SUO: Re: Thirdness
Pierre,
It is always possible to analyze and represent
things in many different ways.
PG> So, if one tries to follow your talk here, one should
> realize that the axiom really involves a quaternary
> relation - past this hypostatic experience - the
> relation is between a relation (hypostatic-abstracted),
> and the three terms involved in the above statement.
> So transitivity-sort-of-seen-as-a-relation is
> quaternary, not triadic.
You can look at it that way if you wish. But as the
theorem says, any quaternary (or tetradic) relation
can be decomposed into triadic or dyadic relations.
In this case, you can think of the two-line definition
below as a triadic relation that links the property
named "transitivity" to a relation R and an axiom
that states a constraint on R.
Then you can think of the bottom line as
a statement that holds for any triple x,y,z.
JS> Yes, transitivity is a property of relations -- i.e., it is
> a metalevel property. It may be considered as a one-word
> abbreviation that a certain axiom applies to a relation:
>
> For any relation R, transitive(R) <=>
>
> (Ax)(Ay)(Az)((xRy & yRz) => xRz).
The only claim is that if an irreducible triad appears
in one analysis, you can't get rid of it by reanalyzing
the same situation in some other way. You might hide
it or ignore it, but you can't represent the total
information without having a triad somewhere.
PG> The way you use this whole thirdness thing on the SUO
> really seems to reduce to a convoluted way of saying that
> there are ternary relations. Do we really need to engage
> in Peirce's exegesis to make that claim?
Peirce's analysis provides much more than the recognition
that there are irreducible triadic relations. He also
showed some very important areas where triadic relations
naturally occur, and he analyzed and classified the types
of participants that occur in those relations. Following
are some of them:
1. Relations that involve signs, representations,
or languages, natural or artificial.
2. Relations that involve purpose or intentionality,
or as Aristotle said "telos" or goal.
3. Relations that involve feedback mechanisms in
engineering (which are actually special cases
of #2, in which some engineer designed some
apparatus -- such as a thermostat, alarm clock,
cruise control, or toilet tank -- which embodies
a triadic relation that achieves a preset goal
of some human agent).
An analysis such as this is important for several reasons:
a) Peirce tells the ontologist to look for triadic
relations in such circumstances.
b) He also classifies many of those relations
and the types of participants in them, which
would give the ontologist a head start in doing
the analysis.
c) And he tells the reviewer that if some ontology
that deals with such topics does not have triadic
relations, then there is probably something
missing, hidden, or implicit.
My primary claim is that people who do ontology
should learn something about their subject. And
Peirce's work is one place to learn -- not the
only one, but an important one.
John Sowa