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