Identity, Structure, and Causal Representation in Scientific Models - Mechanism and Causality in Biology and Economics - page 47

Fig. 3.3 The causal structure
of Cartwright's carburetor

X

g 1

g 2

G A

s 2

s 1

S T

γ ¼ γ geometry of chamber ; ... ð Þ; ð 3 : 24 Þ

σ ¼ σ ð geometry of chamber ; ... Þ: ð 3 : 25 Þ

The system of equations can be represented in a causal graph as in Fig. 3.3 .An
oddity of Cartwright's exposition is that each of the principal equations has only
one coefficient. I do not think, however, that any of her critical points hang on that,
so I will treat them as vectors:

σ 1 σ 2 ]. In Fig. 3.3 , the elements
of these vectors are listed alongside the appropriate causal arrows as indices of the
strength of the influence of each cause over its effect. 10
Cartwright's point is that modularity requires that each cause can be intervened
upon separately. So, for example, if we wish to change A , we have to change

γ ¼ [ γ 1 γ 2 ] and σ ¼ [

σ .

A change in can be achieved through a change in the geometry of the chamber,

but that necessarily changes

σ

as well; so the causal relationship of G and A to X is
neither distinct nor invariant with respect to that of S and T to A . Modularity fails.
(As indeed it does in the closely analogous monetary-policy example of Eqs. ( 3.13 )
and ( 3.14 ).)
The representational conventions of the structural account force us to take a
stand on some of the details of Cartwright's example. First,

γ

are not
parameters as we have defined the term (see fn. 8). Their interdependence violates
the Reichenbach Convention. We must decide, then, whether they are variables or
simply coefficients (a shorthand way of grouping parameters that interact with a
variable when writing a function). Second, the “geometry of the chamber” is
unlikely to be characterized by a single variable or parameter. In practice, the
most natural way of representing it would be as a set of interrelated variables
governed by parameters that conform to the Reichenbach Convention. Imagine
representing the geometry in a computer-automated design program. The designer
can set various parameters independently to generate various shapes that constitute
the “geometry of the chamber.” Aspects of that geometry (which can be represented
as causally salient variables) are what feed into Cartwright's “causal laws” through
γ

γ and σ

.
Figure 3.3 , or even a more elaborate diagram, is too coarse to represent the
refinements to the causal structure of the carburetor needed adequately to flesh out

and σ

10 This makes the inessential, but in this case harmless, assumption that the equations are linear in
variables.