, Inc. Technology Excellence Center (TEC)
>>
>> 8618 Westwood Center Drive, Suite 310, Vienna VA 22182
>> (o) 703-827-0638, (c) 313-204-1740 www.vangent.com
>>
>>
>> -----Original Message-----
>> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F.
>> Sowa
>> Sent: Thursday, February 28, 2008 10:01 AM
>> To: [ontolog-forum]
>> Subject: Re: [ontolog-forum] Search engine for the ontology
>>
>> Azamat,
>>
>> I'll start with a paragraph from the later part of your note because
>> it gets to the heart of our disagreement:
>>
>> AA> The whole history of science consists in attempting to found more
>> > general theoretical representations of objective laws and patterns,
>> > guiding the world.
>>
>> I have no quarrel with the opening sentence, and I would emphasize
>> the word 'attempting'. Science has always been a work in progress.
>> Every new discovery in *every* discipline raises more questions
>> than it answers.
>>
>> 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.
>>
>> 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". 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.
>>
>> JFS>> The state of physics is much worse. See _The Road to Reality_
>> >> by Roger Penrose, for a very good overview.
>>
>> AA> His understanding of reality is very narrow and specific. imho,
>> > this book hardly makes here a good argument.
>>
>> Penrose was not making an argument against foundations, he was just
>> presenting a survey of the chaotic mess that constitutes modern
>> physics. But that is at the most fundamental levels. At the levels
>> of applications, every subdiscipline from mechanics, to astrophysics,
>> to nuclear reactors, to antenna design, to particle accelerators,
>> to aerodynamics, to solid-state physics, to cryogenics, etc., etc.,
>> has a *totally* different methodology and basic toolkit of techniques
>> and assumptions. A physicist who has been working in any one of the
>> specialties I mentioned above (and many, many more) cannot move from
>> that field to any of the others without *years* of study to come up
>> to speed. (Actually, no employer would pay anybody to make such a
>> transition, since it would be cheaper to hire a new PhD who had
>> just written a dissertation in the specialty of interest.)
>>
>> AA> I have no doubts about the high scientific quality of these
people
>> > [at Cyc]... What I doubt, the approach, the way they attack such
>> > unprecedented problems as creating a common sense knowledge base.
>>
>> I also have many serious doubts, but my recommended solution is to
>> go in the *opposite* direction from your proposal: Cyc is already
>> much, much more unified than it should be. I would recommend
>> eliminating *all* axioms from the upper levels, and put them *all*
>> in the lower levels (or in a toolkit of miscellaneous techniques).
>>
>> 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. But trying to use such a design as a foundation
>> for an intelligent computer system is a recipe for *failure*. I
>> know that I can't convince you, but I suggest that you spend a few
>> years working with people like the Cyclers (or any other group of
>> implementers) and try to implement your approach. Following is
>> another epigram by Alan Perlis:
>>
>> A year spent in artificial intelligence is enough to make
>> one believe in God.
>>
>> Alan Bundy at Edinburgh has been working on mechanical theorem
>> proving and problem solving for about 40 years, and he is widely
>> recognized for his accomplishments in the field. At an AI conference
>> in 2006, we were both presenting invited talks. I was talking
>> about problems in natural language understanding, and he started
>> with automated problem solving. But we had both come to the same
>> conclusion: *all* understanding and problem solving is *always*
>> task specific. Perhaps God might have universal axioms, but
>> no mortal has anything that could be considered universal.
>>
>> For Bundy's recent publications on these and related ideas, see
>>
>> http://homepages.inf.ed.ac.uk/bundy/
>>
>> AA> Try and look at the situation from the other side. The natural
>> > and social sciences are disorganized, they are uniformly unordered,
>> > lacking single conceptual order and ontological and methodological
>> > arrangement.
>>
>> Precisely! That is how people think -- and people, with all their
>> flaws, are still much more flexible and creative thinkers than any
>> AI system ever conceived. For simple subjects like chess, computers
>> can beat the world champion. But for complex subjects, every attempt
>> to find widely applicable axioms has *failed*.
>>
>> Systems such as Mathematica are much better at manipulating formulas
>> than any human, and professional mathematicians and engineers use it
>> for manipulating the symbols. But mathematics and physics are very
>> *simple* special cases that abstract as much of the detail as
possible
>> from the incredibly complex world. The social sciences and
> commonsense
>> thinking have to deal with the complexities as they are.
>>
>> John
>>
>>
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