SUO: irreducible triadicity vs. essential triadicity
Dear all,
let me spend my 5 cents (is it the proper expression?) on
this old issue.
At 10:13 AM -0400 14/3/01, John F. Sowa wrote (quoting Whitehead):
> The difficulties which cluster around the relation of
> situation arise from the obstinate refusal of philosophers
> to take seriously the ultimate fact of multiple relations.
> By a multiple relation I mean a relation which in any
> concrete instance of its occurrence necessarily involves
> more than two relata. For example, when John likes Thomas
> there are only two relata, John and Thomas. But when John
> gives that book to Thomas there are three relata, John,
> that book, and Thomas.
At 4:18 PM -0400 14/3/01, John F. Sowa wrote:
>The only point that Peirce, Whitehead, and I have been trying
>to make is that there are concepts in English, such as Give,
>which cannot be defined without using a frame, a lambda
>expression, or some such formal device that contains three
>distinct slots, variables, boxes, or whatever.
Let me first remark the Whitehead's quotation is an ontological
observation, while John's statement has a more "representational"
flavor. Whitehead says that some entities (namely, giving events, or
- if you prefer - occurrences of the "gives" relation) *necessarily*
involve something else, namely three other different entities. [Note:
Whitehead uses a modal notion]
In my understanding, this means that, necessarily, if a giving event
exists, then three other different entities (of suitable kinds) must
exist.
This is basically a form of ternary existential dependence: the
existence of a giving event depends on the existence of an actor, an
object, and a recipient.
This *ontological* truth (which captures, in my opinion, the essence
of Whitehead and Peirce's intuition) can be labelled as a truth about
"essential triadicity". This *can* be syntactically "reduced" to an
expression where only a binary relation appears, namely the
dependence relation. [Note: there are various ways of suitably
characterize this dependence relation - this is another story, see
Simons' book]. So I believe that the notion of "reducibility" is
inappropriate to characterize the ontological relevance of
Whitehead-Peirce-Sowa's distinctions. [Maybe there are other
non-ontological considerations, as Pat pointed out].
A further clarification is needed on the way John uses the notion of
"Mediating entity" in his book. John proposes a plan as an example of
mediating entity, which mediates between a builder and a building.
But a plan, as such, is different from a giving event: the latter is
ternary dependent, while the former is only binary dependent (the
existence of a plan implies the existence of a builder and the
existence of a [potential] building). What is ternary dependent is a
planning event, which requires all three participants. It seems to me
that mediating entities are different from mediation relationships,
and triadicity only applies to the latter.
This is in my opinion a serious and systematic confusion in John's
book, that unfortunately uses the vague term "corresponds" (e.g.:
"mediating corresponds to Peirce's Thirdness") just to suggest some
interesting interpretation keys, which often are not suitably
formalised. [BTW, it is not clear to me whether all binary and
ternary dependent entities always involve some kind of mediating
phenomenon, so I don't know whether the notion of "mediation" is
appropriate to fully characterize these classes].
Bottom line: existential dependence is a formal ontological relation
that can help clarifying (and extending) Sowa's trichotomy: there are
independent entities, unary dependent entities, binary dependent
entities, ternary dependent entities (of course, the list may
continue, but these seem to be the most interesting classes).
-- Nicola
---------------------------------
Nicola Guarino
National Research Council phone: +39 O49 8295751
LADSEB-CNR fax: +39 O49 8295763
Corso Stati Uniti, 4 email: Nicola.Guarino@ladseb.pd.cnr.it
I-35127 Padova
Italy
http://www.ladseb.pd.cnr.it/infor/ontology/ontology.html
(***updated 22/2/2001 ***)