Biology Reference
In-Depth Information
3.1 Modularity
I have referred to the development of Simon's scheme of causal representation as
the
structural account
of causation. While I will not discuss it in detail here, a
causal structure is, I believe, essentially what some philosophers mean when they
refer to
mechanisms
. A causal model is thus the representation of the workings of a
mechanism. The account is “structural,” in a formal sense, in that causal order
depends on nonunique functional relationships among variables acquiring a unique
form or structure through the specification of the parameter space. But what
are the appropriate semantics? That is, how in reference to the world - that is, in
reference not to the representation but to what it represents - should we under-
stand the parameters? A natural reading, suggested by Simon's notion of an
experimenter's ability to control or intervene directly to set parameter values, is
to regard parameters as the loci of interventions. Such an interpretation points to a
similarity to Woodward's (
2003
)
manipulability account
of causation. While the
similarity is genuine, we should distinguish the structural account from the manip-
ulability account.
Although Woodward (
2003
, Chap. 2) provides a detailed and nuanced develop-
ment of the manipulability account, the essential point is conveyed in his definition
of a
direct cause
:
(DC) A necessary and sufficient condition for
X
to be a direct causes of
Y
with respect to
some variable set
V
is that there be a possible intervention on
X
that will change
Y
(or the
probability distribution of
Y
) when all other variables in V besides
X
and
Y
are held fixed at
some value by interventions. (Woodward
2003
, p. 55)
7
Despite Woodward (
2003
, p. 39) regarding causation as fundamentally a type-
level relationship among variables, (DC) defines direct cause in terms of a token-
level action - an intervention. For example, an intervention on the variable
B
in
Fig.
3.1
would set
B
to a particular value, say,
B
b
, and holding it fixed at that
value amounts to wiping out or breaking the arrow from
A
to
B
, indicating that no
change in
A
is allowed to affect
B
.
B
is a direct cause of
C
, according to (DC)if
C
changes (or would change, the intervention being conceived of counterfactually)
as a result of this intervention.
Pearl (
2000
, p. 70) represents interventions by the operators “set(
X
)” or “do(
X
).”
Woodward (
2003
, pp. 47-48) notes “
X
and set
X
are not really different variables,
but rather the same variable embedded in different causal structures
¼
” After the
intervention, we can represent Fig.
3.1
with a new graph as in Fig.
3.2
. The
transition from one graph to the other - from one causal structure to another -
presupposes that the wiping out of causal arrows without affecting other parts of the
graph makes sense. Woodward refers to the property that warrants such an inter-
vention as
modularity
:
...
7
I have written V where Woodward writes V, to remain consistent with the notation of Sect.
2
above.
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