Re: SUO: Re: Parse Of Things Remembered
>Pat,
>
>We went round and round on this issue before, so I don't want
>to repeat the experience.
I didnt go round and round on this issue. I wrote a review of Burch's
thesis which I believe settled the matter conclusively. (J.
Man-Machine Studies, 1995)
> But I just wanted to add a couple
>of new remarks:
>
> >Peirce was misled by an analogy between logic and chemistry, which
> >wasnt a bad idea in 1885, but seems kind of daft in hindsight. He
> >seems to have thought that the associations between relations and
> >their instances, which he was encoding as arcs in his graphs, were
> >like valency in chemistry....
>
>First of all, Peirce was a buddy of Sylvester's at Johns Hopkins
>University, and Cayley was a visitor there. Graph theory in all
>its glory was a big topic there. So he wasn't exactly naive
>about what can and cannot be done with graphs.
I didnt say he was. His result is perfectly fine as a theorem in graph theory.
>Second, Whitehead also remarked that dyadic relations weren't
>sufficient for knowledge rep. Last week, I scanned a few pages
>from Chapter 9 of his book "Concept of Nature," but I don't
>want to bother scanning the whole thing. However, if you have
>it (or can find it), I recommend Ch. 8, in which he remarks
>
>"Other schools of philosophy admit relations but obstinately
>refuse to contemplate relations that have more than two
>relata..." (p. 150)
>
>W. then goes on to discuss "percipient events", which require
>more than 2 relata -- just the kind of examples that P. was
>dealing with.
Had Peirce or Whitehead lived a little longer maybe they would have
become aware of the fact that any n-ary relation can be defined in
terms of binary relations, with the aid of the existential
quantifier. The translation, as I know you know, John, is this:
R(t1,...,tn) ---> (exists e)(R(e) & first(e, t1) & second(e, t2)
&...& nth(e, tn))
where 'first', 'second', etc., are some fixed set of binary
relations. (In case grammar these correspond to cases such as
'agent', 'subject' and so on, and the 'e' is something like an event
or a situation, of type R, corresponding to the verb of the simple
sentence, as in:
Gave(John, Book, Mary, yesterday)
--->
(exists e)(Giving(e) & agent(e, John) & subject(e, book) &
recipient(e, Mary) & time(e, yesterday)) ).
Since a binary relation has a name and relates two other things, it
is conventionally called a 'triple' in data structure terminology (eg
in RDF), and this ghost of trinaricity is where Peirce's simple
graph-theoretic result can be glimpsed. His error was to conclude
that this implied that a trinary *relation* was necessary; and that
in turn was because he made the error of thinking that the assertion
of identity between n things involved an irreducibly n-ary identity
relation.
Pat Hayes
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