NetNews Usenet Archive 1992 #27/NN_1992_27.iso/spool/sci/logic/2054

Internet Message Format | 1992-11-16 | 2.6 KB

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From: [e-mail] (Gary Merrill)
Subject: Re: Are all crows black? => Logic as an essential subject?
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Date: Mon, 16 Nov 1992 13:41:11 GMT
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In article <[e-mail]>, [e-mail] (Vaughan R. Pratt) writes:

It's interesting to see someone who is not a "professional" specialist
in history of logic take such an interest in a topic such as syllogictic
reasoning.  I'm a bit surprised you didn't mention Lukasiewicz's book.
(perhaps you don't care for the perspective?).

|> De Morgan was the first and last mathematician to take a really serious
|> look at syllogisms.  The battle with Hamilton prompted Boole to write
|> up his thoughts on the subject of logic, and within thirty years the
|> research potential of syllogisms had died, replaced by Boolean logic as
|> interpreted by Peirce, Jevons, Schroeder, and others.  The 24
|> syllogisms continued to be taught sporadically for another century,
|> indeed my first encounter with logic was when my high school swimming
|> coach lent me his freshman logic text, which confined itself to
|> syllogisms!

Peirce, it should be pointed out, did quite a bit of work in what might
be called "inductive" syllogisms as a formalization of his inductive
logic.

|> I do not know of tight bounds for the complexity of syllogistic
|> reasoning, can someone supply these?  I would expect it to be decidable
|> in polynomial time, since it should be straightforward to eliminate
|> premises sequentially and deterministically.  Note that Carroll's forms

I would expect a great deal of similarity here to the properties of
monadic predicate logic since syllogistic is (representable as) a
sub-system of that.  Indeed, the primary weakness in syllogistic
reasoning is the inability to express dyadic (and hence more complex)
relations.  As a consequence, it is hard to do foundations of mathematics
via syllogisms since you can't seem to express arithmetic relations.

--
Gary H. Merrill  [Principal Systems Developer, C Compiler Development]
SAS Institute Inc. / SAS Campus Dr. / Cary, NC  27513 / [phone]
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