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

Jlsperanza at aol.com Jlsperanza at aol.com
Sun May 17 22:39:08 EDT 2009

Something to consider, also, vis a vis 'analytic' (or modern analytic)  
attempts to formalise Aristotle's metaphysics, is Code's caveat -- which I have 
 posted already in the first memo to this thread:
   "Rather than following the MORE  USUAL practice 
of discussing essentialist claims  in terms of 
first-order predicate calculus WITH  MODAL
   OPERATORS, I will follow Grice's insights ..."
(my emphasis). But then one sees some of his formulae, involving (in my  
treatment of them, granted) things like "Nec" and one wonders if the 
desideratum  has been fulfilled.
I think the most serious Grice himself got into this is in the formal  
sections of his "Vacuous Names" where he considers various interpretations for  
syntactic structures using model-theory and formal semantics. 
As for the formulas themselves, we should perhaps use "F" and "G" and "H"  
instead of the A, B, and C. -- to quinise things a bit. And proper  

One thing that intrigued me in the Code approach is indeed the close  
faithfulness to the Aristotelian idioms. Alas, I seem to have erradicated the  
Greek, but Code is careful to quote in Greek, e.g. "tode ti", "kath'olou", 
etc.  So it is more like a running commentary on Aristotle for, er, UC/B grad  
I would suggest some reformulations then:
>>             A izz A

Greek, like Latin, was pretty free, grammatical. "Homo est homo" or 'to  
anthropos esti to anthropos' would be things philosophers could say. "Man is  
man" can be the closest. Now, Greek commentators (i.e. Anglophone speakers  
commenting on Greek idioms) will say that "homo est homo" (or its Greek  
equivalent) could not be just _understood_ as "man is man" but also
        a2.  This man is this  man
        a3.  A man is a man
and all sort of confusing variants. Since one may not want to swallow the  
subtletites of Greek or Latin grammar (plus, one couldn't), it's best 
prehaps to  treat "A" as a definite descriptor, "the A" -- true: this sounds a bit 
of a  'constraint' (there is another word but I can't think of it right 
now). In that  case
            "The A  izzes the A"
may be something one can say in English, "The cat is a cat". Now, if we  
stick with Grice to use "I" (izzes) as a predicate, there is the further 
problem  that one would need a formula including two definite descriptors, 
however  identical. Suppose we call the cat, "Little Paw" and symbolise it by "p". 
I  think Grice would want us to have:
           I(p, p).
Which is Frege:  a = a, almost. 
I recall, also that Code has all sorts of rubrics for all sorts of things:  
axioms, postulates, theorems, corollaries. I just erased all that, and 
numbered  the things. Grice's "Aristotle on the multiplicity" cares to give some 
account  of the formation rules, and basic properties of izzing and hazzing 
(transitive?  commutative?). Yet, none of the detail he displays in 
"Vacuous Names" or Myro in  his unpublished "System G" ("in gratitude to Paul Grice 
for the idea").

>> (A izz B & B izz C) ---> A izz C

this seems  to be the mere transitivity of the predicate I:

I(x,y) & I(y,z) ---> I(x,z)
Also formalisable as a 'formation' rule, or metalogical principle with the  
first two conjuncts as premises
         a = b
         b = c
ergo  a = c

>>           A  hazz B  ---> ~(A izz B)

This reminds me of the rather offensive phrase by Grice (in "Actions and  
Events") about the "rednecks of Vienna". Suppose one of them is called, er... 
 Karnap. (Just to tease!). Surely the proper thing to say of Karnap is that 
he  _has_ a redneck, not that he is one. On the other hand, Grice seems to 
be  teasing Strawson and his non-ownership (so-called) theory. We _don't_ 
usually  say, "Apple has smelly". "Apple _is_ smelly; it has smell". So it 
does not hurt  to recall that the 'hazz' is merely Grice's idion (or idiom, 
even) for 'has  among its accidental properties ...' 
           H(x, y)  ---> ~I(x, y)
If an apple merely has a worm (because it's rotten) it doesn't mean the  
apple _is_ wormy. I'm not sure I have symbolised Code's formula alright. 
Perhaps  the scope of ~ should be the whole formula:
          ~(H(x, y) -->  I(x, y)

>>           A  hazz B <---> A hazz Some-Thing that izz B

Well, we should get serious here about this "Some-thing". In ebonic  
English, I am told, they don't say _thing_ any more. They say "some". "I saw  
some" This seems like a good grammatical manoeuvre, since -- things: what are  
                H (x, y) <----> y = z & H (x, z).

