350 Alex Rosenberg
complete in various ways than reducing theories, and therefore incompatible with
them in predictions and explanations. Accordingly, following Schaffner, the re-
quirement was explicitly added that the reduced theory needs to be “corrected”
before its derivation from the reducing theory can be effected. This raised a prob-
lem which became non-trivial in the fall-out from Thomas Kuhn’sStructure of
Scientific Revolutions[1961], and Paul Feyerabend’s “Reduction, Empiricism and
Laws” [1964]. It became evident in these works that “correction” sometimes re-
sulted in an entirely new theory, whose derivation from the reducing theory showed
nothing about the relation between the original pair. Feyerabend’s examples were
Aristotelian mechanics, Newtonian mechanics, and Relativistic mechanics, whose
respective crucial terms, ‘impetus’ and ‘inertia’, ‘absolute mass’ and ‘relativistic
mass’ could not be connected in the way reduction required. No one has ever
succeeded in providing the distinction that reductionism required between ‘correc-
tions’ and ‘replacements’.
More fundamentally, reductionism as a thesis about formal logical relations
among theories was undermined by the increasing dissatisfaction among philoso-
phers of science with the powers of mathematical logic to illuminate interesting
and important methodological matters such as explanation, and theory testing.
Once philosophers of science began to doubt whether deduction from laws was
always sufficient or necessary for explanation, the conclusion that inter-theoretical
explanation need take the form of reduction was weakened. Similarly, reduction-
ism is closely tied to the axiomatic or so-called syntactic approach to theories, an
approach which explicates logical relations among theories by treating them as
axiomatic systems expressed in natural or artificial languages. But for a variety
of reasons, the syntactic approach to theories has given way among many philoso-
phers of biology to the so-called ‘semantic’ approach to theories. The semantic
approach treats theories not as axiomatic systems in artificial languages, but as
sets of closely related mathematical models. On the semantic view the reduction
of one theory to another is a matter of employing (one or more) model(s) among
those which constitute the more fundamental theory to explain why each of the
models in the less fundamental theory are good approximations to some empirical
processes, showing where and why they fail to be good approximations in other
cases. The models of the more fundamental theory can do this to the degree that
they are realized by processes that underlie the phenomena realized by the models
of the less fundamental or reduced theory. There is little scope in this sort of
reduction for satisfying the criteria for post-Positivist reduction.
To the general philosophical difficulties which the post-positivist account of
reduction faced, biology provided further distinct obstacles. David Hull [1973]
was the first to notice it is difficult actually to define the term ‘gene’ as it figures
in functional biology by employing only concepts from molecular biology. The
required “bridge principles” between the concept of gene as it figures in population
biology, evolutionary biology, and elsewhere in functional biology and as it figures
in molecular biology could not be constructed. And all the ways philosophers
contrived to preserve the truth of the claim that the gene is nothing but a (set of)