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reducing theory, or, more interestingly, the language and concepts of the reducing
theory to be recast in the language and concepts of the reduced theory.
From here, Nagel
s two famous conditions can be formulated as follows:
'
1. A condition of
'
connectability
'
which stipulates the reduction postulates
2. A condition of
which states that the laws or theories of the reduced
science are logical consequences of the theoretical premises and coordinating
definitions of the reducing science.
The liberal reading of Nagel that I am proposing here depends on the idea that
we read Nagel
'
s condition of
'
derivability
'
in the sense of a largely unspecified
consequence relation based on a suitable paraphrase of the theories under consid-
eration in some formal language.
The recent reassessments of the Nagelian position (especially the one by Klein
(
2009
) and Dizadji-Bahmani et al. (
2010
)) read this consequence relation largely in
terms of a
'
derivability
'
relation, in which the reducing theory can be modified
in such a way that it
represents
the concepts of the reduced theory. So, for instance,
in the summary by Dizadji-Bahmani et al. (
2010
), a
representation
'
'
generalised Nagel-Schaffner
'
model
in which the reduction postulates are
factual
claims, is alive and well. They
defend the generalised Nagel-Schaffner model against seven specific objections,
concluding that none of them apply. In the terminology of Dizadji-Bahmani
et al. the generalised Nagel-Schaffner model consists of a theory
T
P
reducing to a
theory
T
F
through the following steps:
1. The theory
T
F
is applied to a system and supplied with a number of auxiliary
assumptions, which are typically idealisations and boundary conditions.
2. Subsequently, the terms in the specialised theory
T
F
are replaced with their
'
'
via bridge laws, generating a theory
T
p
.
3. A successful reduction requires that the laws of theory
T
p
are
approximately
the
same as the laws of the reduced theory
T
P
, hence between
T
P
and
T
p
there exists
an analogy relation.
correspondents
'
Two features of this generalised Nagel-Schaffner model are worth noting. The
first one of these is that the reduction postulates are part of the
reducing
theory,
rather than some auxiliary statements that have a primarily metaphysical import.
6
Secondly, of the three types of linkages that may be expressed by reduction
postulates, the first two can be discarded and reduction postulates express
matters
of fact
. This is so, because the aim of scientific explanation is, in their words, neither
'
metaphysical parsimony
'
nor
'
the defence of physicalism
'
(p. 405). Thus the
Nagelian reading they favor is a naturalised one, in which the aim of reduction is
representability
between the reduced and reducing theory, and confirmation of
T
F
entails confirmation of
T
P
for domains where there is significant overlap. In this
manner reductions have a high likelihood of occurring where theories have an
overlapping target domain.
6
A similar point was made in a somewhat neglected paper by Horgan (
1978
), who argues that the
reduction postulates supervene on the reducing theory.
