--- In aristotle-organon@yahoogroups.com, "waveletter" <wavelets@...> wrote:

-----------------------------snip----------------------------------

>
> > 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".

OK. This is an attractive way to pursue the problem. You're making the point that the
"what is X" approach to philosophical problems oversimplifies real situations and causes
us to focus in on, and become distracted by, the name of a thing; instead, it is the context
of the thing named and perhaps the account of the essence of the thing named that must
be brought into the equation...uh, I mean predicate logic statement.

> >
> > 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.

Then you probably need to have another predicate Name(x) or incorporate this into one of
the other predicates. You are getting into a universe that has names, properties, things,
and contexts as the objects over which the variables may range.

To me it seems like Aristotle has individual things, like Socrates and Pegasus and this rock
in the wall to Piraeus, as objects as well as their properties, such as paleness, strongness,
and firmness as objects. I would rather first-order-logicize Aristotle by have these as
elements of the model and other things like names and relations (has, applies to) as
predicates in the language. Does that make sense? Am I missing your point? Completely?!



> >
> > 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 what is a signifier of an abstract object, but a name of that very object? An 'animal' is
abstract. It doesn't refer to a concrete animal. But to a kind of thing.

I think that either we are still exploring here, or I am missing your point entirely.

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.

OK. This is akin to what I was saying--here, there, and everywhere--that A's references to
homonymous things seem to be in the plural, like he is talking about two different things
that are denoted in different contexts (! thanks Eduardo) by the same *single* word. A's
references to synonymous things seem to be in the plural also, like when he is talking
about two different things that are dentoed in the same context (! thanks Eduardo) by the
same *single* word.

Does this ^ capture something of what you are trying to say, or am I a raving idiot?

I used to scrub the washrooms of America myself, by the way. I had a summer job, like
Homer Simpson had a regular one, at the San Onofre Nuclear Station in southern
California, cleaning the offices, work trailers, and toilets around the site. Worked with a
group of off-duty Marines from Camp Pendleton. I was the only guy that didn't have a
buzz cut. Interesting, in its own peculiar way. The Marines were more accepting of a
Berkeley hippy with long hair than the other folks at other workplaces I frequented. Only
thing was: You don't want to leave a streak of dirty crap along one of the wall mouldings
for your supervisor (a Marine 9-to-5! or, I mean 5-to-5!) to discover. Hope I don't get
leukemia tomorrow.

Anyway, back to Athens:

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

Oh, I don't think this follows. From an existential statement, you can't stick in any constant
in place of the bound variable. Safe harbor in arithemtic:

R1. Ex(2*x = 4) {true theorem}
we have a constant in the language for an element '19'
S1. 2*'19' = 4 {false instantiation}

You can stick a constant into a universal, replacing the bound variable, removing the
quantifier, but not into an existential. There may not be a name for the thing satisfying the
existential statement.

> >
> > 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.

I think that this last remark is the key, even if your first-order logic seems, to me, to be
burdened with some flaws.

In a way, A. is jerking our attention away from words (which are social practices) and
towards things and their interrelationships via physical properties (an ox and a human
being are both sensitive beings, animals). There is something else to watch out for.
There's an account of the essence, account of the being of the thing. But this account isn't
just a linguistic formulation; it's an abstract summarization of empirical knowledge. We
don't say that a sycamore tree has a sensitive soul because we like to formulate things that
way. We say that it does not have a sensitive soul because we have observed it to have
none such. Oppositely of the ox; it does have a sensitive soul. So also of the human being.
So the account of the essence is not a mere "definition", something spit forth by a sophist
or a nitwit to distract you, but a 5th century BCE scientific fact, presented in abstract
terms, but based on a generalization from detailed physical investigation.

Or, you know, maybe it's all just words, like Derrida says. And Protagoras. But not
Socrates.

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.

It seems to me that you've made several mistakes, but you are rightly and admirably trying
to analyze (Greek: split apart completely) Aristotle's account of homonymy, synonymy, and
paronymy in the "Categories".

Thanks!
--Ron

> > --- 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
> >
>