Re: Whole and Parts (and boundaries)
I received another offline note that raises some
serious questions about ontology and its goals:
> Boundaries sometimes "have width" and sometimes don't.
> It depends on whether you are talking about a physical
> object (e.g., a river, or a line/curve on a graphic)
> or not. Sure it depends on context. But those two
> alternatives, as far as I can see, are the only
> contextual alternatives that matter.
There have been several issues in this discussion. It
began with the question of applying mereology to the study
of boundaries. The major point I was trying to make is
that the use of high-powered formalisms in this subject
is not only irrelevant and useless, it is positively bad:
1. It is bad physics: In the real world, there is *never*
a boundary that is infinitely thin (i.e., a mathematical
point, line, or surface). Two objects *never* meet or
share an infinitely thin boundary. And there is *always*
a finite boundary layer, ranging from several meters in
the case of rivers and oceans down to a microscopic level
where atoms and sometimes larger pieces, such as paint,
bacteria, or grains of sand are in an ambiguous state of
belonging to either, both, or neither of the objects.
2. All boundaries are by fiat: The obvious cases of fiat
boundaries are mathematically straight lines (or geodesics)
specified by latitude and longitude, but even the so-called
"natural" boundaries are natural only for some purpose,
such as serving as a defensible border against an army.
The purpose is fundamental to both the choice of boundary
and its "natural" thickness.
3. It is bad for artificial intelligence: People *always*
consider the purpose in any reasoning that could be
called common sense. Any attempt to avoid purpose by
using complicated formalisms has no relevance to the
way people think and would actually lead any formal
reasoner to make blunders that any human being with
any common sense would avoid.
In short, I would say that (a) every boundary is by fiat and
(b) the width of the boundary is whatever the person who chose
the boundary decided was appropriate. This point emphasizes
the centrality of purpose or intention to any and *every*
study in ontology. In fact, purpose is the primary criterion
that distinguishes ontology from pure math or physics.
It is possible to do physics independently of anyone's purpose,
intention, or application, but ontology *must* come to grips
with the relationships of the observer, actor, and interpreter
with the subject matter. Otherwise, it's pure physics. (And
even in physics, quantum mechanics raises serious questions
about how the observer is related to the subject matter.)
In short, any attempt at ontology that does not come to grips
with the way people perceive, act upon, think about, or talk
about the subject matter is either physics or it is irrelevant
to anything, *especially* to the problem of designing intelligent
machines.
(Actually, I think that even papers that apply high-powered
formalisms to ontology do have a purpose: they enable the
authors to get papers published in philosophy journals that
would be rejected by any respectable journal of physics or
mathematics. However, that is not a purpose I would condone.)
John Sowa