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Woodward (2002), unsatisfied that then-current accounts of mechanism could expand beyond the life sciences, uses manipulationism as the basis for a generalized account of mechanism. As with MDC, Woodward faults Glennan (1996)1_{for his reliance on direct} causal laws—not only are laws not to be found in, e.g. biology, they often aren’t even found in physics. Given that mechanisms are structured entities whose components are described with causal generalizations (and not laws specifically), Woodward is concerned with how to construct a causal model of a mechanism that adequately captures the mechanism’s structure. He presents a set of necessary conditions for a causal model to be specifically a model of a mechanism.

(MECH)

Woodward begins by considering a block sliding down an inclined plane (Woodward, 2002, p. S367–ff.), as in Figure 3.1. In the ideal case, the effect of gravity on the block’s acceleration is given by the equation

(3.1) a= g sin θ − µkgcos θ

1_{He was, I am supposing, unaware at the time of Glennan’s (2002) concession to invariant}

Θ

a

Figure 3.1: A block sliding with acceleration a down a plane inclined to angle Θ. Adapted from Woodward 2002, Figure 1, p. S376.

where a is the magnitude of the block’s acceleration, g the gravitational constant of 9.8ms2_{, µ}

k the coefficient of dynamic friction, and θ the angle of the incline (p. S368; with corrections).

Equation (3.1) is not (Woodward claims) a law, even while it describes a produc- tive (i.e. causal) relationship. The equation is limited in scope, holds only approxi- mately, and only holds at all within a narrow region of space (that is, near the surface of the earth) (p. S368). But it does correctly describe how, for example, altering the angle of the incline or greasing the slope would change the acceleration experienced by the block. That is, it correctly describes the causal relationship between gravity, friction, and angle on the movement of the block. It is an invariant generalization, in the manipulationist sense of the term.

Woodward, agreeing with Machamer, Darden, & Craver (2000) and Glennan (2002), claims that mechanisms, such as the mechanism for the acceleration of the block, should be construed as relying on, not laws, but what he calls invariant gen- eralizations.2 _{This concept, he claims, does not suffer the drawbacks of an appeal to}

2_{Although Machamer (2004) has individually rejected manipulationism as anything more than}

laws—there are invariant generalizations in biology, invariant generalizations need not be necessary, unlimited in scope, or even widely applicable to correctly underwrite our causal claims. They need only be such that they correctly predict the consequences of (some) interventions into the causes—the variables on the RHS. (For a more detailed treatment of causal interpretation of equations, refer back to Chapter 1.)

Woodward considers too how mechanism parts fit with invariant generalizations. He argues that that modularity constrains the possible decompositions of a mecha- nism. The modularity condition, recall from §1.2, requires that in a causal model of more than one equation, that interventions into one equation not disrupt the remain- ing equations. Put slightly differently, if an intervention into one equation does disrupt the remaining equations, then there is likely a problem with the model, specifically, that there is some causal relationship involving the intervened-into variable that is incorrectly represented in the model (or not represented at all). But how does mod- ularity constraint the decomposition of a mechanism?

The components of a mechanism each engage in one or more distinct behaviors, each of which, Woodward assumes, can be captured with an invariant generalization. The interactions or activities within a mechanism are the result of the components engaging in these behaviors. Components of a mechanism are distinct insofar as they engage in distinct behaviors. Removing or disrupting a component will remove the behaviors it contributes from the working of mechanism as well. Likewise, remov- ing a behavior from a mechanism can only be achieved by removing the component responsible for it. The removal of a behavior from a mechanism is captured by the account of activities presented in Machamer, Darden, & Craver (2000) does at least begin to point down this path (cf. Psillos, 2004). They say that activities support regularities that are “non- accidental and support counterfactuals to the extent that they describe activities. For example, if this single base in DNA were changed and the protein synthesis mechanism operated as usual, then the protein produced would have an active site that binds more tightly” (pp. 7–8). While not explicitly manipulationist in character, this passage suggests that their conception of activities is nevertheless amenable to the manipulationist view.

elimination of the invariant generalizations that describe that behavior from the rep- resentation. Modularity requires that, if when we remove or disrupt one behavior, a second behavior is removed or disrupted as a result, those behaviors must belong to the same component. Thus, we can know if we have decomposed a mechanism cor- rectly when our model comprises distinct behaviors. And we can know if our model comprises distinct behaviors because the generalizations will conform to modularity. From the notions of invariant generalizations and modularity, Woodward con- structs this characterization of a mechanistic model:

(MECH) A necessary condition for a representation to be an acceptable model of a mechanism is that the representation

(i) describe an organized or structured set of parts or components, where (ii) the behavior of each component is described by a generalization that is

invariant under interventions and where

(iii) the generalizations governing each component are also independently changeable, and where

(iv) the representation allows us to see how, in virtue of (i), (ii) and (iii), the overall output of the mechanism will vary under manipulation of the input to each component and changes in the components themselves.

