Re: Whole and Parts (and boundaries)
Gary and Azamat,
The idea of using excruciatingly formal mathematics to
axiomatize "common sense" independent of any specific
application is not only misguided, it destroys any hope
of practical application and even intellectual honesty.
GBC> A place to start might be Peirce's spot puzzle–
> “Which color is the line of demarcation between
> a black spot and a white background? (1893, p. 98)
>
> Is this metaphysical speculation or of ontological interest?
> I think it exposes some assumptions and pragmatically tests
> our conceptualization.
I would say that it depends entirely on the application.
Peirce was using the example to illustrate a mathematical
principle, which is OK if you are doing mathemtics. But
if you are trying to formalize anything for the purpose of
reasoning about some practical problem, you cannot answer
that question independent of the application.
As an example, I would cite the discussion by Achille Varzi,
who is a smart man who has done some decent work. But his
discussion of Peirce's question is totally useless for any
serious work on knowledge representation:
What color is it? Suppose we proceed along a path connecting
the interior of the spot with the exterior. Clearly, given
the density of the continuum, we do not pass through a last
black point x and a first white point y; otherwise we should
have to admit an infinite number of further points between x
and y which would somehow be neither black nor white.
Source: http://www.columbia.edu/~av72/papers/Topoi_2001.pdf
The first question to ask is why do you care? What kind of
spot are you looking at? A spot on an illustration in a book
printed on paper? What kind of paper? How smoorh is the
surface? Or is it a spot to be displayed on a computer screen?
At what resolution? Dithered or not? Or a spot painted on
canvas? In oil? Or acrylic? How thick is the brush? How
many layers of paint? What do you really want to know? Why?
All talk of a continuum with infinitely many points is sheer
nonsense. You have to look at the application, the medium, and
the purpose. Otherwise, all that discussion is pure garbage.
It is worse than a waste of the author's time because it is
wasting the time, effort, and very expensive tuition of innocent
students who are hoping to learn something worthwhile.
If you need more examples, look at the paper by Smith & Varzi
in which both of them are discussing that example and other
related ones:
To be sure, natural language does not distinguish between true
topological contact (or connection, as we may also say) and mere
physical closeness. We have seen that as far as the bona fide
outer boundaries of John and Mary are concerned, no genuine
topological contact is possible at all. In general, the surfaces
of distinct physical bodies cannot be in contact topologically,
though the bodies may of course be so close to each other that
they appear to be in contact to the naked eye.
http://ejap.louisiana.edu/EJAP/1997.spring/smithvarzi976.html
This short excerpt is not merely false. It shows that two intelligent
people are capable of producing garbage and getting it published by
other intelligent people and thereby misleading some untold number
of readers who are hoping to learn something.
Two reasons why it's false:
1. Complete misunderstanding of the nature of natural language:
"natural language does not distinguish..." It is not the
role of any NL to "distiguish" anything. The basic purpose
of NL is to express any and every distinction that anybody
chooses to make for any purpose under heaven. It is the
role of the speaker to distinguish, not the language.
2. Incredible ignorance of physics: "In general, the surfaces of
distinct physical bodies cannot be in contact topologically..."
Two physical bodies, such as two billiard balls colliding or
two people shaking hands, *most definitely* come into contact,
in the sense that some proportion of atoms, molecules, and
electrons of each are interacting with, interpenetrating each
other's fields of force, and even being transferred from one
body to the other. You don't even have to go down to the
atomic level -- contact and transfer occur at the level of
sweat, DNA, bacteria, cosmetics, and other things most people
would rather not think about.
GBC> I agree with Smith and Varzi that these types of puzzles
> “serve together to call into question the (naive) realist
> attitude towards boundaries,”
No. Most people who have never studied philosophy have a much
better understanding of boundaries than anything in that paper.
Summary: I believe that philosophy, linguistics, logic, physics,
and other subjects are very important sources for ontology and
knowlegede representation. But nobody can represent common sense
unless they *have* common sense. And the first questions that
anybody with any common sense must ask are the basic questions
of pragmatism: What is your application? And what difference
would any answer to these questions make in what you actually do?
John Sowa