SUO: Re: Representation Invariant Ontology
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
RIO. Note 2
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Contemporary notions of objective reality all involve the notion of
invariance under transformation, and this makes the need to discuss
mappings between superficial syntactic systems a constitutive piece
of scientific ontology. By "contemporary" I mean from the times of
Pythagoras in mathematics and Copernicus in physics. The same idea
was stocked on the shelves of AI in the days of McCulloch and Pitts,
and Minsky and Papert, and it was featured in the work of Piaget in
psychology and Levi-Strauss in anthropology, but not everybody will
be expected to be current with the rush of these more recent events.
So let's take the time to refresh our memories and update our views.
For the sake of continuity, we might go back to the type
of situation that was illustrated in this generic Figure:
o-----------------------------------------------------------o
| M |
| |
| o-------------o o-------------o |
| / \ / \ |
| / o \ |
| / / \ \ |
| / / \ \ |
| o o o o |
| | | p | | |
| | U | o | V | |
| | | | | |
| o o o o |
| \ \ W / / |
| \ \ / / |
| \ o / |
| \ | / \ | / |
| o------|------o o------|------o |
| | | |
| | | |
o--------------------|-----------------|--------------------o
| |
f | | g
| |
o--------------------|-----o o-----|--------------------o
| X v | | v Y |
| | | |
| o----------o | | o----------o |
| / \ | | / \ |
| / o | | o \ |
| / / \ | | / \ \ |
| / / \ | | / \ \ |
| o o o | | o o o |
| | | f(p)| | | | g(p)| | |
| | f(U) | o | | | | o | g(V) | |
| | | | | | | | | |
| o o o | | o o o |
| \ \ / | | \ / / |
| \ \ / | | \ / / |
| \ o | | o / |
| \ / | | \ / |
| o----------o | | o----------o |
| | | |
| | | |
o--------------------------o o--------------------------o
Figure 1. Overlapping Coordinate Maps f : U -> X, g : V -> Y
It pefectly conceivable that Agent 1 and Agent 2 might accidentally
in the offing, or deliberately in the end, assign the same names to
the test point p, thereby rendering f(p) = g(p), in the latter case,
where there is a sufficient reason to do so, perhaps conferring the
status of an essential mark, with its attendant aura of ontological
security, upon the label affixed to the point, but I think that all
of us recognize how unlikely such events will in general tend to be.
So there is little hope of finding invariance in the nominal coordinates
of single points. What invariance we find will come from looking at the
relationships that exist among entities, and here I mean relations whose
minimum valence is greater than 1.
Jon Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o