The Blackwell Guide to the Philosophy of Science - The Department ...

Reduction, Emergence and Explanation
Theoretical-derivational
The classic notion of intertheoretic reduction in terms of theoretical derivation,
as found in Kemeny and Oppenheim (1956) or in Ernest Nagel’s classic treatment
(1961), descends from the logical empiricist view of theories as interpreted formal
calculi statable as sets of propositions of symbolic logic. Intertheoretic reduction
is the derivation of one theory from another; and so constitutes an explanation
of the reduced theory by the reducing theory. This model treats intertheoretic
reduction as deductive, and as a special case of deductive-nomological explanation.
Thus if one such theory T1 could be logically derived from another T2, then
everything T1 says about the world would be captured by T 2. Because the theory
to be reduced T 1 normally contains terms and predicates that do not occur in the
reducing theory T 2, the derivation also requires some bridge laws or bridge principles
to connect the vocabularies of the two theories. These may take the form
of strict biconditionals linking terms in the two theories, and when they do such
biconditionals may underwrite an ontological identity claim. However, the relevant
bridge principles need not be strict biconditionals. All that is required is
enough of a link between the vocabularies of the two theories to support the
necessary derivation.
One caveat is in order. Strictly speaking, in most cases what is derived is not
the original reduced theory but an image of that theory within the reducing
theory, and that image is typically only a close approximation of the original rather
than a precise analogue (Feyerabend, 1977; Churchland, 1985).
Nagel’s account (1961) of intertheoretic reduction has become a standard for
this type, and all alternative accounts are in one way or another amendments to
it or reactions against it. So, let us look at it a little more closely, and see how
problems for this account have arisen. Nagel distinguishes two types of reductions
on the basis of whether or not the vocabulary of the reduced theory is a subset
of the reducing theory. If it is – that is, if the reduced theory T1 contains no
descriptive terms not contained in the reducing theory T2, and the terms of T1 are
understood to have approximately the same meanings that they have in T2, then
Nagel calls the reduction of T1 by T2 “homogeneous” (Nagel, 1961, p. 339).
From a historical perspective, this attitude is somewhat naïve (Sklar, 1967, pp.
110–11). The number of actual cases in the history of science where a genuine
homogeneous reduction takes place are few and far between. One escape for
the proponent of Nagel-type reductions is to distinguish explaining a theory (or
explaining the laws of a given theory) from explaining it away (Sklar, 1967,
pp. 112–13). Thus, we may still speak of reduction if the derivation of the approximations
to the reduced theory’s laws serves to account for why the reduced
theory works as well as it does in its (perhaps more limited) domain of applicability.
The task of characterizing reduction is more involved when the reduction is heterogeneous,
that is, when the reduced theory contains terms or concepts that do
not appear in the reducing theory. Nagel takes as a paradigm example the (apparent)
reduction of thermodynamics, or at least some parts of thermodynamics, to
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