Schaffner, Kenneth - Ernest Nagel and Reduction

04/18/2013

The Journal of Philosophy, Aug/Sept 2012

This is a long paper that explores Nagel's theory of reduction; how it has changed over time and how it relates to a current example. The author first gives Nagel's theory of reduction and its motivations. Nagel was following in the scientific tradition that was able to "absorb" other branches of science into mechanical models. Nagel's prototypical example is the reduction of "classical thermodynamics to statistical mechanics (SM)" (pg535). There were two types of reduction:
-homogeneous: no novel properties are introduced
-heterogeneous: properties are explained in terms of other ones: e.g. temperature to molecular energy
It was the heterogeneous reductions that were the more interesting, though they do not eliminate the earlier "folk" categories. (pg535-6)
Author recaps the various conditions that Nagel placed on theory reduction:
-That hypotheses and axioms take the form of explicit statements whose meanings are fixed by the discipline (pg536-7) (these were Nagel's first and second conditions; author calls them "0").
-Deriviability: the laws of the reduced science are the logical consequence of the reducing science's "theoretical assumptions" (pg537).
-Connectability: terms in the reduced science must be connected somehow to the reducing science using additional "assumptions" (pg537-8).

Author then discusses the extensions and revisions to Nagel's model, first from his own work in creating the "Generic Reduction Replacement" system, in which obsolete or discredited theories could also be reduced (pg540). Also discussed were alternatives like Wimsatt's claims that it isn't theories that should be reduced but "mechanisms" (pg541-2) or a kind of eliminatist-reconstruction "New Wave" advocated by the Churchlands (pg542). Finally, author talks about the functionalist approach to mind and the complications brought on by arguments about multiple realizability (pg543-4). The next section talks about the response to Nagel's model in the 21st century, starting with Hartmann's and (separately) Butterfield's defense of Nagel. The first part of this discussion is about derivability where the concern is over whether the reducing theory's connections can be stronger than a "strong analogy" to the reduced theory (pg545-6). The emerging defenses mainly argue that there is no need to have an overarching concept or definition of "analogy", and that reducing theories need only have an analogy to the reduced (pg545-8). Next is a discussion of connectability, specifically about the nature of the "bridge-laws" or "connectability assumptions". Here author defends his own view that these are synthetic, extensional connections against the two-part analysis of Dizadji-Bahmani that argues that identity statements are internal to a reducing theory, but bridge laws are external to that reducing theory (pg548).

Because "actual reduction is hard to do", there has been a rise in discussions about partial reduction (pg549). Author advocates that the more common types of reduction are 'patchy/local/creeping', at least in the e.g. biological or neurosciences (pg550). However, author gives a lengthy summary in the next section of a systematic reduction of optics undertaken by Sommerfeld (pg551-9). The extended example begins with stressing the importance of Nagel's first condition, that the formulations for both reduced and reducing theories be explicitly stated and connected. Another primary take-away is that the equations used for reduction are more simple than the more "complex and rigorous" (pg556) Maxwell ones, and that in some places, notably when experimenting with diffraction, the Maxwell equations do not provide a rigorous reduction (pg557-8). But author's reading of this, backed up by successive analyses from e.g. Boooker & Jackson, Saatsi & Vicker is that this is a good case of his GRR, where the reducing theory corrects the reduced but does not give a rigorous reduction because it relies on analogy (pg558). However, all-told, even in sciences where there can be significant reduction, there are failures "at the margins" (pg559).

In the penultimate section author talks about the conditions for partial reduction. Author gives a general suggestion: partial reductions should be treated as completed reductions but ones that have exceptions (pg562-3). Author also adds another condition to his GRR that is much like Nagel's original condition of explicit formulations, roughly, that there must be enough codification of hypotheses and theories that can allow for a judgment about whether reduction is successful (pg563).