# Download e-book Causal Nets, Interventionism, and Mechanisms: Philosophical Foundations and Applications

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## Causal Nets, Interventionism, and Mechanisms

Articles Cited by. Philosophy of the Social Sciences 44 5 , , The British Journal for the Philosophy of Science 67 4 , , European Journal for Philosophy of Science 7 2 , , Journal for General Philosophy of Science 49 3 , , Articles 1—20 Show more. Help Privacy Terms. Causation: Many Words, One Thing?

How to model mechanistic hierarchies L Casini Philosophy of Science 83 5 , , Not-so-minimal models: Between isolation and imagination L Casini Philosophy of the Social Sciences 44 5 , , Feel Bad, Live Well! How Theoretical Explorations Explain. If not explicitly stated, we will by default assume that the background contexts of the systems we are interested in do not vary.

When satisfied, it connects causal structures, which describe AF or model unobservable causal relationships, to empirically accessible probability dis- tributions cf. The causal Markov condition is essentially the causal interpretation of the Markov condition see subsection 2. It works exactly like the Markov condition in Bayesian networks and is intended to hold only for causal systems whose associated graphs are DAGs: Given a causal graph, the causal Markov condition im- plies a set of probabilistic independence relations that have to hold in any compatible probability distribution.

So causal models or hypotheses generate predictions; they are empirically testable. Note that the causal Markov condition CMC is formulated as a condition, and not as an axiom. It is not supposed to hold for all causal models. It will be regularly violated in systems whose variable sets V do not contain every common cause of every pair of variables in V. CMC can, however, be expected to hold in causal systems whose T variable sets V contain every such common cause. Such variable sets V are called causally sufficient cf.

In case our system of interest is not causally sufficient or we do not know whether it is causally sufficient, it is typically assumed that AF CMC holds for some expansion of the system cf. So what causal relations do is to produce correlations; they explain regularities T or the absence of regularities in case of d-separation. One important difference between CMC and the d-connection condition is that the former is assumed to hold only for causal models whose graphs are DAGs, while the latter AF is assumed to also hold for causal systems whose associated causal structures are directed graphs featuring causal cycles.

Let me briefly illustrate this on the graph depicted in Figure 8: According to the DR causal Markov condition, every Xi in this graph has to be probabilistically independent of its non-effects conditional on its direct causes. Xj are causally separated by M. So the d-connection condition implies only one of T the three probabilistic independence relations implied by CMC, viz.

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The d-connection condition is preferable to CMC because it does—contrary to CMC— AF fit the idea that blocking all paths between two variables should render them indepen- dent. Before we can go on, some critical remarks on CMC seem to be apropriate: Till now it is quite controversial whether CMC is or can be satisfied by certain systems in quantum mechanics. Hausman, , p. This would be no problem if the two states could be explained by some direct causal connection, but such a connection is excluded by the theory of relativity, or more precisely: by the fact that no causal influence can spread faster than light.

Because the role of CMC in the quantum domain seems to be more or less unclear at the moment, I prefer to exclude the quantum world T from the domain to which CMC should be applied. But there are not only counterexamples of CMC-violating systems from the quantum domain, but also from the macro world. Cartwright , p.

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In this scenario we have a DR simple common cause structure: The reaction Z is a common cause of the substance X and the byproduct Y i. Thus, CMC is violated.

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Strictly speaking, however, CMC is as already mentioned earlier formulated as a condition that may or may not hold. So the scenarios described can in the best case show that assuming CMC to hold for all kinds of systems may be problematic. But even if CMC would be assumed for all kinds of systems, then these scenarios could not be straightforwardly interpreted as counterexamples to CMC.

What they can show is that CMC is violated given that certain additional causal assumptions hold, such as the assumption that there are no hidden variables, the assumption that no selection bias is involved, and the assumption that there are no additional causal arrows. T This means that typical counterexamples to CMC only show that there is no underlying causal structure satisfying the conjunction of CMC and these additional assumptions.

For other convincing defenses of CMC, see, e.

