Re: SUO: Re: Parse Of Things Remembered
>Yang Yun wrote:
> >
> > > > It also argues for a divide and conquer approach.
> > > > This is why I support Nicola Guarino's recent call
> > > > for a modular approach to reference ontologies.
> >
> > > Modular is nice, of course, if and when you can get it.
> > > There is a catch here though, "triadic irreducibility".
> >
> > Google search for "triadic irreducibility"
> > did not match any documents, whatever ..
> > yy
>
>¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
>
>Y^2,
>
>FAST Search:
>
>http://www.alltheweb.com/cgi-bin/advsearch
>
>gave this very interesting one from the CG List:
>
>http://www.virtual-earth.de/CG/cg-list/msg02192.html
>
>If you use the exact phrase option then you will probably also
>need to try "triadically irreducible" and "irreducibly triadic".
>Or you could always try reading about it in Peirce -- his work
>is in all of the big libraries -- you remember libraries dontcha?
Allow me to interject a note of caution, before we waste yet more
time on this old chestnut.
Peirce proved a result which he thought very important and
fundamental. It is indeed correct, but it isnt deep or very
important, so he was both right and wrong about it. The result was
this. Consider nodes in a graph and classify them by their 'degree',
ie the number of arcs that link to them. Then in order to build
'arbitrary' graph structures one must have at least one node of
degree three. (Roughly, if you only have nodes of degree 2 then all
you can do is make long rows of nodes; but once you have degree-three
nodes, you can build arbitrarily branching structures by imitating
degree-n nodes by sequences of n trinary nodes linked together, as in
LISP or RDF.) This is Peirce's 'irreducible triadicity', and he
thought that it meant that there was something fundamentally trinary
about identity. However, the result is very fragile. If you allow
hyperlinks in the graphs, it fails immediately. If you take Peirce's
own algebra of identity and close it under inverses, there is an
operation that merges two binary links into a trinary one, so that
irreducibiity fails. And in any case the logical conclusion only
follows if you restrict yourself to algebraic notations: as soon as
you allow quantification into the language, everything can be said
using binary and unary relations, as has been well-known now for
about 50 years or more. So for this particular issue, don't bother
with the library: just ignore it. It has absolutely nothing whatever
to do with modularity.
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, so that relations (including that of
identity) had a kind of intrinsic associated 'atomic number', from
which it follows that the relation of two things being identical has
to be different from that of three things being identical. This
particular analogy was similar in some ways to Kepler's idea that the
planetary distances from the sun arose from packing the regular
solids into nesting spheres: neat, ingenious, apparently successful;
but wrong.
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