Aristotle's horse in De Morgan's harness.

From: Kenneth Doyle (nobody_at_notmail.com)
Date: 11/19/04 

Date: Fri, 19 Nov 2004 12:53:58 GMT

http://www.math.psu.edu/simpson/papers/philmath/node9.html

"... the 19th century logician Augustus DeMorgan noted that the inference
all horses are animals,
therefore, the head of a horse is the head of an animal

is beyond the reach of Aristotelean logic. Yet this same inference may be
paraphrased as 'if all horses are animals, then for all x, if x is the head
of some horse then x is the head of some animal.'"

Lacking an academic grounding in aristotlean logic, I'm guessing that in
this context, "beyond the reach" in the above quote is merely a matter of
form. Certainly, the inference seems valid but the aristotlean syllogism
has no power to express it(?). If someone out there happens to have done a
recent essay on this, I'd be interested to read it.

I'm struggling at the moment, to aquire the discipline to ignore what seems
intuitively obvious in order to learn the formal limitations of logical
systems; it's an interesting exercise.

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