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counterfactual relations that maps out the underlying mechanisms through which
one thing is used to control or manipulate another.” While mechanism is defined
freely in this definition, the general idea of mechanisms developed in various
mechanist accounts can surely apply to it.
With respect to Hoover's description of causal structure, each causal path
between any two variables within a causal structure is represented as an invariant
counterfactual conditional relation. It is called “counterfactual” because it claims
that if there is a “hypothetical” change in (or manipulation of) the supposed causal
variable, then the supposed effect variable will have a corresponding degree of
change. If we represent the causal relation between two variables p and q as the
equation q
represents the degree of change of p in
q , then the adjective “invariant” means that, against the background of a compli-
cated network of the causal structure, whatever unit of change in p there is, the
corresponding effect of
¼ α
p +
ε
, where the parameter
α
degree of change of p in q will “remain unchanged.” In
that case, the fact of invariance can be used as a criterion, as was pointed out by
Herbert A. Simon in his 1953 article, that would permit us to discriminate among
competing structural representations that are consistent with the same set of data.
Based on this view, it is no wonder that Hoover remarks that “causal structure is
characterized by a parameterization that governs the manner in which variables are
related to each other
α
The patterns of relative independence, dependence, and
interdependence among variables—the causal structure—are dictated by the
parameterization” (Hoover 2001 , p. 59). Hoover's structural account of causality
can be regarded as a classic metatheoretical account that aims to characterize
scientists' attempt to use their limited methodological lever—such as the available
statistical techniques—to tease out, from the probabilistic distribution of those
relevant variables, the indications of the answers of causal inquiries. Hoover's
chapter in this volume goes further to explicate the structural approach by
contrasting with Woodward's manipulability account, arguing that modularity —a
critical characteristic of Woodward's account indicating that each equation in a
system of causal relations corresponds to a distinct causal mechanism—fails in
certain cases, because in reality individual equations in a causal structure do not
necessarily correspond to distinct mechanisms. Furthermore, Hoover argues that,
unlike Woodward's manipulability account in which the notion of causality is
defined in token level (causal relations hold among particular events), the structural
account explains causal notion in type level (causal relations hold among variables)
and could be more explanatory for causal relationships in a practical sense.
...
5 Representing Causal Structures and Mechanisms
Given the importance of understanding both causal structures and mechanisms,
there is a need for inquiring into the possibilities of providing epistemological
access and representation to them. One pivotal question concerns whether we can
completely know causal structures and mechanisms. Recall that the notion of
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