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Re: [ontolog-forum] rant on pseudoscience

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 22 Jan 2010 09:57:35 -0500
Message-id: <4B59BCDF.6050100@xxxxxxxxxxx>
Ali and Rob,    (01)

AH> A slight aside that might be helpful is to consider scientific
 > endeavors as non-monotonic reasoning.    (02)

The application of a theory might use classical deduction, which
is monotonic.  But there is no way to derive a new theory by
deduction.  You must use the nonmonotonic operations of induction,
abduction, and revision.    (03)

JFS>> First of all, it is essential to distinguish empirical sciences
 >> from pure mathematics.  In empirical sciences, the ultimate test
 >> is agreement of predictions with observations.  Mathematics,
 >> however, is not an empirical science.    (04)

RF> Greg Chaitin might have issue with that statement.    (05)

No.  He wouldn't object to that statement.    (06)

RF> He wants us to accept a certain amount (Omega?) of maths is
 > random, admitting of no proof but observation (Chaitin:
 > "Is mathematics quasi-empirical?")    (07)

Note his term "quasi-empirical".    (08)

Before trying to prove a general theorem about a function,
mathematicians usually start by performing "quasi- experiments"
to "observe" how the function behaves on typical values.    (09)

But those so-called observations are thought-experiments,
even when the thinking is carried out by a computer.
They are not observations of the physical world.    (010)

Chaitin noted that for some perversely complex functions
general proofs are not possible, and the only way to find
out how the function behaves is to make quasi-experiments.    (011)

RF> But undoubtedly there is a difference of emphasis in mathematics.
 > You might say it is "top down", where science tries to be "bottom up".
 > Even if there is a degree of abstraction which escapes them both.    (012)

No.  That is not the crucial difference.  Mathematicians use bottom up
methods when they play around with thought experiments before forming
their generalizations.  Physicists use top-down methods when they
use deduction to make predictions from their theories.    (013)

RF> [Kuhn] p. 167
 > ... Just how special that community must be if science is to survive
 > and grow may be indicated by the very tenuousness of humanity's hold
 > on the scientific enterprise. Every civilization of which we have
 > records has possessed a technology, and art, a religion, a political
 > system, laws, and so on. In many cases those facets of civilization
 > have been as developed as our own. But only the civilizations that
 > descend from Hellenic Greece have possessed more than the most
 > rudimentary science.    (014)

I have a high regard for Kuhn's work, but that statement requires
a great deal of qualification. The Muslim world inherited the great
library at Alexandria and the great centers of learning in Damascus
and Baghdad. Until the 12th century, they were vastly more advanced
than Europe.  Just skim through any English dictionary for words
beginning with al-, such as algebra, algorithm, alchemy, alkali,
alcohol, alfalfa, alembic, almanac -- and star names such as
Aldebaran, Algol, Alioth.  They also combined Greek science with
Indian science and popularized the Hindu-Arabic numerals.    (015)

In a note yesterday, I mentioned the book _The Measure of Reality_
by Alfred Crosby, which discussed the rapid growth of European
science and technology from the 13th to the 16th centuries.
That was only indirectly inherited from the Greeks, since the
most direct line of inheritance was from Islamic Spain in the
11th and 12th centuries.  But the big question is why Europe
took off so suddenly while the rest of the world stagnated.    (016)

Crosby attributes the rapid development to the growth in
methods and precision of measurement, and I'm sure that made
an important contribution.  Crosby mentions the development
of European universities, starting with Paris and Oxford in
the late 12th century and rapidly expanding throughout major
cities in Europe during the 13th.  But he doesn't go into
any detail about the role of the universities or how they
differed from the older centers of learning.    (017)

The crucial feature of Plato's Academy and Aristotle's Lyceum
was the highly stimulating debates.  (Stylized hints of those
debates can be found in Plato's dialogs.)  The Greeks continued
the debating for a few centuries, but it gradually lost much
of the excitement of the early years.  But when the European
universities opened up, they renewed an active form of debate,
which they called "disputation".    (018)

Those debates could get very lively and even entertaining
(in Latin, of course).  As late as the 16th or 17th century,
the English Court would go to Oxford or Cambridge for the
graduation exercises.  Queen Elizabeth I even served as the
"magister" or moderator of the debate.  King James was very
fond of his hunting dogs, so one of the debates was on the
topic of whether dogs can think.  King James enjoyed it
thoroughly and rooted for the dogs.    (019)

The end of innovation comes when the powers that be feel
threatened by the debate and start burning books and imposing
censorship.  Hegel said that the best thing that ever happened
to Europe was the Protestant Reformation.  He didn't think that
the Protestant ideas were any better than the Catholic ones,
but that the debate invigorated both sides and kept them
from stagnating.    (020)

John    (021)

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