Re: Whole and Parts
Jack,
In general, I like the idea of using category theory.
But I have some doubts about that particular approach:
> I may have missed it: did anyone mention Barry Smith's
> riff on mereotopology
> http://ontology.buffalo.edu/smith/articles/mereotopology.htm
> pointed to me by Murray Altheim?
>
> I like the blending of mereology and category-theoretic
> thinking. What do others think?
There are two basic problems with that approach:
1. It is an attempt to define parts and wholes in a
purely extensional way. And as Peirce's list of
many different kinds illustrates, the most serious
issues are modal, intentional, and intensional
(with both an S and a T).
2. Barry is trying to characterize boundaries as pure
geometrical surfaces that have no thickness, but every
boundary in the physical world has a definite thickness.
He is pushing formalism for the sake of formalism when
it has no correspondence to either the physical world
or the way that people think about the world.
As examples of the first point, I would refer to Peirce's
discussion of the many different ways of thinking about
wholes and parts. Peirce was talking about sign relations,
which are all fundamentally triadic.
As for the second point, if you want to get into the way
the world is independently of any human, you are talking
about physics, and then you have to deal with physical
reality, which has no such thing as sharp boundaries and
infinitely thin surfaces.
I discuss some of these issues in my paper on Signs,
Processes, and Language Games (see excerpts below).
I also discuss a "debate" in which Barry Smith and
John Searle talked past one another. Smith was trying
to apply his dyadic relations, but Searle said that
Smith kept missing the point:
http://wings.buffalo.edu/philosophy/faculty/smith/articles/dksearle.htm
The Construction of Social Reality: An Exchange
I don't fully agree with Searle, but at least Searle
recognizes the need for triads in order to do anything
at all in analyzing and characterizing human social
relationships. You just can't do it with dyads.
John
______________________________________________________________
Source: http://www.jfsowa.com/pubs/signproc.htm
Signs, Processes, and Language Games
[From Section 2]
One example is Barry Smith (1995, 1998, 1999, 2001), who has struggled
to eliminate mental notions by defining all aspects of human life in
terms of mereological sums of physical objects and processes. His
resulting ontology has two basic categories, continuants (physical
objects) and occurrents (processes), which can be combined by mereology
to form complex entities called physical-behavioral units and social
objects:
* Smith considers Aristotle's early substance-property-accident
view as "common sense" and accepts Strawson's claim that objects are
ontologically prior to processes, because "occurrents require a support
from continuants in order to exist." But as Rescher observed, one could
with greater justification say that continuants are existentially
dependent on the occurrents that generate them and maintain the
conditions necessary for them to continue.
* Examples of physical-behavioral units include "Wendy's Friday
afternoon class, Jim's meeting with his teacher, your Thursday lunch,
Frank's early morning swim." These units are similar to Barwise and
Perry's situations, but Smith prefers the hyphenated adjective because
it makes them sound more "observable" and therefore more "objective."
* Examples of social objects include legal entities such as
"juries, courts, contracts, lawsuits", cultural entities such as "works
of music and literature", and human social groups such as "families and
tribes, nations and empires, but also orchestras and chess clubs,
battalions and football teams, as well as those more or less short-lived
social groupings, which arise when strangers are formally introduced, or
pair up on the dance floor." To ensure that these entities are purely
physical, Smith defines them as mereological sums of rather disparate
conglomerations. A contract, for example, includes not only the signed
piece of paper, but also the people who signed it, the act of signing,
and all the objects and processes involved in fulfilling the contract
throughout its duration. The only things missing from Smith's definition
are the intentions of the people who signed the contract and carry out
its provisions.
Although Smith claims objectivity for his definitions, they violate the
requirements for an effective operational test. His social objects, for
example, include so many physical entities scattered over long intervals
of time that itemizing them on paper is difficult and observing them in
action is impossible. When arguing about a contract in a court of law,
lawyers do not consult the mereological sum of physical actions, but the
propositions stated on paper or uttered by witnesses. In every one of
Smith's examples of social objects, the fundamental requirement that
determines the nature and extent of the physical entities involved is
some sign or structure of signs that may be written in symbols, uttered
by some humans, or embodied in some artifact. In effect, the
mereological sum of physical entities involved in any social object is
"dependent" on the propositions entailed by the constitutive signs of
that social object. A sounder formalization of Smith's approach should
be based on the semiotic processes that involve the people (or other
animals) who create the social objects, use them, and live with them and
in them. As Carnap recognized, the "construction" of the sign relation
from physical objects "is more difficult than any of the other relations
which we have hitherto undertaken." An easier and more fundamental
approach is to start with signs as the prerequisites for any social
entity and to follow the signs to determine what other entities may be
involved.
[From Section 4]
Even more recently, Barry Smith and John Searle debated some issues, or
rather talked past one another about some topics, which could have been
clarified by an application Peirce's trichotomy (Smith & Searle 2001).
Smith began with a criticism of Searle's book _The Construction of
Social Reality_, which he tried to interpret in terms of his own
ontology of social objects. Searle replied
I think in the end he makes many useful points, but I also
believe that he misunderstands me in certain very profound
ways. I believe his misunderstandings derive from the fact
that he approaches this topic with a set of concerns that
are fundamentally different from mine, and in consequence,
he tends to take my views as attempts to answer his questions
rather than attempts to answer my questions.
In Peircean terms, Smith was trying to use the dyadic partOf relation of
mereology to represent fundamentally triadic relations of people, social
institutions, and their purposes. Searle, however, recognized the need
for a triadic relation, which he expressed in the pattern X counts as Y
in context C. This relation gave Searle greater flexibility than Smith's
dyads, but Smith criticized that flexibility as too loose and imprecise.
In particular, Smith noted that a context itself is a social object that
requires some independent definition. Both authors made valid points:
Searle's book illustrates the power of triadic relations for analyzing
social institutions, but Smith's criticism shows the need for greater
precision in distinguishing different kinds of triads. Peirce's
trichotomy is the key to resolving this dispute: instead of using a
single triad, Peirce formulated a metalevel principle for generating
different triads when applied to different phenomena.
When applied to the modes of existence, Peirce's trichotomy generates
three fundamental ontological categories, which correspond to Kant's
triad under Modality: Possibility, Actuality, and Necessity.