I'm not sure that above symbolises the thing. I tend to recall  that 
whenever I use the biconditional, <----->, is to mark a  mere stipulation or 
definition. I guess my feeling if that you are going to  present the whole thing 
or attempt of metaphysica more geometrico as  a chain of definitions, who'll 
buy it? Biconditionals look more  honest.

>>            Each  universal is a form.

This has to do, and can be ignored, with Code's attempt to prove Aristotle  
over Plato. So he needs to rephrase Platonisms like 'form' (eidos) and 
universal  in "Aristotelian" terms. I was so flabbergasted when I read that 
'theorem' that  I became formally illiterate!

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

H(x, y) &  [x is a spatio-temporal continuant?] -->
Problem there is that while _spatio-temporal continuants_ seem, to me,  
basic particulars, or individuals, I'm not sure that was the case for Aritotle. 
 "White" is a _particular_ colour, for example. Or "the white" as the 
Greeks  would say. 

But I do think that it's best to stick to _particulars_ in the lower  
eschatological stages of our methaphysical endeavours (this reminds me of  
Borges's dedication to himself in "Fictions": 'an argentine lost in  metaphysics') 
to 'prima substantia', prote ousia. Things like Socrates, you, and  me, 
rather than the colour white, or the Republic of Indonesia. 
>>         A is predicable of  B <---> ((B izz A)  
v (B hazz Something that izz A)

Jones is right, if I understood him  alright, that 'predicable' seems to 
metalinguistic to be true. In any case,  shouldn't there be a quote there, 
              "A" is predicable of B?
I wouldn't say that my mother is predicable of my father. It's predicates  
which are predicable. This is where our use of variables condemns us. And  
definite descriptors seem to be of no better avail. We need simpler 
predicates  like "clumsy", "silly", "forgetful", etc.
I still think "B" above, could be "my uncle", i.e. a definite  descriptor.

My uncle is  forgetful, clumsy, silly, and only a political one, anyways.

>>      A is essentially predicable of  B  <---> B izz A

Perhaps using Phi and  Khi could do too. Or Phi-1 and Phi-2. Yes, that 
would be the best. Now the  'lexical' trick here is that 'essence' (for it's all 
about the essence in  Aristotle) has become a lexical expression (as 
Mussolini said of Italy, "Italy  had become a mere geographical expression"). 
"Essentially predicable" is  ambiguous. First, nobody should be forced to 
predicate anything. "predicable in  the essential mode" sounds softer. Here I do 
think something like
versus membership is, as R. B. Jones suggests, what is at stake. 
              homo est rationalis
therefore 'rationalis' is predicable of 'homo' in the essential mode.
(Ex) Mx & ~Rx --->  E!
should there be a man who is not rational, ERROR! -- the item  

>>          A is  accidentally predicable of B  
<---> B hazz something that izz A

Well, I suppose that in a world  where things are either accidentally or 
essentially predicable, there is an  easier way to define 'predicable in the 
essential mode' by excluding the other  possibility.

>>          A = B  <---> A izz B & B izz A

x  = y <----> I(x, y) & I(y, x)
Here one _should_ consult, Myro, "Time and Identity", in PGRICE -- the  
example of Hobbes's wooden ship. For this requires a chronological logic with  
time indexes. So that x = y is relative to time 1. Grice/Myro borrowed this 
from  Geach.

>>          A is  an  individual <--->  
(Nec)(For all B) B izz A ---> A izz B

So here we distinguish  'particular' (as in "particular" colour) from 
'individual'. "Individual color"  is possibly obsolete or pedantic.
           <---->  Nec (y) (I (y, x) ---> I (x, y))
I fail to see how that transmogrification _clarifies_ the simpler  
'individual' ('atomon', in Greek).

