SUO: Re: Ontology, Epistemology, Semiotics
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Mike,
Peirce is talking about relations, and relations are subsets of cartesian products.
In relational data base terms, one may think of a k-adic relation L as a k-column table,
whose rows list the k-tuples <x_1, ..., x_k> that are in the relation L c X_1 x ... x X_k.
For the example, the Giving relation, in a given context of discussion,
may be presented as a 3-column table G with Donor, Gift, and Recipient
as the column labels.
If it is true that A gives B to C, then you enter the triple <A, B, C> in the table.
But the relation is the whole set G of triples, and not the single triple <A, B, C>.
Nor should the relation itself, the set of triples, be confused with any syntactic
representation of it, and especially not with a syntactic representation of just
one triple, like:
| (giver GIVINGEVENT001 A)
| (gift GIVINGEVENT001 B)
| (givee GIVINGEVENT001 C)
Only confusion will come of that.
Naturally, when it comes to relations with infinite numbers
of instances, or even just inconveniently large numbers of
instances, we cannot or would rather not present them by
direct enumeration, and so we have to invent linguistic
and graphical representations for thinking about their
properties and inter-relations. These representations
can be very useful maps of the underlying territory,
but a roadmap is only useful if you already know
what a road is.
Jon Awbrey
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Mike Pool wrote:
>
> At 01:10 PM 9/11/2003 -0500, 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.
>
> Cathy,
>
> I'm one of the Peircean unwashed and hence appreciate the attempt at a simple example.
> Could you say a bit more about how this example illuminates or exemplifies the notion
> of Thirdness? I'm still a bit confused. After all, couldn't I say more about
> GIVINGEVENT001, e.g., (date GIVINGEVENT001 D), (eventOccursAt GIVINGEVENT001 E),
> etc,, and wouldn't this then involve an implicit quartic, quintic, etc. relation
> of identity? So why does this demonstrate Thirdness as opposed to, say,
> Fourthness or Fifthness or whatever?
>
> best,
>
> Mike Pool
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