Reduction and Elimination in Philosophy and the Sciences

do not pick out pain in a system by considering whether a
property causes “P” to appear on a cerebroscope. Further,
instances of pain with a realizer other than P may not
cause “P” to appear on a cerebroscope. But we cannot
conclude from this that pain in humans does not have this
power. For example, presumably pain in humans causes
aspirin seeking behavior. Yet it is doubtful that this will
feature in a functional characterization utilized to pick out
pain in a system; likewise, pain does not contribute this
power to nonhuman systems. But just as we cannot
conclude from this that pain in humans does not cause
aspirin seeking behavior, we should not conclude from like
considerations that pain in humans does not cause “P” to
appear on a cerebroscope. Analogous considerations can
be advanced in response to the other cases put forward in
favor of S1, 2 and it thus remains open for the reductionist
to contend that he has not been given adequate reason to
relinquish his thesis that a realized property inherits the
powers of its realizer in a system.
4. An Eliminativist Response
Suppose that in at least some cases a realized property
only has a proper subset of the powers of its realizer in a
system. Contra Shoemaker, this does not entail S3. This is
because S3 does not follow from S2, since S2 does not
rule out nonconservative eliminativist reduction. That is,
the nonreductive import of the subset view comes entirely
from the claim that where the powers of M are a proper
subset of those of P, M cannot be identified with P. However,
the reductionist can reject the assumption that reduction
requires identities and maintain that if we cannot identify
realized properties with realizers, we should consider
the possibility that there are only realizers. While this is not
ontologically conservative, it can be considered a form of
reduction, given its contrast with more radical versions of
eliminativism.
This eliminativism is motivated by noting that under
the subset view, realized properties are superfluous in that
all effects brought about by realized properties are
redundant, since they are also brought about by realizers.
Now, Shoemaker and Wilson have argued that this should
not be regarded as objectionable overdetermination
(Shoemaker 2001 and 2007, Wilson 1999). But whether
this overdetermination is objectionable is beside the point,
since the reductionist can appeal to parsimony to support
his commitment to exclusively realizer properties. 3 This
amounts to the suggestion that we cease to take those
proper subsets of the powers of realizer properties
associated with realized properties to determine any such
properties.
Further, this eliminativism does not require denying
that systems have the powers associated with realized
properties. For example, we may have to deny that there is
a property of human pain determined by a subset of the
powers of pain’s realizer in humans. But this does not
require denying that the relevant systems have the powers
associated with pain; rather, the claim is just that these
powers do not determine a property. That this
2 For example, Shoemaker and Wilson, following Yablo 1992, consider the
case of Alice, a pigeon conditioned to peck at scarlet things but not at shades
of red other than scarlet, and argue that scarlet thus has at least one power
not possessed by red: the power to produce a pecking response in Alice
(Shoemaker 2001 and 2007, Wilson 1999). But even if this power is not ordinarily
associated with red and shades of red other than scarlet do not have
this power, this does not rule out taking red to have this power in virtue of
being realized by scarlet in the system in question.
3 This is similar to the reductionist argument recently presented in Gillett 2007.
Functional Reduction and the Subset View of Realization — Kevin Morris
eliminativism does not require denying that systems have
the powers associated with realized properties arguably
provides a basis for taking such systems to satisfy
functional concepts even if we cease to regard the powers
in question as determining functional properties. 4 While
this is not conservative, it is not the more radical sort of
eliminativism under which systems just do not have the
powers associated with eliminated properties (Churchland
1979). Nor does it entail that the concept of an eliminated
property cannot be useful, since certain powers could be
of interest for epistemological and pragmatic reasons
without these powers determining a property.
5. Conservative Reduction under the
Subset View
While nonconservative eliminativist reduction is a viable
response for the reductionist, the subset view does not
entail that realized properties cannot be conservatively
reduced via identities. Even if S1 entails S2, it does not
entail the following:
S4. There is no physical property Q such that Q = M.
This is because even if S1 entails that M cannot be reduced
to its realizer P, it does not entail that M cannot be
identified with some physical property Q determined by a
proper subset of the powers of P. To get S4 from S1, we
need the following:
S5. For any realized property M, if there is a physical
property P such that M = P, it must be the physical
property that realizes M.
This says that if a realized property is reducible via identities
at all, it is reducible to its realizer. Given that S1 entails
S2, S1 and S5 together entail S4. But if we assume, in
contrast to the eliminativism just sketched, that some
proper subset of the powers contributed to a system by a
physical property determines some other property, the
question is why this latter property should not itself be
regarded as physical. Thus we can consider two theses:
R1. Possibly, M is realized by a physical property P
but is identified with Q, where Q is a physical property
determined by a proper subset of the powers of
P.
R2. If a proper subset of the powers of a physical
property P determines a property M, there must be
a physical property Q determined by this set such
that M = Q.
If R1 holds, then S5 fails and so we do not have a valid
argument for S4. The truth of R2 entails the falsity of S4.
While both R1 and R2 are in need of an argument, nothing
in the subset view entails even the falsity of R1, which is to
say that the subset view does not entail S5 and so S4.
This means that the subset view at most implies that realized
properties cannot be reduced via identities to realizers.
4 This is similar to the eliminativism that reductionists have advanced in response
to multiple realization: given the reduction of M in S to P, M in S* to P*,
and so on, we should consider the possibility that there is no structure unrestricted
property corresponding to our concept of M (Kim 1998, Lewis 1980).
However, given that there is M in S, M in S*, and so on, we can arguably take
such systems to satisfy the concept of M.
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