# Interventionist Analysis of Causation

The interventionist analysis of causation makes explicit the experimental strategy used in science for discovering causal relations among variables. It is not intended to provide an analysis of causation as a relation between individual spatio-temporally localized events, but an analysis of causation as a relation among properties of events^{1}, which can be represented by variables.

The fundamental idea of this approach is this. One variable X causally influences a second variable Y if and only if there is an intervention (satisfying certain conditions) such that modifying the value of X by such an intervention also modifies the value of Y. In Woodward’s terms, “X causes Y if and only if there are background circumstances B such that, if some (single) intervention that changes the value of X (and no other variable) were to occur in B, then Y or the probability distribution of Y would change” (Woodward (2010: 290)).

The interventionist conditions for the existence of a causal relation between variables X and Y correspond to experimental and observational criteria on which scientific method grounds the judgment that X causally influences Y. The general idea of the recipe is this. Find a variable I, corresponding to a possible way of modifying the value of the cause variable X, which satisfies the following conditions for being an intervention variable on X with respect to Y (Woodward (2003: 98)):

- (IV)
- 1. I directly influences X but does neither directly influence Y nor any other variables influencing Y that do not lie on the causal path from I to X to Y.
- 2. I completely “controls” X, in the sense that the intervention I cuts off all other influences on X.
- 3. The intervention I has an origin independent of the variables that are being investigated. In particular, I is not statistically correlated with any causes of Y that do not lie on the causal path from I to X to Y.

Then manipulate X by way of I and observe whether changes in X are accompanied by changes in Y. If and only if they are, X causally influences Y.

In the original framework of interventionism (Woodward (2003)) it is impossible to justify causal judgments in which a higher-level variable X acts as a cause of a lower-level variable Y, as soon as lower-level variables SB(X) in the supervenience base of X are also taken into account (Baumgartner (2009), (2010), (2013); Marcellesi (2010)). This leaves open the possibility to justify that X causes Y by simply not taking into account any lower-level variables SB(X) on which X supervenes. However, such a justification would be *ad hoc*, given that the main challenge consists in justifying the causal role of X, against the claim that all causes of Y lie at the same level as Y, i.e., at the level of the variables SB(X) in the super- venience base of X. Moreover, even if the omission of variables SB(X) might make it possible to provide a formal justification of a downward causal claim X^Y, higher-level variables could never be causes in situations where variables in their supervenience base are also causes. Thus, such a justification would exclude by stipulation the possibility that *both *SB(X) and X causally influence Y.

Shapiro and Sober (2007) and Woodward (2015) have suggested to modify the interventionist framework so as to make it possible to justify causal statements according to which supervenient variables are causes without

58 *Max Kistler *excluding variables in the supervenience base from consideration. Such a modification opens up the possibility to use the interventionist framework to argue against eliminativism and epiphenomenalism with respect to higher-level variables.

Both the conditions (IV) on intervention variables and the definition of direct causation must be modified with respect to Woodward’s (2003) original analysis. The leading idea for the modification of (IV) is that the variables SB(X) in the supervenience base of the cause variable X should be excluded from the set of variables that must be held fixed during an intervention in X. “To assess whether X causes Y, the common causes of X and Y must be held fixed, but not the microsupervenience base of X” (Shapiro & Sober (2007: 8)). For it is not only impossible by definition of supervenience to hold variables SB(X) fixed during an intervention on X, but such a requirement does not correspond to scientific standards of experimental control of causal hypotheses. “It is inappropriate to control for supervenience bases in assessing the causal efficacy of supervening properties” (Woodward (2015: 323)).

In the framework that results from the modification of (IV) along these lines - let us call it (IV*) - a variable I may count as an intervention on X with respect to Y even though every change in the value of I that changes the value of X also necessarily changes the value of SB(X), as sketched in Figure 4.1.

*Figure 4.1* Sketch of an intervention by I on X, which is also an intervention on SB(X). The cross represents the rule that for the variable I to be an acceptable intervention variable, it must not directly influence Y. There is no cross on the arrows I^X and I^SB(X), which represents the fact that I may influence both X and SB(X).

In the same spirit, the conditions for a variable X to be a direct cause of variable Y can be weakened in the following way, so that it becomes conceivable that a higher-level cause X is a direct cause of Y (which may be at the same level as X or at a lower level):

(M*) A necessary and sufficient condition for X to be a (type-level) direct cause of Y with respect to a variable set V is that there be a possible intervention on X that will change Y or the probability distribution of Y when one holds fixed at some value all other variables Z_{i} in V, with the exception of the variables in the supervenience base of X and of Y (if V contains such variables).

