From: Lee Corbin (lcorbin@tsoft.com)
Date: Sat Jan 18 2003 - 12:52:17 MST
"Development of Western science is based on two
great achievements: the invention of the formal
logical system (in Euclidean geometry) by the
Greek philosophers, and the discovery of the
possibility to find out causal relationships by
systematic experiment (during the Renaissance)."
-Albert Einstein
This quote precedes the dedication and table of contents of Judea
Pearl's book "Causality", an overdue tome restoring the irreplaceable
concept of causality to its rightful intellectual status, and,
evidently, suggesting a useful formal tool for statisticians.
The author obviously selected this quote because of its second
phrase about causal relationships. But what about the first phrase?
I don't think it's true!
Claim: formal logic played no part in the development of
Western science. (Einstein was mistaken.)
Lee
P.S. I have included in this post a defense of my claim, but
in case I too clearly delineate the issue along biased lines
and thus hold back good arguments, perhaps some perhaps may
wish to analyze this thesis in its absence. So don't "page down".
(This isn't just egotistical on my part, for I did last summer
on this list suffer accusations that the way I lay out arguments
is often, along these lines, manipulative and disingenuous.)
Defense of the above claim:
(page down)
I say that formal logic is to be distinguished from informal
logic as follows. Suppose that a dog returns from a romp
and finds that his master's shoes still aren't on the front
porch. It's quite possible that the dog in effect uses logic
to conclude that his master isn't home yet, by (again, in
effect) thinking "if he were home, then his shoes would be
here; as they are not, he has yet to return". This is known
as utilizing the *contrapositive*, a logical equivalent to
"p implies q" which takes the form "if not q, then not p".
Since awareness in dogs is problematical, you may wish to
replace that animal in the above argument with a small or
pre-verbal child. I think that we ought to still consider
this to be logical behavior.
Formal logic, on the other hand, arises when there is a
conscious awareness not only of the logic that is occurring,
but also of its formal aspect. On this reading, most people
(even the most intelligent) are unaware of formal logic and
never resort to it. Many highly intelligent people are even
able to solve rather abstract puzzles such as the following:
State the logical conclusion:
(1) No ducks waltz
(2) No officers ever decline to waltz
(3) All my poultry are ducks
They solve it several methods, one of which is a rapid "trial
and error" of quickly generating and testing hypotheses,
which Popper and others have elevated to the key principle
behind evolutionary epistemology (and PCR). Another is
to employ a kind of visualization similar to the manipulation
of Venn-diagrams, to get a "feel" for what is the needed
conclusion. Yet others seize at random upon pairs of sentences
to extract---if possible---simple syllogisms of the sort "if A
implies B, and B implies C, then A implies C".
(The latter method shows that by taking (3), then applying
(1), and finally comparing that result with (2), the answer
rapidly obtains.)
But logicians can cast each of (1), (2), and (3) into sentences
of the predicate calculus, which includes quantifiers "for all"
and "there exists", and solve such problems symbolically. I say
that this is what should be taken as meant by "formal logic".
Aristotle practically invented formal logic, at least in
my opinion, and yet long before Aristotle mathematicians
were solving geometry problems that required little more
than pure logic. And far before them, chiefs, shamans,
hunters, and family wranglers had also employed logic IMO,
just not formal logic.
Finally, then, a tiny bit of Western mathematics, but no
Western science should be said to be based upon formal
logic.
Lee
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