Hey Ron, sorry for not being clear. You are right. What I wrote requires a lot more explanation. To begin with UI means Universal instantiation and EI means existential instantiation.

What I am trying to do is to use predicate logic to show that Aristotle is really talking about things and not words. "P" is the unbounded variable that should mean a "name" that can be used as a description or referent to a given object. The formalization came really from my reading of Plato's early dialogues. Where the main question is "what is x?" And I took that Socrates was really looking for an answer of the form "All x are P if and only if there is something that qualifies x as P and that something is a form". Of course the problem here is that it will always lead us to the third man argument. Now this is beside the point, but It seems helpful to introduce it as to show that when Aristotle names an object to some extent he is using the same blue print. That is, he seems to be answering the question "what is?" but without using it for forms. So, to me the issue of Homonymous or synonymous can be cleared up by showing that whenever we make an
instantiation that the name that we use to describe or refer is close connected to the definition of the object. This would make us believe that Aristotle is talking about "names" or words in the way we are using them. However, when we pay attention to the instantiation we see that the main focus is on the object itself and its relation to other objects via their definition (or nature) more than the names or words that we use to describe or refer to them.

So the general form of the answer to the question "what is" I changed to the following because I thought it could be confusing to use Form or F-ness to talk about Definition. Hence I wrote it as follow:

1. Ax[Px <--> Ey(Q(y,x,P) & Dy)]
Px = x has the property of P (or a name P)
Q(y,x,P) = y qualifies x as p
Dy = y is a definition (or a account)

Now if we assume that Aristotle is merely talking about words or names, then instantiations would be used only as a testing devise to find a counter examples or to show that the definition truly is consistent. So that the names or words are mere signifier which allow for the definition to be convey as the signified. Then the question is not "what is x" but

(a) "what is meant by x in a given context y".

Notice that x in (a) can only be satisfied if we are using words or names, that is, the set that (a) covers is of words or names and so the only instantiations that we can make are of words or names.

The x in 1 can only be satisfy by either abstract or concrete objects. Now just to make sure, abstract objects are not part of the set of words or names, since words or names are tokens which convey the abstract objects by functioning as signifiers of the abstract object. But this is not sufficient for us to know that Aristotle is talking about objects. What would make it sufficient is that when he is using the relations of Homonymous and Synonymous, he is in fact relating two objects in a particular way. Hence the instantiation would clarify that Aristotle is talking about objects. Again let me restate the example.

Lets assume that "P" is the name "animal" and "s" for Socrates and "m" for the picture of a monkey and "r" for a rational animal and "t" for the figure of an animal. So we have the following

1. Ax[Px <--> Ey(Q(y,x,P) & Dy)]
2. Ps <--> Ey(Q(y,s,p) & Dy) UI from 1
3. Ps <-->(Q(r,s,P) & Dr) EI from 2

1b.Ax[Px <--> Ey(Q(y,x,P) & Dy)]
2b. Pm <--> Ey(Q(y,m,P) & Dy) UI from 1
3b. Pm <--> (Q(t,m,P) & Dt) EI from 2

What is important for Aristotle are line 3 and 3b, since they give us what s and m have in common (the name P) but also the necessary condition for s and m to be name P. Although it sounds as if Aristotle cares about the conditions for s and m to be called P in so far as P is concerned only, he is truly focus on the objects themselves and how their natures relate to each other. When we instantiate s and m as P, we see no difference, but when are are asked to show their nature, that is, "q(t,m,P)" and "Q(r,s,P)" we notice that s and m are qualify as p for two different reasons--their definitions are not in common. This is exactly what he means in Cat. 15a "For should any one define in what sense each is an animal, his definition in the one case will be appropriate to that case only."

I have to stop here...But Ron let me know if this is helpful or is it that I am just missing the point.

