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In invoking causes and effects, these definitions are not circular, since whether
or not the relevant causal relationships exist can be determined from the parame-
terization of the system in line with our elaboration of Simon's structural account. 6
When variables are distinguishable because we possess independent means of
measuring, observing, or characterizing them, a failure also to be causally distinct
will be rare. Causal identity is more likely to be a property of an impoverished
representation of the world, arising most naturally in cases in which a few variables
stand in a tight relationship. Causally, identity will rarely arise in nondeterministic
cases, as the variables that describe such cases are, in general, subject to “shocks”
that distinguish one from another. However, models are nearly always highly
simplified, and shocks that are small enough in the world may be neglected in a
model, so that, if the world produces “near causal identity,” a good model of the
world may produce exact causal identity (cf. Suppes 1970 ,p.33on
- direct cause).
Similarly, in selecting a simplified representation of the world, we may choose to
ignore some ways in which variables could be causally distinguished - again,
producing causal identity in the model.
There is one type of case of causal identity that is not rare, but a pitfall to be
carefully avoided. Conceptual identities or variables that are “equal by definition”
belong to a special class of causal identity that does not depend on modeling
choices but on the meaning of the variables. For example, the price (per dollar of
coupon payment) of a perpetual bond or consol ( P C ) is, by definition, the inverse of
its yield ( R ): P C
ε
1/ R . Anything that affects the yield affects the price; yet we
should not regard these variables - conceptually different and with different units of
measurement - as causally related. A system of equations that embedded this
identity would, according to our definitions, find P C and R to be causally identical
and, therefore, not stand in any other sort of causal relationship with each other.
This is exactly as it should be.
3 The Structural Account Versus the Manipulability
Account of Causation
So far the discussion of causal order has been formal. But the importance of a
representational scheme arises from its power to illuminate genuine scientific
issues, a matter to which we now turn.
6 Causal identity can be thought of as a metaphysical property of the world and as a property of a
model or representation. Elsewhere I have argued in favor of a perspectival realism in which a
successful model tells us the truth about the world from a particular point of view (Hoover 2012b ,
see also 2012c ), which reduces the force of a distinction between the metaphysics and the
properties of the model.
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