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Fig. 3.2 Causal graph of
Fig. 3.1 after the intervention
set (
B= b
)
C
A
b
a system of equations will be modular if it is possible to disrupt or replace (the relationships
represented by) any one of the equations in the system by means of an intervention on (the
magnitude corresponding to) the dependent variable in that equation, without disrupting
any of the other equations. (Woodward
2003
, p. 48)
And while he recognizes that representations of causal relationships may not
always display modularity, he assumes
that when causal relationships are correctly and fully represented by systems of equations,
each equation will correspond to a distinct causal mechanism and that the equation system
will be modular. (Woodward
2003
, p. 49)
Cartwright (
2007
, part II) objects to modularity as an essential feature of
causation.
8
The structural account illuminates both what is right and what is
wrong in Cartwright's objections. Cartwright denies that all well-defined causal
systems are modular. And she is correct. We should notice, first, that the system
defined by Eqs. (
3.13
) and (
3.14
), which has a well-defined causal order on the
structural account, is itself not modular, since the individual equations do not
represent distinct mechanism, but can function only as a pair (see Hoover,
2011
,
section 16.3.2). Cartwright herself argues largely through counterexamples. The
first example is a carburetor (Cartwright
2007
, pp. 15-16). Cartwright describes the
operation of the carburetor through a system of equations in which key coefficients
depend on the geometry of its chamber
9
:
we can see a large number of [functional] laws all of which depend on the same physical
features - the geometry of the carburettor. So no one of these laws can be changed on its
own. To change any one requires a redesign of the carburettor, which will change the others
in train. By design the different causal laws are harnessed together and cannot be changed
singly. So modularity fails. [Cartwright
2007
, p. 16]
Cartwright illustrates her point with a set of causal laws from which I reproduce
two (in an altered notation):
X
(
h
ð
G
;
A
;
γÞ;
ð
3
:
22
Þ
A
(
j
ð
S
;
T
;
σÞ;
ð
3
:
23
Þ
where
X
¼
gas exiting the emulsion tube;
G
¼
gas in the emulsion tube;
A
¼
air
pressure in the chamber;
S
¼
suck of the pistons;
T
¼
throttle valve; and
8
Cartwright's chapters are her side of a vigorous debate over modularity carried on with Hausman
and Woodward (
1999
,
2004
).
9
I write “coefficients,” not “parameters” as Cartwright does, since she assumes that they are
functions of other things, violating the usage established in Sect.
2.3
above.
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