[hist-analytic] Aristotle's Metaphysics: The Izz and the Hazz

Roger Bishop Jones rbj at rbjones.com
Thu May 14 09:23:09 EDT 2009

I have spend some time cogitating on Speranza's interesting
pastiche on Aristotle's metaphysics.

There is resonance with the direction I am heading with
metaphysical positivism, and in some future message I
hope to give an account of where I stand there and what
kind of interest in Aristotle it engenders.

However, for now, some minor observations on Speranza's

When I first read of the IZZing and HAZZing distinction
it made my think of the conflation in Aristotle's notion
of predication of two things which set theory carefully
distinguishes, viz. set membership and set inclusion and
for a very short while I though the two distinctions
connected (I now see that they are pretty much orthogonal).
I played with giving an account of Aristotelean predication
in terms of both for a while.  This would have taken us
along the lines of treating Aristotlean predication using
a predicate calculus, which we are assured is common though
Speranza had no examples of this apart from the material
he supplied at the end (of which more anon).

It wasn't very clear what milage was made out of IZZing
and HAZZing, since Grice seems here to be providing duplicates
for Aristotle's use of SAID OF and IN, and Code apparently
in discussing Grice declined to use his terms and invented
a third pair for the same purpose.

I am guessing that the virtue in the exercise was not in
this colourful terminology but in some substantive analysis
which followed, and perhaps yielded the conclusions
which Speranza presented in a formal manner.
My knowledge of Aristotle is not good enough to give a
proper critique of Speranza's 31 propositions, but
some things stuck out and I shall mention them.

On Sunday 10 May 2009 00:21:22 Jlsperanza at aol.com wrote:

>I offer some symbolisation alla Grice/Code:
>1. A izz A.
>2. (A izz B & B izz C) --> A izz C.
>3. A hazz B  -> -(A izz B).
>4. A hazz B iff A hazz Some-Thing that izz B.
>5. Each  universal is a form.

>6. (A hazz B & A is a particular) -> there is a  C such that (C =/= A) &( A
>izz B).

The premise of 6 entails (using (3)) the denial of the second conjunct in the
conclusion.  Is there a typo here?

>7. A is predicable of B iff ((B  izz A) v (B hazz Something that izz A).
>8. A is essentially predicable of B  iff B izz A.
>9. A is accidentally predicable of B iff B hazz  something that izz A.
>10. A = B iff A izz B & B izz A.
>11. A is an  individual iff (Nec)(For all B) B izz A -> A izz B
>12. A is a  particular iff (Nec)(For all B) A is predicable of B -> (A izz
>B & B  izz A)
>13. A is a universal iff (Poss) (There is a B) A is predicable  of A & -(A
>izz B & B izz A)
>14. If A is Some Thing, A is an  individual.
>15. If A is a Form, A is Some Thing and Universal.
>16. A is  predicable of B iff (B izz A) v (B hazz Some Thing that Izz A).
>17. A  is essentially predicable of A.
>18. A is accidentally predicable of B ->  A =/= B
>19. - (A is accidentally predicable of B) -> A =/= B.

On the face of it 18 and 19 (with excluded middle) give A =/= A.

>20. A is a particular -> A is an individual.
>21. A is a particular  -> No Thing that is Not Identical with A izz A.
>22. No Thing is both  particular & a Form.
>23. A is a Form -> nothing that is not identical  with A izz A.
>24. X is a particula -> there is no form B such that A izz B.

No X on right hand side, so we can delete the condition (if there are
any particulas) and hence conclude -(A izz A)?

>25. A is a form -> ((A is predicable of B & A =/=  B) -> B hazz A)
>26. (A is a form & B is a particular) -> (A  is predicable of B iff B hazz
>27. (A is particular & B is a  universal & predicable of A) -> there is a C
>such that (A =/= C  & C is essentially predicable of A)

>28. If there are particulars, of  which universls are predicable, not every
>universal is Some Thing.
>29. Each universal is Some Thing.

Don't 28 and 29 together deny the premise of 27 (and hence make its conclusion

>30. If A is a particular, there is no  B such that (A =/= B &  B is
>essentially predicable of A).

>31.  (A is predicable of B & A =/= B) -> A is accidentally predicable of

Don't we have:

A is essentially predicable of B -> - (A is accidentally predicable of B)

If we do then using 31 we can get A =/= B -> -(B izz A), and with the
above -(B izz A) for any A and B.

31 seems to be denying essential predicability except where A and B are

Hopefully these are mostly typo's on Speranza's part or
misundertandings on mine.

I would be interested to know the sources in Aristotle of these
conclusions, presumably there are references in Grice's paper,
and I would put up a page linking to the relevant paragraphs if
this information could be unearthed and any problems resolved.

Ideally one would come up with formal definitions of the relevant
concepts and prove these claims, but coming up with suitable
definitions could be tricky.

I will to try to come up with a concise account of why a
"Metaphysical Positivist" might be interested in
Aristotle's metaphysics and what kind of interest
he might have in it.

Roger Jones

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