RE: SUO: RE: Ontology, Epistemology, Semiotics
Cathy Legg wrote:
> On Mon, 8 Sep 2003, Richard Cooper wrote:
>
> > There are no such formal structures, IMHO. John McCarthy's
> > paper "Recursive Functions of Symbolic Expressions", which
> > provides the mathematical concept behind the first Lisp
> > interpreters, indicates that any function, of any arity,
> > can be modeled by a decomposition of the same mapping
> > into dyadic and monadic functions.
> >
> > In formal logic, the concept of an event E7 (in which multiple
> > participants play a role) can be modeled as a set of dyads
> > with with any detail expressions S[i] designating participants
> > can be related dyadically. So there is no formal need for arities
> > greater than 2. The unifying event E7 is the "thing" that ties
> > all the participants together.
> >
> > So I don't feel enlightened by this explanation. Certainly
> > a triadic (or quadratic, or ..) relation is more intuitively
> > expressive than a bunch of line items in a unifying event, but
> > it is still not formally necessary. Therefore Thirdness is
> > not necessarily defined by describing it as a triadic function.
> >
> > But beyond formality, if Thirdness can be used to explain
> > both animate agents and inanimate processes, then Thirdness
> > is a poorly defined concept, whether relational or individual.
> >
> > The way its being explained in this thread so far, Thirdness
> > is merely a nonterminal connector that is familiar (and therefore
> > acceptable) to Peirceans, but which isn't any fundamental idea.
> >
> > The concept of relativity (not just as in physics, but as in
> > art, drama, engineering, and nearly every other modern disciple)
> > where the observer plays a role in the world, and is included
> > in the model, needs no Thirdness as an explanation IMHO. Most
> > people agree that animate agents drive some forces in the real
> > world, but how is that related to ontologies?
> >
> > I could use some deeper explanations about Thirdness, including
> > how it's manifested in specific examples of situation descriptions.
>
> Hi Rich,
>
> I am very sympathetic to the request for concrete examples
> and understand
> how it often seems to those who haven't spent much time with Peirce's
> thought that those who have are merely trading an overly-general,
> unfalsifiable, smug 'private language'.
>
> So - consider a gift. A gives B to C. Peirce says at one
> point that this
> situation does not consist in A's throwing B away, and B's hitting C.
>
> So, how would you decompose such a situation description into dyadic
> relations? One might perform a 'hypostatic abstraction' of the giving
> event (Davidson-style) and say:
>
> (giver GIVINGEVENT001 A)
> (givee GIVINGEVENT001 C)
> (gift GIVINGEVENT001 B)
>
> However, note the implicit triadic relation of identity which
> links the
> denotata of the three tokens of GIVINGEVENT001 together, which is
> actually required for the representation to mean what we want it to.
>
> Cheers,
> Cathy.
Thanks Cathy, I think the irreducible triad concept is beginning
to sink in. It seems to be more concerned with expressivity than
with formal irreducibility. Even your example above could, in
formal terms, be represented in a table of pairs (CAR, CDR) of
course, but I think you mean irreducible with the same intuitive
content, rather than strictly formally irreducible.
I'll continue to ponder it.
Rich