ONT Re: Modus Ponens
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JA = Jon Awbrey
JD = Jean-Luc Delatre
MW = Matthew West
JD: Some of the "assumptions" that, to me, seem questionable and shared by
most people involved in ontology projects (alas, not only SUO!) are:
JD: 1) There exist ultimately a *perfect* all encompassing ontology that allows
describing everything, and we have to chase for it however distant it be.
JA: the problem is not thinking it exists ---
the problem is not having to chase it - -
the problem is thinking one's arrived ---
MW: I agree very strongly with this. You can only have arrived after
gaining complete knowledge of the world, which I guess will not
happen within the next century (ever the optimist).
Yes, indeed, and one of the reasons I that adduced
the subject of topology to our topicological space
here is just the circumstance that you remarked on
a while ago, now tucked away in my "unfinished biz"
file, where I had been getting around to extending
the discussion like so:
I see that I still need to write up a clearer
exposition of the whole adic/tomic problematic.
JA: I am not especially interested in the tangle between
3-dim and 4-dim, as I think that it's a mistake to
get trapped in such diminished dimensionalities,
but the problems to which you point here do
illustrate a vastly more generic issue that
affects the whole way some people seem to
make use of ontological forms of thought.
JA: I have discussed this before under the heading of the contrast between
k-adic and k-tomic thinking, the difference between thinking in k axes
and thinking in k parts of a partition of the universe, that is, parts
that are thought to be mutually exclusive and possibly exhaustive sets
or classes or categories or whatever.
JA: For a maximally generic example, let's say you have divided the world
along the lines of "abstract" versus "physical" or "logos" & "physis" --
what then? doing this, the way some people do it, anyway, completely
misses the utility of mathematics in talking about objective reality,
which is bound up in the recognition of the synthetic unities of form
and matter, in which thinkers as early as Aristotle were sufficiently
well-versed not to be saying the silly things that we hear hereabouts
on a daily basis.
MW: The critical point behind what I was trying to convey is that different ways
of looking at the world will actually discriminate different objects in it.
I think it is a useful lesson to ponder on how arbitrarily different the
way we see the world can be.
!
@
-|- <<<---<<< nail on the head sign
/ \
JA: Let me try another example: particles versus waves.
you can say that there is a particle-view and a wave-view.
what there really is -- the real object of nature's ontology --
that is likely beyond our comprehension, but we have to work
with the glimpses that we have in the process of seeing more.
But if you go ahead and write down an axiom for "wave" that
says "not a particle", then you have rendered the concepts
logically incompatible -- in your own mind -- whereas
nature may not care a fig what you write or think.
MW: Indeed. Historically I come from the data modelling arena, and I have
spent much time reviewing over constrained data models that prevented
the business from doing what it really needed to. So I have tended
to be conservative (or perhaps I mean liberal) when it comes to
defining axioms (constraints to everyone else).
JA: I am not a person who says that all reality is constructed by us --
even if there are definitely some realities that we do construct --
but i am a 'constructive thinker' in the sense that i would say that
we construct our knowledge of things, and the raw materials of that
construction are called 'signs', which for me includes concepts and
the data of experience. And we organize our thoughts in such a way
that we might as well go ahead and say that we are often talking
about this or that abstract, formal, hypostatic, or ideal object,
like numbers, propositions, spaces, etc. And then the question
becomes: how do these formal, logical, mathematical objects
compare with the real objects and problems that nature,
including our own nature, keeps tossing our way?
JA: Now, with regard to viewpoints, John Sowa was
careful to say in his knowledge rep book that:
| The physical/abstract distinction is
| independent of the observer's viewpoint,
| but the continuant/occurrent distinction
| depends on the choice of time scale.
|
| John Sowa, 'Knowledge Representation', page 71.
JA: I would probably agree with the latter half of that,
and worry a while what the former half depends on,
but a relative distinction is a different sort
of thing from an absolute distinction, TWISI,
at least from my current POV.
MW: Hmmm. Well maybe, but you can still construct the
two world viewpoints that Pat identifies, and they
are still logically incompatible (i.e. at least
some objects of one cannot be in the other).
JA: The question is: Are these real objects or imaginary objects?
Put another way: Are the objects of these opposed predicates
real beings that have their own properties independent of the
theoretical model, or nothing more than constructed entities
and ideal fictions that live but for the grace of the model
space and thus have only those properties that we grant to
them, to the extent that our gratuities are consistent?
JA: Another example: the three post-classical geometries:
elliptic, hyperbolic, parabolic. Three relatively
consistent geometries -- as we gather from being
able to build a model of each geometry inside
each one of the other two geometries -- but
there can be at most one that holds true
of 'the' physical geometry of space.
Which is it? Probably none of them!
Physical space is turning out to be
much weirder than anybody dreamed
just a few years ago. So the
utility of each geometry has
to be evaulated on another
basis than the very idea
of its being supreme.
MW: This may just mean that at least one of them is
sufficiently far off the mark that it should be
considered a "bad" model (e.g. earth, fire, and
water as the elements). Alternatively you can
do what we do with waves and particles, and say
that they are both useful models, and there is a
relationship between some waves and some particles,
whilst not pretending that waves are particles, and
that there may be some underlying reality that we
have yet to discover that will reconcile them.
JA: And what is the method for comparing models with realities,
and by this comparison telling the good from the bad model?
There's the rub!
But the thing that exhibits the properties of a particle
is the same thing that exhibits the properties of a wave.
The way that I personally think of this distinction is in terms
of category theoretic factorization diagrams like the following: ...
[the account trails off at this point ...]
With that refresher,
maybe I'll now remember
what I was going to say ...
Jon Awbrey
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