From: Mike Lorrey (mlorrey@yahoo.com)
Date: Sun Jan 19 2003 - 19:21:00 MST
--- Lee Corbin <lcorbin@tsoft.com> wrote:
> "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.)
No, you were mistaken. Logic originated with the Greek philosophers,
though, as with any early development, there were errors made that took
time to root out. Today we have entire taxonomies of logical errors
that have taken time to identify and classify.
>
> 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".
The dog may simply determine only that the master is not present,
making no determinations about whether he had returned (and then left)
or not.
> 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.
On the contrary, dog awareness is rather interestingly higher than most
people expect. A friend of mine has a rather smart dog. Last Easter,
when the kids' easter eggs were filled with candy and hidden in the
yard, and the family was in the kitchen (where my friend has a monitor
for the security camera that scans across his yard), the dog was
observed coming to the kitchen door every minute to make sure that
everybody was still in the kitchen. He would then go out in the yard
and sniff out a hidden easter egg and raid its contents, only to return
to the porch to determine that everybody was still in the kitchen and
his poaching had not raised any alarm.
>
> 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".
Syllogisms are useful, but only if one takes into consideration all
significant variables. You did not in the above example, which is why
it's conclusion is nonsensical. Therefore, your alleged disproof fails
to demonstrate logic of its own.
>
> (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.
On the contrary, since all real science is based on mathematics, your
conclusion fails.
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