New Wave Reductionism

One approach to reducing one scientific theory to another is called new wave reductionism (Bickle, 1996; Endicott, 1998).  In new wave reductionism, one does not reduce a secondary theory directly to a primary theory.  Instead, one takes the primary theory and constructs from it a structure that is analogous to the secondary theory, but which is created in the vocabulary of the primary theory.  Theory reduction involves constructing a mapping between the secondary theory and its image constructed from the primary theory. "The older theory, accordingly, is never deduced; it is just the target of a relevantly adequate mimicry" (Churchland, 1985, p. 10).  One example of new wave reductionism is provided by Dawson et al. (2000).  They converted a primary theory (a decision tree) for mushroom classification into a particular image (a production system).  They trained an artificial neural network on the same mushroom classification problem, and were able to map its internal states on to the same production system.  This completed a new wave reduction of a decision tree into a connectionist network.

References:

1. Bickle, J. (1996). New wave psychophysical reductionism and the methodological caveats. Philosophy and Phenomenological Research, LVI, 57-78.
2. Churchland, P. M. (1985). Reduction, qualia, and the direct introspection of brain states. The Journal of Philosophy, LXXXII, 8-28.
3. Dawson, M. R. W., Medler, D. A., McCaughan, D. B., Willson, L., & Carbonaro, M. (2000). Using extra output learning to insert a symbolic theory into a connectionist network. Minds And Machines, 10, 171-201.
4. Endicott, R. P. (1998). Collapse of the new wave. The Journal of Philosophy, XCV, 53-72.

(Added April 2011)