(Woodward, 2002, p.S375)

(i) simply restates the basic idea of a mechanistic explanation due to, e.g., Machamer, Darden, & Craver (2000); (ii) is where Woodward connects activities with invariant generalizations; (iii) and (iv) together comprise a statement of the modularity con- dition described above, which governs how a mechanism can be decomposed into parts.

(MECH) is specifically designed to bridge the qualitative analyses of mecha- nism with Woodward’s manipulationist framework, and hence stands as a qualitative analysis of mechanism. A graphical model of a mechanism would use, (MECH) tells us, variables to stand for components, and directed edges to stand for activ- ities, as Woodward (explicitly, but perhaps unreflectively) links components with variables, and activities with edges. Invariant generalizations, recall, represent causal connections; the causal relata are the components themselves. Thus do activities qua invariant generalizations correspond to edges and components to variables.

But this is the full extent of Woodward’s attempt to harmonize his account with the forgoing qualitative accounts. (MECH) falls flat as an attempt to bridge the qualitative and quantitative, as it runs roughshod over several important aspects of the qualitative accounts of mechanism. First, although Glennan and MDC are careful to point out that mechanisms are always mechanisms for some behavior, (MECH) places no such constraint on mechanisms, nor does it offer a principle by which to determine which components are or are not relevant to the mechanism. Second, mechanisms are posited to explain known (or hypothesized) cause-and-effect relations; (MECH) makes no attempt to link a putative cause to an effect, or to offer constraints on how to model a mechanism that does. I turn now to examine these shortcomings in detail.

(MECH) and Mechanism Bounding

My first objection to (MECH) arises from the fact that it fails to offer a bound- ing principle. Notice that Woodward has eschewed Glennan’s idea that there are no mechanisms simpliciter : Where Glennan argued that mechanisms are defined with reference to an explanandum phenomenon, Woodward makes no such requirement. MDC are adamant that mechanisms have start and stop conditions, but such a con-

straint makes no appearance in (MECH). The only constraint that (MECH) places on the structure of a mechanism is that it contain component parts and their behav- iors. (MECH) in particular permits any component to participate in a mechanism, so long as it is causally relevant. Similarly does (MECH) permit us to arbitrarily exclude any component as a member of a mechanism.

One might defend Woodward at this point by observing that (MECH) only characterizes representations of mechanisms, and not mechanisms themselves; that therefore it is not incumbent on (MECH) to lay out any membership or other struc- tural constraints as these are well-handled by the qualitative accounts themselves.

Such a defense is disingenuous, however, as neither do Glennan’s account nor MDC’s account provide such principles of membership; indeed, many had hoped that the formal apparatus of manipulationism might supply such principles. The onus should be on the quantitative accounts to supply these principles. In which case, we should prefer to (MECH) a quantitative account that can add such a principle to the extant descriptive accounts.

(MECH) and Mechanistic Explanation

My second objection to (MECH) arises from the lack of bounding principles. With no bounding principles, Woodward does not constrain mechanisms to lie between an explanandum cause and an explanandum effect. Thus, (MECH) does not require a mechanism to link an explanandum cause to an explanandum effect—Woodward has identified mechanisms with causal structure simpliciter, and leaves for mechanisms, therefore, no explanatory work to do. The explanatory heavy lifting, on Woodward’s (2003) view, is borne entirely by invariant generalizations.

A mechanistic explanation is a response to a request to explain how it is that a cause and an effect are so linked. We may observe that A causes B, and then ask:

What explains the link between the two? The response, on the mechanistic view, is a description of the mechanism that links A to B. But for Woodward, what explains the link between A and B is a relationship of counter-factual dependence that is invariant under intervention—that we can manipulate B by intervening to change A explains the causal link between A and B.

Thus, for Woodward, an invariant generalization that describes the relationship between A and B is (minimally) explanatory, where for the mechanist, it is not explanatory at all (because generalizations are not mechanisms).3 _{There remains a} fundamental disconnect between (MECH) and the descriptive accounts of mecha- nism about what is doing the explanatory heavy lifting, a disconnect that must be bridged before we can harness manipulationism to mechanism.

Craver (2007) picks up this challenge, by arguing that, in mechanistic explana- tion, the hierarchical organization of mechanisms, which can also be modeled using invariant generalizations of a particular sort, are bearing some of the explanatory work. He offers an account of constitutive relevance that draws upon manipulationist concepts, which I turn now to consider.