--- On Fri, 1/2/09, waveletter <wavelets@...> wrote:

> From: waveletter <wavelets@...>
> Subject: [aristotle-organon] Re: Aristotle thing/words
> To: aristotle-organon@yahoogroups.com
> Date: Friday, January 2, 2009, 11:39 PM
> Hi Eduardo:
>
> I'm not sure what you're trying to develop with
> this formalization. Are you trying to explain
> what it means for a thing to have a property? Or are you
> trying to offer some equivalent
> account that would help us understand something else?
>
> It seems like you are introducing new concepts: (1) for
> something to qualify something
> else as yet something else, and (2) for something to be a
> definition or account.
>
> Some more questions below.
>
> --- In aristotle-organon@yahoogroups.com,
> "csikirk" <gonzalez8988@...> wrote:
> >
> > Hey Ron and Kevin!!! This has been a wonderful
> discussion thanks to
> > both of you guys. I would like to contribute and I
> would like to give
> > the following formalization that maybe would help us.
> But it is just a
> > maybe. Just to let you guys know Ax= for all x, Ex =
> for at least one
> > x. I don't have the backward E or the upside down
> A. Anyways, here we go.
> >
> > 1. Ax[Px <--> Ey(Q(y,x,P) & Dy)] That is
> >
> > Px = x has the property of P (or a name P)
> > Q(y,x,P) = y qualifies x as p
> > Dy = y is a definition (or a account).
> >
> > Lets assume that "P" is the name
> "animal" and "s" for Socrates and
> "m"
> > for the picture of a monkey and "r" for a
> rational animal and "t" for
> > the figure of an animal. So we have the following
> >
> > 2. Ps <--> Ey(Q(y,s,p) & Dy) UI from 1
> >
>
> What does "UI" mean? Is that an instance of the
> axiom #1?
>
> > So since it is Socrates, we would have to choose
> "r".
> >
> > 3. Ps <-->(Q(r,s,P) & Dr) EI from 2
> >
>
> I'm not sure what "EI" means. Above ^.
>
> I would agree, given the choices you list, that we'd
> choose "r". But, how do we know that
> these are the only choices? And if there are more, what
> tells us which one to choose? What
> if the figure of the animal was a portrait of Socrates?
>
> > Here is where I have to stop because I cannot choose
> "t", since the
> > rule of EI says that I cannot choose another object.
> Like we all know.
> > So let me start over for "m".
> >
> > 1.Ax[Px <--> Ey(Q(y,x,P) & Dy)]
> > 2. Pm <--> Ey(Q(y,m,P) & Dy) UI from 1
> > 3. Pm <--> (Q(t,m,P) & Dt) EI from 2
> >
> >
> > Of course, like everyone knows, this is not
> Aristotelian Scholar
> > talking here--just a janitor who find this stuff
> fascinating. It seems
> > to me that I would have to make two separate arguments
> for me to know
> > what s and m are. In other words, P is not as
> important as to what
> > type of thing s or m is since the corresponding
> definition has to be,
> > by their nature, different. But if two things have the
> same nature (or
> > definition) then I can keep using the same argument.
> That is the
> > following: Let us say that "b" is Plato and
> "a" is Aristotle.
> >
> > 1.Ax[Px <--> Ey(Q(y,x,P) & Dy)] Assumption
> > 2.Ax[Px <-->(Q(r,x,P) & Dr)] EI from 1.
> > 3. [Ps <-->(Q(r,s,P) & Dr)] UI from 2
> > 4. [Pa <-->(Q(r,a,P) & Dr)] UI from 2
> > 5. [Pb <-->(Q(r,b,P) & Dr)] UI from 2
> >
> > And so on. That is whatever individual that fits in
> the definition. So
> > for me to know when two things are Homonymous, I must
> have a separate
> > argument and when they are synonymous I only need one
> argument. I
> > guess the main problem is that a syllogism would not
> help us because I
> > am always using the same middle term for two different
> conclusions. So
> > homonymous and synonymous are proper for Categories
> although there are
> > in some way remove from simple apprehension or that
> is:
> >
> > 1. All P are r
> > 2. s is P
> > Therefore 3. s is r
> >
> > 1. All P are t
> > 2. m is P
> > There fore 3. m is t.
> >
> > Or I guess I could be more respectful to Aristotle and
> W-R by
> > formalizing in the following way.
> >
> > 1. AxAz{H(x,z) <--> En ED1 ED2[ C(nx,D1) &
> C(nz,D2) & ~(D1 = D2)]} where
> >
> > H(x,z) = x is homonymous with z.
> > C(nx,D1) = x's name corresponds to definition 1
> (D1)
> > C(nz,D2) = z's name corresponds to definition 2
> (D2)
> > ~(D1 = D2) = D1 is not identical with D2.
> >
> > I will continue later. I have to clean some toilets.
> LOL.
> >
>
> OK, thanks, Eduardo. It would help me if you could motivate
> these logical reconstructions
> in some what. I'll keep mulling over what you've
> said and see if the lights come on.
>
> Thanks!
> --Ron