[hist-analytic] hazzard at first fence
Roger Bishop Jones
rbj at rbjones.com
Wed Jun 24 10:05:04 EDT 2009
I have been trying since my return from Guernsey to
get my Aristotelean models moving forward.
I found that the fifth and most interesting model
in which izzing and hazzing are integrated with
the rest, did not cleanly enough separate the
categories, so I rewrote it.
It is more complicated than any of the others
and did not succumb to the brute force proof
methods I used for them, so I returned to
Aristotle to get closer to how he did things.
Right back to the Prior Analytic, Book 1, Part 1.
And there on the very first conversion which
Aristotle "proves" hazz fell on its face.
After a while wondering why that conversion:
if no A is B then no B is A
was proving hard, and hard to prove, it dawned
on me that it was false (the most common
reason for diffulty in a proof).
Perhaps my model is wrong, but I suspect not.
It looks to me like, after doing all this
great syllogistic logic Aristotle went off to
dissect predication into the essential and
inessential parts in his Metaphysics and came
up with a notion of predication for which
syllogistic reasoning is unsound!
The trouble is that hazz is really
very asymmetric by contrast with izz.
In hazz the subject must be substantial
and the predicate must not be substantial.
So far as hazz is concerned
no A hazz B
will always be true if B is substance
but we don't want that to mean that
no B hazz A
just because B is substance do we?
I have no idea whether anyone has noticed this.
On the basis of the above account it doesn't
look like it's a defect in my model, unless
it's one which arises from a defect in my
understanding of Aristotle which is apparent
in that argument.
I don't know whether this is an isolated failure
or the tip of an iceberg, but I suspect somewhere
between the two. There must be plenty of syllogisms
normally held valid which have something of this
in them, and which will trip up once hazzing is
Either way, its an entertaining bit of payback
for messing about in models (though one *could*
have got it less formally).
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