Azamat, (01)
I'll start with a paragraph from the later part of your note because
it gets to the heart of our disagreement: (02)
AA> The whole history of science consists in attempting to found more
> general theoretical representations of objective laws and patterns,
> guiding the world. (03)
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. (04)
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. (05)
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. (06)
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. (07)
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. (08)
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 problemspecific axioms. The axioms always come at the *end*,
not the beginning of any mathematical research. And they are
*always* problem specific, not universal. (09)
JFS>> The state of physics is much worse. See _The Road to Reality_
>> by Roger Penrose, for a very good overview. (010)
AA> His understanding of reality is very narrow and specific. imho,
> this book hardly makes here a good argument. (011)
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 solidstate 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.) (012)
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. (013)
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). (014)
AA> Here you need a great conceptual design, uniform ontological
> design, single conceptual framing, a consistent and comprehensive
> top ontology. (015)
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: (016)
A year spent in artificial intelligence is enough to make
one believe in God. (017)
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. (018)
For Bundy's recent publications on these and related ideas, see (019)
http://homepages.inf.ed.ac.uk/bundy/ (020)
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. (021)
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*. (022)
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. (023)
John (024)
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