Re: Aristotles logic decidable?

From: Keith Ramsay (kramsay_at_aol.com)
Date: 03/15/05 

Date: 14 Mar 2005 22:44:54 -0800

Klaus Glashoff wrote:
[...]
|In Aristotelian logic, the terms X and Y are no classes or sets!
[...]
|"Aristotle's logic was not only misrepresented by logicians who came
|from philosophy, since they wrongly identified it with traditional
|syllogistic, but also by logicians who came from mathematics.
[...]
|He applies logic only to universal
|terms, like `man' or `animal'. \ldots{}The syllogistic of Aristotle
|is a theory neither of classes nor of predicates; it exists apart
|from other deductive systems, having its own axiomatics and its own
|problems." LUKASIEWICZ, 1957

So what's an example of a problem that belongs
to it and not to some other area? The problems
about it that people I've read have described
have never turned out to have any more content
than trying to figure out what historical figures
meant by various things they wrote. Since I haven't
made a serious study, I'm not claiming this as
evidence that that's all there is to the "problems"
of Aristotelian logic, but perhaps you'll excuse
me for wondering if it is?

|I think that this as clear as it could ever be. What Lukasiewicz
|found out is widely accepted today by the experts in the field,
however,
|has not found its way into textbooks on logic.

I don't know what "universal term" means, except
as a description of a linguistic custom, unless
it is somehow connected with a description of a
class, or a "mereological sum" (like the water
of the world, which although we now know it to be
composed of water molecules, was not always known
to be so).

I think Frege is correct to say that the meaning
of a term is what it contributes to the meaning of
a sentence containing it. Such terms as "man" have
one obvious way of being used, which is associated
with sentences of the form "{singular term} is a
man". Then there are uses that are harder to
formalize in ways familiar to use today, like
collective uses ("man is today estranged from
man"). I don't know whether those matter here!

The meaning of "...is a man" also depends
intensionally upon the term "man" (even if the set
of men is the same as the set of male featherless
bipeds, the meaning of "Fred is a man" is not
necessarily the same as "Fred is a male featherless
biped", and the difference is especially relevant
for people who happen not to know that the two sets
are the same). This could also make a difference in
the presence of modalities-- two coextensional
predicates might not be *necessarily* coextensional.

I can readily believe that Aristotle didn't have such
an analysis in mind. But that leaves open the question
of whether such an analysis works correctly. It's not
a very deep departure from a theory of predicates (say)
if to each "universal term" (whatever that means) there
is a corresponding class, and the relationships under
consideration between "universal terms" are in fact
equivalent to corresponding properties of the predicates
associated to them. Perhaps there are some "universal
terms" that don't correspond to predicates (as "is a
man" corresponds to "man"). The closest I can come to
an example is the kind of thing that is sometimes called
a mereological sum-- a mass quantity like the water of
the world, which (before the atomic theory) wasn't known
to be composed of individuals.

I agree that for historical purposes it's important
to avoid anachronisms, and not to confuse Aristotle's
thinking here with ours, but that doesn't mean we can't
analyze the relationships our way.

Keith Ramsay

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