A novel justification of an axiom assuming CMC by an inference to the best explanation will be developed in subsection 4. Satisfying the minimality condition guarantees that every causal arrow in a causal model is probabilistically relevant. When deleting the arrow of a minimal causal model, the resulting causal model will not satisfy CMC anymore.

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Note that minimality, as it T is typically introduced see Condition 3. Minimality can, however, be generalized in such a way that it can be formulated AF without requiring CMC to hold. DR The main idea behind the productivity condition is basically the same as behind the minimality condition: In a causal model hV, E, P i satisfying the productivity condition it is guaranteed that every causal arrow is probabilistically relevant, i. Unproductive causal ar- rows, which do not leave any kind of empirical footprints, cannot explain anything and, T thus, should be eliminated.

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Axiom 3. It is typically formulated only for causal models that satisfy CMC or the d-connection condition : If hV, E, P i is a causal model satisfying CMC, then hV, E, P i satisfies the causal faithfulness condition if and only if P does not feature a conditional or unconditional probabilistic independence relation not im- plied by hV, Ei and CMC cf. The faithfulness condition can be generalized in such a way that its formulation does not require CMC to hold cf. Condition 3.

DR The equivalence of Condition 3. Since most of the time it will be convenient to have a notion of faithfulness that is independent of CMC or the d-connection principle , I will rather make use of Condition 3. For faithfulness not to hold i. It is because of this that non- faithful causal systems can be expected to be extremely rare. Definition 3. The faithfulness condition is probably the most controversial condition of the causal nets formalism.

There are several plausible possibilities for faithfulness to not hold. In DR the following, I will briefly discuss the most important cases of non-faithfulness. From an empirical point of view it is, however, reasonable to assume only such causal relations which are at least in principle testable. We only assume theoretical relations when we are forced to by empirical facts. This theoretically justifies why we should assert that causal systems are not non-faithful due to non-minimality. We distinguish two kinds of this sort of non-faithfulness: non-faithfulness due to canceling paths and non- faithfulness due to canceling causes.

Non-faithfulness due to canceling paths arises when the probabilistic influences transported over two or more causal paths d-connecting two variables X and Y exactly cancel each other such that IN DEPP X, Y. In case of non- faithfulness due to canceling causes there is no other path between two variables X and Y canceling the influence of some d-connection between X and Y.

For an example, see Pearl, , p. Non-faithfulness due to deterministic dependence This kind of non-faithfulness arises in models in which some variables depend deterministically on other variables or on sets of other variables. AF Authors such as Cartwright b, p.

These kinds of non-faithfulness are quite typical in self-regulatory systems such as evolutionary systems or artificial DR devices. Evolution has produced systems that balance external perturbations and many man-made devices are made to render a certain behavior of a system independent from external influences.

An example for the latter would be an air conditioner: The outside temperature directly causes the inside temperature, which directly causes the state of an air conditioner, which, in turn, directly causes the inside temperature i. What can we say about such violations of faithfulness? Since faithfulness is equivalent to parameter stability recall Definition 3. Based on this fact, faithfulness is typically defended by the formal result that non-faithful systems have Lebesque measure zero, given the parameters of the respective system are allowed to vary cf.

This result, however, can only be used as a defense of generally T assuming the faithfulness condition in case the parameters of all or almost all systems in the actual world fluctuate over time.

### 2. Basic Tools

Such parameter fluctuation can be represented by adding so-called external noise variables to a causal model. A noise variable NX represents all kinds of perturbations on X not represented in the model cf. If the noise assumption is true, then non-faithfulness due to cancelation and intransi- tivity non-faithfulness due to internal canceling paths should almost never occur. Even T the prior distributions over the noise variables of evolutionary systems and artificial de- vices can be expected to fluctuate at least slightly. Already very small perturbations suffice to destroy non-faithful independencies.

AF Unfortunately there are still problems with non-faithfulness due to deterministic de- pendencies. There are two cases: Either our world is deterministic or it is indeterministic. In both cases non-faithfulness due to deterministic dependence may arise.