SUO: Re: Policy On Substitutions

[Jon Awbrey <jawbrey@oakland.edu>]

Robert Meersman wrote:
> 
> At 12-02-01 13:00, Jon Awbrey wrote:
> >
> > Where was I!?  Oh yes, we have this ability to capture the "forms" --
> > the very forms, no more, no less -- of the objects that are dreamt of
> > in our ontologies, in the forms of various classes of signs and ideas,
> > among the most important of these being the brands of classes and the
> > classes of classes that we dub "equivalence classes" and "partitions".
> 
> ### I vote "yes".   :-)
> 
> --Robert Meersman
> =============================================================
> Prof Dr Robert A Meersman                         VUB STARLab
> Department of Computer Science     Vrije Universiteit Brussel
> Bldg. G-10, Pleinlaan 2               B-1050 Brussels Belgium
> phn (+32|0) 2 629 3308                 fax (+32|0) 2 629 3525
> http://www.starlab.vub.ac.be/staff/robert/                 
> =============================================================

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Robert,

Uh oh, did somebody call for a re*vote while I was snoozing, again!?

Well, whatever, given the freedom of interpretation that
I elect for myself, I will take this as an affirmation
of sorts, and consider myself encouraged to proceed.

Let me re*cite a simple example that I have used on many previous occasions,
by way of illustrating this re*constitutional and re*constructional theme
in a nigh unto trivial, but not completely trivial, concrete instance.

In the "Story of A and B", the "object ontology" (OO) is very simple:
it consists of the two objects A and B, and thus, in one perspective,
could be represented by a lattice or a partially-ordered-set (poset),
that is, the order that is generated by a set {A, B} of two elements:

|        {A,B}
|          o
|         / \
|    {A} o   o {B}
|         \ /
|          o
|          ø

In the highly restrained language that A and B are allowed to use in order
to talk about "what there is to talk about" in their universe of discourse
X = {A, B}, they have only the set of four signs S = {"A", "B", "i", "u"}
in what we are calling their "syntactic domain", consisting of the signs
that can appear in either of two roles in their associated sign relations,
as "initial signs" in the relational domain S, or as "interpretant signs"
in the relational domain I, which is identical as a set to S in this case.

Each interpreter, A or B, induces a "semiotic equivalence relation" (SER),
also called a "semiotic partition" (SEP), on their common syntactic domain
S = I = {"A", "B", "i", "u"}.

For interpreter A, the SEP is given by {{"A", "i"}, {"B", "u"}}.
For interpreter B, the SEP is given by {{"A", "u"}, {"B", "i"}}.

This may seem like such an easy thing to contemplate, but it's the very sort of
lesson that Tarzan has to learn before he can get out of the Jungle -- the jury
is still out, of course, on whether that was really all that much of good thing.

The point that I have been struggling to make, and not just for the sake of this
absurdly impoverished case, but for what it suggests about the general situation,
is that each of these SEP's or SER's, each in its own concretely distinctive but
abstractly isomorphic way, "mimics" the structure of the bare objective ontology
that they share in common between them.

| For Interpreter A:
|
|        {{"A","i"},{"B","u"}}
|                  o
|                 / \
|    {{"A","i"}} o   o {{"B","u"}}
|                 \ /
|                  o
|                  ø

| For Interpreter B:
|
|        {{"A","u"},{"B","i"}}
|                  o
|                 / \
|    {{"A","u"}} o   o {{"B","i"}}
|                 \ /
|                  o
|                  ø

In summary, I think that the basic strategy that is illustrated here
is very typical -- arch-typical?  proto-typical? -- of how we manage
to recover the structures of the ontological object domains of major
interest in our world by messing about with the data, the signs, the
texts, the theories, and so on, that we constellate round about them.

Jon Awbrey

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