Whole and Parts
The thread on mereology and set theory started
from Avril's note and her comments that the
member-of relation in set theory is useful
for modeling part-whole relations.
In an offline note, Gary Richmond mentioned
Peirce's discussion of the various kinds of
part-whole relations. I decided to put that
selection on my web site, since it is a very
good reminder that there is a lot more to
the part-whole relation than just what could
be modeled by the member-of relation:
http://www.jfsowa.com/peirce/whole.htm
Whole and Parts
A serious limitation of both set theory and most
versions of mereology is that they are purely
extensional theories: two sets are considered
identical if and only if they have exactly the
same members. But many of the kinds of part-
whole relations that Peirce (and others) address
depend on modal or intentional relationships.
Note that Peirce introduces semiotic issues,
because some of his kinds of part-whole relations
are defined in terms of signs. That is one way
of handling modal and intentional issues.
John Sowa