SUO: Re: Parse Of Things Remembered
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Pat,
I am sorry if this seems like too well-worn a rut
for you, but it has taken on a fresh significance
for me, not so much over this particular question
of reduction to dyadic relations -- I may a well
tell you that I know several people who believe
that all knowledge can be expressed in terms of
a single dyadic relation, namely "membership",
and I can even understand the reasons why they
think that this is an adequate conception, but
I take exception to it, not on theoretical, but
only on practical grounds, so if you imagine to
catapult us to the end of all inquiry and discuss
things from that perspective, then I am willing to
admit that the issue is moot -- so, no, the reason
why this is taking on a critical importance for me
in the present time frame is that it is forcing me
to entertain the notion, relatively novel to me,
leastwise, not since my adolescent Wanderjahren
when I tasted just about every style of ci-devant
yclept "deviant logic" that I was able to wrap my
brain around, have I dared to contemplate it, that
maybe "logic" is just bound to mean different things
to different sorts of people. And I begin to lose my
faith that inquiry is possible about matters of logic,
and if not there, then where? So, as I think that you
can probably see, I take this whole matter very seriously.
Therefore, if you still have any patience or tolerance for it,
I would like to try and inquire about the things that come to
mind as I read once again trough your presentation below, and
just see if I can figure out what you believe to be true here.
Pat Hayes wrote:
>
> > 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))
Okay, to begin, the first questions that I need to ask will no doubt
seem rather elementary, even dumb, but it is necessary to do this to
test if we have any sorts of common notions or readings of notations
in our several minds at this time. As I have explained to you a few
times, I try to maintain a "functional interpretation" (FI) for just
about everything in sight, at least, as one of the available options,
and so it is possible that this will pose an insuperable block to my
being able to understand how you see things, still, I cannot see how
at present, since I do try to maintain a properly abstract or formal
level of (non?)interpretation, too, even if I am forced to fall back
on the resorts or supports of various concrete models just to get by.
Anyway, the reason why I said all that is just to see whether it is
okay with you if I try to drag along as I proceed my safety-line of
the "functional interpretation" (FI), with an understanding that no
critical issue should depend on whether it is workable or otherwise.
Now this will seem really silly, but I do have to ask, just to check:
Are we talking about the brands of relations that have extensions as
sets of entities, entities that we may treat as primitives, like the
elements in the denotation, domain, range, whatever you want to call
it, of the variable name "e" above, elements that we can also regard
as being analyzable, projectable, or relatable, or whatever you call
it, in terms of the n-tuples <t1, ..., tn>?
Maybe I should break here, as it would be futile to go on
if I should happen to be wrong about this aspect of things.
Until Later,
Jon Awbrey
P.S. Slight look-ahead --
Is there an extra right parens in the
expression that I pretty-printed below?
J.A.
> 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)) <<<---<<< Here?
> ).
>
> 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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