>>           A  is a  particular <---->  
(Nec)(For all B) A is predicable of B --->  
(A izz B & B izz A)

Nec.  (y) ... I(x, y) & B(x, y)

>>           A  is a universal <---->  
(Poss) (There is a B) A is predicable of A  
& -(A izz B & B izz A)

I think the use of "Poss" (definable of  course in terms of "Nec") is that 
a 'kath'olou' need not be _instantiated_. I  will not name 'circular 
squareness', but something like "being the mother of 54  children". 
               & ~(I(x, y) & I(y, x)
Most of these formulae seem to be dangerously ending with the same  

>>              If A is Some Thing, A is an  individual.

I suppose one _may_ want to include here, "individual colour"? Mary uses  
hats with very _individual_ colours. She is very _individual_ as to clothes.  
Note that with 'particular' it seems otiosely  appropriate.

>>               If A is a Form, A is Some Thing and Universal.

This is more like the Platonic side to Aristotle. With 'eidos' as form. Or  
sometimes 'morphe' (as in 'hylemorphism).  

>>         A is   predicable of B <----> (B izz A)  
v (B hazz Some Thing that Izz  A)

I(x, y) v H(y, z) & I(x, z)

>>              A  is essentially predicable of A

Not Socrates is Socrates, but 'a silly man is a silly man'. Note that 
people  overdo this: boys will be boys. Surely not: they will be silly men,  

>>           A  is accidentally predicable of B --->  A =/=  B
>>          ~(A is  accidentally predicable of B) ---> A =/=  B.
>>          A is a  particular ---> A is an  individual
So, it's the other way round, "particular car", "individual car". "A 
particular  car with an individual colour", or "an individual car with a 
particular color"  (Or chariots if you want to keep the Grecian spirit)

>>    A is a particular  ---> No Thing  that is Not Identical with A izz A
             I(x,  x)
>>     No Thing is both  particular & a  Form.
>>      A is a Form ---> nothing that  is not identical with A izz A
             I(x,  x)
>>      X is a particular ---> there is  no form B such that A izz B
             I(x,  y)

>>         A is a  form ---> ((A is predicable of B & A =/=  B)  
---> B hazz A)

Back to the 'eidos':
                                    ---> H (y, z)

>>      (A is a form & B is a  particular) --->  
(A is  predicable of B <----> B hazz  A)

<---> H(y, x)

>>     (A is particular & B is a   universal & predicable of A) 
---> there is a C such that (A =/= C   
& C is essentially predicable  of A)
>>        If there are  particulars, of  which universals are predicable,  
not every  universal is Some  Thing.
>>          Each  universal is Some  Thing.
>>            If A is a particular, there is no  B such that (A =/= B  
&  B is essentially predicable of A)
>>              (A is predicable of B & A =/= B) --->  
A is accidentally predicable of B.
As R. B. Jones says, one should have a clue or key as to where Aristotle in 
 his Rossian metaphysics says all this. 
And second, _why_!
Never mind, _what for_!
One thing to keep in mind here is Neivens. He has worked a lot on what I  
call 'general ontology'. Evans too. It's all general ontology we are 
treading.  Only then we should try ontologia specialis which comes in two flavours:  
cosmologia, and my favourite, anthropologia or psychologia rationalis -- 
but I  have discussed them elsewhere, -- in my "Aristotle's Idiocies" 
(rejected for the  Classical Association of Aristotelian Scholars, South Pacific).
If you can't schiffer, grice (Kemmerling)
If you can't Aristotelize, platonize blatantly. 
And if you can't either, join the 
Oddly, Chapman keeps misspelling 'eschatology' in her book on Grice as  
'skatology' -- which may be a reminder of what Karnap would say of all this,  
"Sh--t" (implicating: "To hell!"). But little did he know.
J. L. Speranza
            "All  metaphysics has been but footnotes to Plato"
**************Recession-proof vacation ideas.  Find free things to do in 
the U.S. 

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