There has been a controversy over whether these new definitions determine the conditions for X to be a direct cause of Y in such a way as to distinguish them from the conditions under which it is rather SB(X) that causes Y. In case Y is a variable at the level of SB(X) the question is whether these conditions make downward causation (X^Y) empirically distinguishable from lower-level causation (SB(X)^Y).

Before I answer this question on downward causation, let me consider the question whether (IV*) and (M*) make the higher-level causal claim that X causes Y empirically distinguishable from the corresponding lower-level claim that SB(X) causes SB(Y).

It seems to be conceivable that there are situations of both following types:

- 1) Situations (sketched in Figure 4.2, following Woodward, forthcoming, p. 10) containing two higher-level variables M
_{1}and M_{2}, supervening respectively on variables N_{1}and N_{2}, where there is causal influence at*both levels,*i.e., N_{1}influences N_{2}and M_{1}influences M_{2}. - 2) Situations (sketched in Figure 4.3) containing two higher-level variables M
_{1}and M_{2}that are*not*causally related but which supervene on variables N_{1}and N_{2}which*are*so related.

If both situations are conceivable and empirically different, the statement that M_{1} causes M_{2} has an empirical content that is independent from the statement that N_{1} causes N_{2}. The fact that N_{1} causes N_{2} leaves it open whether or not M_{1} also causes M_{2}.

However, it has been questioned whether the objective difference between these two kinds of situation is sufficient to justify the claim that the modified interventionist framework provides verification conditions, and thus gives empirical content, to higher-level causal claims (Baumgartner and Gebharter (2016)). The problem is that there seems to be no *sufficient* empirical condition that would establish that a given situation is one where there is causation at both lower and higher levels (as in Figure 4.2).

Let me explain. M_{1} and M_{2} are causally related in the framework of (M*) iff there is at least one possible change in the values of M_{1} (brought about by

*Figure 4.2* Model of a situation in which there is *both* lower-level causal influence N_{2}^N_{2} and higher-level influence M_{2}^M_{2}.

*Figure 4.3* Model of a situation in which there is lower-level causal influence Nj^N_{2 }*but no* parallel higher-level influence M_{2}^M_{2}.

an intervention) that would change the value of M_{2}. And M_{2} and M_{2} are *not *causally related in the framework of (M*) iff there is *no possible change* in the values of M_{2} (brought about by an intervention) that would change the value of M_{2}. Figure 4.2 illustrates the former, Figure 4.3 the latter.

Both Figures 4.2 and 4.3 represent possible situations containing higher- level variables M_{1} and M_{2}, and variables N_{1} and N_{2} in their respective supervenience bases, where N_{1}, the supervenience base of M_{1}, exercises a causal influence on N_{2}, the supervenience base of M_{2}. The comparison of the two situations sketched in Figures 4.2 and 4.3 shows that the higher-level influence M_{1}^M_{2} can be experimentally distinguished from the lower-level influence N_{1}^N_{2}. One causal relation can exist without the other. This shouldn’t be so surprising, given that the concept of superve- nience is mostly used in situations in which it is asymmetric, i.e., in which changes in the supervenient variables are always accompanied by changes in the supervenience base, but in which the reverse does not hold, i.e., where some changes at the level of variables in the supervenience base are not mirrored by any changes and causal influences at the level of the supervenient variables. This is the case when supervenience is used to characterize the relation between psychological properties and neurophysiological properties: the former are supposed to supervene on the latter but not the reverse. One psychological property can correspond to many underlying neurophysiological properties, whereas only one psychological property is compatible with any given neurophysiological property.

What is special in the case sketched in Figure 4.3 with respect to usual situations of supervenience, is that not only are some particular interventions at the level of N_{1} that cause changes in N_{2} not mirrored by parallel changes at the level of the supervenient variables (and thus, some causal influences at the level at the level of the supervenience basis are not mirrored by causal influences at the level of the supervenient variables), but that there is *no causal relation* at the higher-level *between the variables themselves*. This means that it is objectively *impossible* to influence M_{2} by intervening on M_{1}, i.e., by modifying the value of M_{1}.

The problem is that there is no empirical criterion that could justify the judgment that a given situation is of the type represented in Figure 4.3, i.e., of a sort in which it is *impossible* to modify M_{2} by intervening on M_{1}. One can justify that it is possible to modify M_{2} by intervening on M_{1}, simply by doing it. But no finite set of observations can guarantee that it is impossible to modify M_{2} by intervening on M_{1}, and in particular, it is not sufficient to show that so far, no intervention on M_{1} has modified M_{2}.

