Chemistry Reference
In-Depth Information
8.3 The Basic Principles of Mereology
To explain and make plausible the principles of mereology for the thinking in any
disciple one could illustrate their meaning by setting out a range of examples of
their use in making sense of the phenomena in a certain domain. However, since the
early part of the twentieth century it has become popular to try to express such
principles in terms of some well-established formal system. The system of choice
for displaying mereological principles, such as those enunciated by Stanislaw
Lesniewski, as presented by Srzednicki and Rickey (
1984
) has been set theory.
Lewis (
1991
: 1) proposes the term
for any whole composed of some parts.
There is a unique being which is the
fusion
of a collection of beings which consists of only
these beings. For example a particular chemical molecule is such a being.
fusion
'
'
He notes that these parts might be atomic or they might be arbitrary bits of some
sort of
. As we will see mereology in chemical thinking has made
use of both. This definition expresses the way that certain collections of atom-cores
behave as individuals and so can be considered parts of higher order entities. Water
molecules, in the commonest aqueous form of H
2
O, are fusions of hydrogen and
oxygen atom-cores and as such are parts of lakes and oceans.
The basic steps to a formal treatment of mereology were taken by Stanislaw
Lesniewski
'
s mereology (Srzednicki and Rickey
1984
) is a basic system of rules for
valid reasoning about wholes and their parts. David Lewis carried through the
mapping of intuitive mereological rules onto the formal system of set theory.
To do so he began with two definitions (
1991
:73).
'
atomless gunk
'
D1: X and Y
overlap
if and only if they have some common part. If and only if not,
they are entirely distinct.
D2: Something is a
fusion
of some things if and only if it has all of them as parts and
has no part that is distinct from each of them.
From these definitions we can derive the notion of
part
.
Xisa
part
of Y if and
'
'
'
only if everything that overlaps X also overlaps Y
.
'
Lewis
s axiom for mereology are similar to the original proposals of Lesniewski.
'
Axiom 1 Mereological transitivity: If X is a part of some part of Y and then X is a
part of Y.
as a unit such as NH
3
plays a similar role to an atom-
core in the constitution of a molecule such as ammonium chloride. By mereological
transitivity the hydrogen atom-core which is part of the radical is also part of the
molecule and is treated as such in its many roles in chemistry.
Lewis added two more axioms:
The concept of
radical
'
'
'
whenever there are some things, then there
exists a fusion of those things
it never happens that the same things have two
different fusions
'
. These axioms seem to be a poor fit to the way chemical wholes
are fusions. They do not distinguish between structured wholes such as ammonia
molecules and mass wholes such as ammonia gas. How do we incorporate enan-
tiomorphic sugars into the scheme? It seems that structure is an ineliminable
and
'
'
