Mechanisms, Modularity, and Constitutive Explanation in Causality

1. Mechanisms, Modularity and Constitutive ExplanationMechanisms and Causality in the Sciences 10.9.2009 University of Kent, Canterbury, UK Jaakko Kuorikoski Jaakko.kuorikoski@helsinki.fi Trends and tensions in intellectual integration www.helsinki.fi/filosofia/tint/ Philosophy of Science Group University of Helsinki

2. The argument • Mechanisms are causal structures (Craver, Glennan, Steel, Woodward) and causal structures are modular. • Common criticism: Many ordinary mechanisms seem to break the modularity condition. • Answer: Causal models are always models of specific causal structures, not causal systems as whole. • Models of causal structures can have different modularity properties which determine what can and what cannot be explained with the model. • Causal explanation requires variable modularity and constitutive explanation parameter modularity. • Criticism based on failures of parameter modularity, and therefore only shows that in such cases a constitutive explanation of system properties is impossible, not causal explanation of the workings of the system as it is.

3. The Woodward –stuff • Causal explanation is about tracking dependencies that are invariant under interventions.  • Explanations relate variables: they are contrastive both in the explanandum and in the explanans. • Intervention = an ideally surgical manipulation that directly affects only a single explanans variable of interest. • distinguishes genuine causal dependencies from inferential connections between variables • clarifies cases of confounding and multiple causal pathways • links causal dependence to manipulability

4. Woodward –stuff and modularity • A (static) model of a causal structure :  X1 = f1(X1;p1) X2 = f2(X2;p2) … Xn = fn(Xn;pn), • the values of a variable Xi on the left hand side of the equality are (directly) caused by the values of the (set of) right hand side variables Xi, according to a sub-mechanism described by the function fi and the parameter set pi.

5. Woodward –stuff and modularity • Modularity in models: it has to be possible to intervene on individual variables of the causal structure in such a way that the causal dependencies (functional forms or parameter sets) not directly targeted by that particular intervention do not change • Modularity in mechanisms: is it possible to disrupt or break individual sub-mechanisms of the system without affecting other sub-mechanisms? • Cartwright: Toasters and carburetors surely are mechanisms, but they are not modular.

6. Systems and structures • It is impossible to model a causal system completely, i.e. to endogenize everything as dependent variables.  • A causal system is a spatiotemporally delineated piece of the world, a concrete thing that has a boundary with its environment that is recognizable without knowing the inner causal workings of the system (such as a machine, an organism, an organ or an economy). • A causal structure (a mechanism) is a set of causal relations within a system, definable only against a background of causal properties ignored or held fixed. • A causal system is comprised of multiple causal structures and what is left as the fixed background for a given causal structure determines the parameters of that structure. • It makes sense to ask what the modularity properties of a given causal structure are, but not whether a system is modular tout court.

7. The observationalequivalence-problem U V • (1) Y = aX + U  • (2) Z = bX + cY + V • has the same solutions, and thus says exactly the same things about the observable, unmanipulated behavior of Z, X and Y, as • (1) Y = aX + U  • (3) Z = dX + W in which d = b + ac and W = cU + V,by definition. Y X Z X U W Z Y

8. The observationalequivalence-problem • Woodward: both systems cannot be modular at the same time Do(Y = y’): • (1) Y = y’   • (2) Z = bX + cy’ + V • Woodward: the coefficient (parameter) a is implicitly set to zero and that this is possible to do in a modular fashion only in the first system, but not in the second • (1) Y = aX + U  • (3) Z = dX + W since the coefficient d is dependent on a (d = b + ac). I U V a = 0 Y X Z X U W Z Y I?

9. Solving the observationalequivalence • No need to invoke the idea that an intervention on Y would have to be implemented by setting the coefficient a to zero • the system of equations (1) and (3) is not modular even in variables. According to it, • setting Y = y’ via an intervention should not change the value of Z, whereas, if the first system is correct, it does. (even if we respect the analytical constraints that guarantee the observational equivalence or transform these constraints into additional causal dependencies) • It is not possible to intervene independently on U and W because they are analytically linked (due to the definitional constraints). • Breaking arrows is a representational device: the analytical work done by the intervention-concept does not depend on “annihilating” anything. “Overriding” or “bypassing” suffice.

10. Cartwright’s carburetor gas in chamber = f (airflow, pumped gas, gas exiting emulsion tube; a) airflow = g (air pressure in chamber; b) gas exiting emulsion tube = h (gas in emulsion tube, air pressure in chamber; c) air pressure in chamber = j (suck of the pistons, setting of throttle valve; d) where a,b,c and d are parameter sets, all dependent on the geometry of the carburetor chamber. • Since the parameters in all of the functions are dependent (in a non-specified way) on the geometry of the carburetor, one cannot individually meddle with a single equation without affecting the others. Hence, the carburetor is not modular.

11. ExplainingCartwright’s carburetor • The carburetor model is (or is naturally interpreted to be) modular in variables but not modular in parameters. This difference is crucial for the kinds of explanations the model does and does not provide: • does not specify the dependency between the geometry and the parameters (it does not tell how to go about in designing the geometry if one had in mind specific dependencies between the causal variables) • the failure of modularity in the parameters severely limits our understanding of the constitutive role of the geometry

12. On constitutive explanation • Constitutive explanations provide information on why, or in virtue of what, a system has some property, not how it (etiologically) came to have that property (Craver, Cummins) • The basic ideas of Woodward’s theory of causal explanation can be extended to constitutive explanations: • the macro-property depends constitutively on the micro-properties in the sense that if the micro-properties had been different, the macro-property would have been different as well (in some systematic way) • When explaining system level properties, we are not asking what the system level property would be like if we intervened on a causal variable in the underlying mechanism model.

13. On constitutive explanation • The realizing mechanism itself is a causal structure. its functional forms and parameter values, should not change under interventions on variables  • In order for the constitutive dependency supply correct answers to w-questions, it has to be invariant under local changes in the values of the micro parameters.  •  the underlying mechanism model has to be modular in parameters in that local interventions in the parts of the mechanism (parameter values) should not change other parts of the mechanism (other parameter values).

14. Conclusions • The interventionist theory of causation and the conception of mechanism as a causal structure do entail that it should be possible to causally change some parts of the mechanisms without affecting the properties of other parts of the mechanism. • But this does not yet mean that examples of mechanisms lacking modularity with respect to every imaginable intervention would invalidate the theory. • This is because causal structures are always identified against a background of causal factors regarded as immutable and making sense of the causal structure requires only that the variables of the structure can be independently intervened on, not parameters regarded as invariant.   • Distinguishing between types of modularity also helps to make sense of what kinds of explanations can be presented on the basis of a model of a mechanism (model of a causal structure).

15. Somelooseends • Consequences of the metaphysical difference between causation and constitution? • Craver: mutual manipulability criterion? (Asymmetry of constitution) • In what sense do micro-properties have to be intervenable?(Changing a property vs. changing a component?)