🚀 go-pugleaf

In article <1992Nov9.153536.3892@ariel.ec.usf.edu>, mccolm@darwin.math.usf.edu. (Gregory McColm) writes:

|> "Proof theory", which is based on the idea of having some 
|> hypotheses and using rules of inference to generate 
|> conclusions, all within some artificial language, has 
|> Aristotle's syllogisms as the oldest example.  200 yrs ago, 
|> Kant said that Logic had not progressed since Aristotle, 

This is, of course, incorrect (gasp!  Kant wrong?).  A look at
the late medievals suffices to show some significant differences
to Aristotle.  Even before that there were some improvements.
Note, for instance, that the common example (also given in this
thread) of

	All men are mortal.
	Socrates is a man.
	Therefore, Socrates is mortal.

is not in fact an *Aristotlean* syllogism, but a Galenic syllogism.
(It is the presence of the *particular* term 'Socrates' that is
at issue here.)

|> and it wasn't until Boole, DeMorgan, & co., that Logic 
|> began its modern adventure:  what happened was the appearance 
|> of abstract algebra.  A lot of sci.logic is on the modern 
|> systems (eg, Peano's Predicate Calculus under Goedel's rules 
|> of inference) which are still quite Aristotilean.

The late medievals knew (and argued at some length) that Aristotle's
logic was inadequate.  (See in particular Jean Buridan's _Sophisms
on Meaning and Truth_.)  Unfortunately, although they had some quite
sophisticated ideas and some very good contributions at the semantic
level, they never developed a good notation for formalization.
-- 
Gary H. Merrill  [Principal Systems Developer, C Compiler Development]
SAS Institute Inc. / SAS Campus Dr. / Cary, NC  27513 / (919) 677-8000
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