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A Semantic View on Reduction

Soshichi Uchii

Course materials for Philosophy of Biology
July 6, 1999

A Confusing View on Reductionism

Ruse's discussion of reductionism draws on Ayala's threefold distinction: ontological, methodological, and theory reductionism. However, Ruse's discussion is sometimes confusing; in particular, as regards theory reduction (pp. 26-30). Ruse does very little to clarify the issues between reductionist and non-reductionist. There are several reasons, but presumably the most important reason is that he sticks to the old-fashioned view of theory reduction maintained by Nagel and others. However, if we appeal to the semantic view of scientific theory (as referred to on p. 20), the situation may be greatly improved.

As Ruse says, traditional reductionists assert that the older theory is absorbed within the newer theory, and there is a continuity between them. Further, this "absorption" means that the older theory would be shown to be a deductive consequence of the newer theory. But I would say, there are very few people now who support this view, even in the field of philosophy of physics.

A Semantic View: theoretical activity as model-building

A theory provides a method for model building and a few basic principles are contained as a core of such a theory. Since model building is essentially an informal activity, it is wrong to regard this activity as governed by only such tight relationship as deductive connection; rather, we introduce ceteris paribus clause every now and then, and we try to improve our models by changing implicit or tacit conditions, while keeping the basic principles intact. A classic example of this is the discovery of Neptune. Despite inconsistency between observed data of Uranus and "theoretical predictions" made by the "Newtonian astronomy", astronomers did not regard this as a falsification of the Newtonian laws (three laws of motion and the inverse-square law); instead they looked for a substitute for as yet unspecified conditions of the planetary system, and they eventualy succeeded in finding a new planet, Neptune.

On the semantic interpretation of theory (or rather, on my version of it), this may be rendered as follows: The Newtonian laws are essential principles for building models for explaining (predicting, etc.) planetary motions. But for this model building, we need extra conditions as well, such as the number of the planets, their distances from the sun, the mass of each of them, etc.; and these are largely subject to revision and correction (hence the informal character of model building). What Leverrier accomplished was that he made a new model of the planetary system, by adding a new planet with a certain mass and a trajectory in accordance with the Newtonian laws, and this model fitted the empirical data, including the data on Uranus. Notice the folloing two points: (1) The prediction of Neptune was newly constructed, changing the extra assumptions implicitly made so far; it was not derived from the Newtonian astronomy together with these old assumptions. (2) Thus although the previous astronomy and the new prediction are not connected by deductive relations, it is perfectly all right to claim the continuity between them; the essential laws of the Newtonian astronomy are intact in this process.

Applications to Theory Change and "Reduction"

Is the preceding view applicable to the problems of theory change, and to theory reduction in particular? Of course, we have to take theoretical changes into consideration, and modify the view accordingly; but the point is that model-building is far more flexible than constructing a deductive system, and it is much easier to find continuous elements through the theoretical changes.

One thing is clear. In the process of theory change, such as from Mendelian genetics to Molecular Biology, say, the set of theoretical concepts and assumptions change, and therefore it seems quite difficult to claim the continuity between the theories in terms of basic or essential laws. Still, as Ruse points out, "the worth of an older theory's concern are not denied. It is just that new avenues of attack are opened up" (Ruse, 28). Thus here is at least one element of continuity, it seems. "Their previous work, with Mendelian genes and the Hardy-Weinberg law and so forth, is not thrown overboard, but is rather given a deeper backing through our new knowledge of the molecular basis of life" (ibid.). But how is this possible despite theoretical changes---say, from Mendelian genes to molecular DNA's and their workings? The answer seems to be in the structures of models constructed according to the old and the new theories.

On the semantic view, you don't have to establish a continuity in terms of deductive relationship between older theory and newer theory; what count are models (or sets of models) constructed and compared to empirical data (recall our example of blood-types as an illustration of Hardy-Weinberg law. That is a model satisfying the law). Since these models have a logical or mathematical structure, it is quite easy to compare them in respect of their structure; they can be identical, similar, or incompatible. It would be crazy to assert "incommensurability" as regards the structure of models! Thus if the new models constructed according to the new theory are sufficiently similar to those according to the old theory, you can give a good sense to "continuity", especially if newer models turn out to have finer structure than the older ones, in some or many fields of inquiry.

At the same time, the semantic view can also clarify the reason why it is hard to claim literal "reduction" of the old theory to the new one, even if we can find continuity in the preceding sense. Since the basic concepts and laws are different between the two, it is hard to expect exact "translation" or "correspondence" between the laws or models accroding to the two. At best, one can expect older laws or models are reproduced in a modified form, according to the new theory, and that's exactly what Ruse is pointing out on p. 27.

You know already that I am against the literal "reduction" even as regards physical theories such as the kinetic theory or statistical mechanics (Theory Reduction: the case of the kinetic theory of gases); I claimed that what's going on there is not "reduction" but extension of an old theory to a new theory. The new theory has new conceptual appratus so that it may be impossible to find conceptual identity or contuinuity; still it is perfectly all right to see continuity (in the preceding sense) between models produced by the new and the old theory and survived empirical tests.         

Last modified, May 6, 2008. (c) Soshichi Uchii