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Re: [ontolog-forum] On dyads and triads

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Thu, 28 Mar 2013 23:07:23 -0400
Message-id: <5155056B.6040909@xxxxxxxxxxx>
Hassan, Steven, and William,    (01)

The reason why this thread has become so confused is that people are
mixing two completely different issues:  The ontology and the data
structures and algorithms used to represent and process the ontology.    (02)

> all that is computable is fundamentally dyadic    (03)

Even for computation, it's important to distinguish the ontology
of the operations from the notation for specifying them.    (04)

If you consider the ontology of addition, for example, you have
three participants:  two input numbers and one output number.    (05)

Some computer architectures have 3 explicit addresses for the
participants, some have 2 addresses plus an implicit accumulator,
some have one address and an implicit accumulator, and some have
zero addresses and an implicit stack.    (06)

But note that numbers themselves can be treated as vectors of bits.
Some machines process varying numbers of bits in parallel, and
others have streaming processors that treat an entire vector of
numbers as one addressable unit.    (07)

> The results you [HAK] refer to deal with "computable numbers" and
> not with conceptions in general. This is a very different question
> than the subject at hand.    (08)

I agree.  I used 'give' as an example to get away from the issues
of computation and to emphasize the physical participants.  Peirce,
by the way, also used 'give' as an example of an irreducible triad.    (09)

When you convert the triadic relation gives(x,y,z) to a conjunction
of three dyadic relations agent(w,x) & recipient(w,y) & theme(w,z),
there is still a triad in the graph.    (010)

See http://www.jfsowa.com/figs/give.gif    (011)

By the way, Donald Davidson's "event semantics" corresponds to the
ontology of the graph on the right.  But Peirce was quantifying over
events long before Davidson -- and so was Whitehead, who made events
the fundamental elements of his ontology.    (012)

Interesting factoid:  Davidson took the last course that Whitehead
taught before he retired from Harvard.  He later said that it was
Whitehead's course that inspired him to continue in philosophy.    (013)

Unfortunately, Davidson got stuck with Quine as his thesis advisor,
and Williard Q. was extremely unsympathetic to Whitehead's ontology.
Davidson had to wait until he got tenure before he had the courage
to publish his article about event semantics.  Even so, he got
a lot of flack from philosophers who wanted to make objects the
fundamental units of ontology.    (014)

> Your examples is certainly the way I like to do it, especially as
> in your second picture.  To unpack an ontology completely, I think
> it is critical to label arcs with roles, or other fundamental,
> non-domain specific semantic relations...    (015)

Yes.  I believe that event semantics is much closer to the implicit
ontology of natural languages.    (016)

> Does your statement that there will always be triads in the graph apply
> if you make the following dyadic assertions...
> Giving has a giver role
> Giving has a receiver role
> Giving has a given role...    (017)

These are metalevel statements about the representation.  You can,
if you wish, make dyadic observations about parts of a more complex
graph (or linear representation that is equivalent to the graph).    (018)

> Can't the three role relationships that 'giving' has be separate diatic 
>relations, as in
> Sue punched Bob
> Sue smiled at Jim
> Sue likes ice cream    (019)

I agree that you could take three dyadic graphs and paste them together
on a common node, such as the one that represents Sue.    (020)

But Peirce would consider this an accidental triad that combined
three independent actions in one graph.  If you stated them
on three separate occasions, the person who heard or read them
would get the same information.    (021)

But the act of giving must have three participants, even if one
of them might be left implicit.  For example,    (022)

  - Who contributed the most to the fund?    (023)

  - Sue gave $25.    (024)

John    (025)

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