Re: SUO: RE: Ontology, Epistemology, Semiotics
Mike, Rich, and Cathy,
Rich's example is just one more illustration of
the attached diagram give.gif:
RC> 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.
The unifying event is the central node, which in the case
of Give has three connections. Whether you connect a relation
named Gives directly to the three participants or you connect
a concept named Give indirectly to three dyads does not get
rid of that central node with three connections.
Before doing anything else, stop using the words "relation"
and "arity". Just look at those two diagrams. All you see
is a central node with three connections to it. Whether the
connecting arcs are decorated with additional dyadic "relations"
is irrelevant. Both diagrams have a central node with three
connections.
Cathy's example illustrates where "purpose" or "intention"
enters the picture:
CL> 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.
The two separate verbs "throw" and "hit" are dyadic, and what is
missing is any intentional connection between the two. As another
example, consider the following story:
John left a book. Mary took the book.
There is no indication that John intended Mary to have the book.
She might have been stealing a book that John was planning to
come back for. But consider the following story:
Mary asked John for a book. John promised to leave it.
John left the book. Mary took the book.
Now the first line of the story establishes an intention,
and the second line can be interpreted as fulfilling that
intention. The verb "give" includes the intention in
a single verb, which has three participants. It is not
possible to break that verb into multiple dyads without
losing information about the intention.
Mike Pool asked
MP> ... 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?
Because there are two relevant mathematical theorems:
1. You cannot decompose triads into dyads without leaving
some nodes that are still triadic in the graph.
2. But you can always decompose a graph that has nodes
with more than three connections into a graph that
has no node with more than three connections.
Example: A sentence with four participants "John sold Mary
a book for $10" can be transformed to two sentences with
three each: "John sold Mary a book. She paid him $10."
John Sowa
