New Wave Reductionism

Models of reduction that are nowadays commonly subsumed under the heading of New Wave Reductionism have been developed in a series of articles and books by Clifford Hooker (1981), Paul Churchland (1979, 1985) and, more recently, by John Bickle (esp. 1998), and they build on some aspects of Schaffner s model (1993) and earlier versions of it (Schaffner 1967, 1976). Here is a formulation of Hooker s definition, which nicely captures the basic strategy  

Within Tb construct an analog, T r, of Tr under certain conditions Cr such that Tb and Cr entail T r and argue that the analog relation, AR, between T r and Tr warrants claiming (some kind of) reduction relation, R, between Tr and Tb. Thus (Tb Cr — T r) and (T r AR Tr) warrants (Tb R Tr). (Hooker 1981, 49)  

The conditions, CR, consist of limiting assumptions and boundary conditions that guarantee that if Tb is more comprehensive than Tr, the application of elements 

Nagelian reduction (more or less broadly construed, for example taking Schaffner s version to be a Nagelian model (Endicott 1998,2001 Dizadji-Bahmani et al 2010)). 

In cases lying at or near the retentive endpoint, the In is the exactly equipotent isomorphic image of the To, and no counterfactual limiting assumptions or boundary conditions are required for the derivation of In. (Bickle 1992, 223) 

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New-Wave reductionism repeats and adds a number of non-formal aspects to the list of additional criteria we are already familiar with. Let me add five of them, all of which state that there is a specific link between reduction and explanation ... 

The role identity plays in these models is similar to the role it plays in Schaffner s model. First of all, cross-theoretic identities form a limiting case. Moreover, for monistic worlds, this limiting case will be the relevant case. Accordingly, cases of reduction relevant for the monist will be identity-cases of this model. Reduction as based on cross-theoretic identities is required to make sense of at least some reductions that go together with correction. The way correction is conceived in New Wave reductionism is captured by Fig. 7.2 ... 

This stems from some pre-theoretic descriptions, the bridge law interpretation in Nagel, identity-theories in the philosophy of mind, it is Moulines candidate for an amendment of semantic models and it occurs in New-Wave reductionism as a candidate for grounding smooth reductions . 

This and other analog relations underlie new-wave reductionism and structuralist versions of reduction. This covers weaker syntactic forms of bridge-law interpretations (c/. van Riel 2011). 

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