Reduction and Elimination in Philosophy and the Sciences

Functional Reduction and the Subset View of Realization
Kevin Morris, Providence, Rhode Island, USA
1. Introduction
Functional reduction is the view that functional, realized
properties are reducible to realizer properties. One way to
challenge this reductionism is to develop an account of
realization under which realized properties cannot be so
reduced. Thus Sydney Shoemaker has argued, and others
have concurred, that it follows from the “subset view” of
realization that realized properties are typically irreducible.
In what follows, I argue that the reductionist can adequately
address the challenges raised by this account of
realization.
2. Reductionism and the Subset View of
Realization
A functional property is one that can be exhaustively characterized,
or defined, in terms of a causal role. Arguably at
least some mental properties are functional in this sense
and it may be that most nonbasic (for instance, biological,
mental, economic) properties can be understood in this
way (Lewis 1972, Chalmers 1996, Kim 1998 and 2005).
Such a property is said to be realized by another in virtue
of the latter play the role individuative of the former. The
reductionist contends that a functional property can be
reduced, in a given system, to its realizer in that system
(Lewis 1972, Kim 1998 and 2005). There are at least two
reasons we might draw this conclusion. First, if a property
M is “second order,” such that having M is defined in terms
of having some other property that plays a certain causal
role, it seems that a system’s having M cannot be anything
beyond its having whatever property P realizes M. Second,
it seems that the causal powers of M—the effects that the
instantiation of M is apt to bring about—will be identical
with those of M’s realizer P in a system. If we adopt even a
weak causal theory of properties under which different
properties cannot have the same powers in the actual
world, we are thereby compelled to identify M in S with P
(Kim 1998).
While there are a number of issues that will
determine whether realized properties can be reduced in
this manner, perhaps the most crucial concerns the nature
of realization. Of the accounts of realization that have been
developed in recent years, Shoemaker’s subset view
arguably presents the most serious challenge to functional
reduction. As on the view just sketched, functional
properties are again defined in terms of causal roles and
again realization consists in a certain relationship between
the role that individuates a functional property and the role
played by some other property in a system. Under the
subset view, however, P is a realizer of M just in case the
effects that the instantiation of P is apt to bring about
include as a subset those that M is apt to bring about
(Shoemaker 2001 and 2007). 1 Shoemaker and Jessica
Wilson have argued that realized properties will typically
1 In Shoemaker 2007, realization is officially defined not only in terms of
causal powers, but also in terms of “backward looking causal features,” what
brings about the instantiation of the properties in question. However, Shoemaker
suggests that the issues here of interest can be addressed by considering
the simpler formulation in terms of powers. Because of this my focus in
what follows will be on causal powers, what Shoemaker calls the “forward
looking causal features” of the properties.
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be irreducible under this account (Shoemaker 2001 and
2007, Wilson 1999 and 2002). This will be the case
whenever the powers of M are a proper subset of those of
P. Since M and P have nonidentical powers, they cannot
be identified; thus M cannot be reduced to P (Shoemaker
2001 and 2007, Wilson 1999 and 2002). Shoemaker
suggests that paradigmatic cases of realization (for
instance, the mental by the neurophysiological) are like
this. Thus we have the following argument:
S1. Where P realizes M, the powers contributed by
M are typically a proper subset of those contributed
by P; thus, in these cases,
S2. M ≠ P; thus, in these cases,
S3. M is irreducible.
I believe that the reductionist can adequately
respond to this argument. First, S1 can be rejected by
maintaining that a realized property inherits whatever
powers are contributed by its realizer to a system and that
Shoemaker does not provide reason to think otherwise.
Second, the inference from S2 to S3 can be challenged by
appealing to the possibility of nonconservative
“eliminativist” reduction. Finally, even if S2 follows from S1,
this does not entail the failure of conservative reductionism
about functional properties.
3. The Subset View and Causal Inheritance
The arguments advanced by Shoemaker and others in
favor of S1 are inconclusive at best. Moreover, the reductionist
can explain why the powers of a realized property
might seem to be a proper subset of the powers of its realizer
even if this is not the case.
First, the reductionist need not claim that the powers
we ordinarily or apriori associate with realized properties
correspond exactly to the powers of any realizer. But it
does not follow from this that every realized property does
not inherit the powers of its realizer in a system (Kim
1998). The picture here is one in which realized properties
are understood in terms of a limited set of powers but in
which we further reason that given that P realizes M in S,
the powers of M in S are identical with those of P, and thus
that M “inherits” the powers of its realizer. This reasoning
is legitimate in at least some cases, as it amounts to the
possibility of discovering powers of realized properties in
addition to those typically associated with such properties.
Moreover, that realized properties are understood in terms
of a limited set of powers can explain why it might seem
that the powers of a realized property will be a proper
subset of those contributed by its realizer even if this is not
the case.
Shoemaker considers several cases in which it
seems that a realizer has powers beyond those of a
realized property. For instance, consider a mental property
M, say pain, and its neurophysiological realizer P in
humans. While the instantiation of both M and P are apt to
cause the subject to wince, it seems that P will have
powers beyond those of M: P might contribute the power
of producing a “P” reading on a cerebroscope attached to
a person’s head (Shoemaker 2001). Now, it is true that we