So can the causal influence of supervenient variables be assessed (by interventionist means) independently from the assessment of the causal influence of variables in their respective supervenience bases, as Woodward ((2008a), (2008b), (2015), (forthcoming)) and Menzies and List (2010) claim? In other words, can it be justified on empirical grounds that a situation is of the type sketched in Figure 4.2 rather than of the type sketched in Figure 4.3? The answer is that it can, but that the fact that the situation corresponds to Figure 4.3 may in some cases be established only on inductive grounds (Baumgartner and Gebharter (2016)). This is the case if not all possible values of M_{1} and M_{2} are known and also if the dependence of M_{2 }on M_{1} is probabilistic rather than deterministic.

In such situations, single experimental manipulations can only establish that M_{1} causally influences M_{2} (because they can establish that some changes in the value of M_{1} are followed by a change in the value of M_{2}, by provoking such changes in the value of M_{1}). However, if one does not know all the possible values of M4 or if the influence of M4 on M_{2} is probabilistic, neither single manipulations nor finite series of such manifestations can establish that Mj *does not* influence M_{2}, i.e., that there can be no change in the values of Mj that would be followed by a change in M_{2}.

With respect to downward causation, Baumgartner (2010), (2013) has argued that an interventionist account based on conditions (IV*) and (M*) does not provide a framework that would allow empirical justification of downward causation. In that account, relations of causal influence remain “underdetermined” (between downward and same-level causal influence) because it yields the result that two causal statements - that X directly causes Y and that SB(X) directly causes Y - are true under the same conditions, so that the analysis violates the interventionist maxim according to which different causal claims must be justified by different relations of manipulation.

Here is Baumgartner’s argument: If M_{1} is a higher-level variable, P_{1} a variable characterizing its supervenience base, then the statement according to which M_{1} causes P_{2} (which may be at the level of the supervenience base P_{1}), as sketched in Figure 4.4, and the statement according to which it is rather P_{1} that causes P_{2} (as sketched in Figure 4.5) are “empirically indistinguishable” (Baumgartner (2010: 19), (2013: 22)).

*Figure 4.4* Intervention on higher-level variable with downward causation.

*Figure 4.5* Intervention on higher-level variable *without* downward causation.

“The epiphenomenalist structure” sketched in Figure 4.5 “generates the exact same difference-making relations or correlations under possible interventions as” (Baumgartner (2013: 21-22) the structure sketched in Figure 4.4, in which variable M_{1} exercises downward causal influence on P_{2}. However, it is not true that both statements have the same empirical truth-conditions. Just as for higher-level causal judgments, the empirical content of a downward causal statement differs from the content of the corresponding lower-level causal statement. Here is a sketch of the formal structure of two situations in which there is causal influence between two lower-level variables N_{1}——N_{2}. In the first (sketched in Figure 4.6), there is also downward causation M_{1}—N_{2}, whereas there is no such downward causal influence in the second (sketched in Figure 4.7). The very conceivability of the second

*Figure 4.6* Model of downward causation with parallel lower-level causation.

*Figure 4.7* Model of lower-level causation, without downward causation.

situation shows that a downward judgment such as M^N_{2} has empirical content.

In situations that have the structure of Figure 4.6, there is lower-level causation because interventions on N can make a difference to the value of N_{2}, but there is also downward causation because interventions on Mj can change the value of N_{2}: a switch shifting the value of Mj from *m _{11}* to

*m*brings about a switch of the value of N

_{12 }_{2}, from (either

*n*or

_{21}*n*to (either «23 or П24).

_{22})However, the fact that N influences N_{2} at the lower level does not by itself entail that there is also downward causal influence from Mj on N_{2}. This is shown by the existence of situations that have the structure of Figure 4.7. In such situations, there is lower-level causation N^N_{2} because some interventions (such as a switch from *n _{n}* to n

_{12}) change the value of N

_{2}(from n

_{21}to n

_{22}). But there is

*no downward*causal influence M

_{1}^N

_{2}because no switch in the value of M

_{1}induces any reliable switch in the value of N

_{2}. Each of the values of M

_{1}(m

_{1}and m

_{2}) can yield n

_{21}and each can yield n

_{22}, so that the difference between

*n*

_{21}and

*n*

_{22}does not correspond to any difference between different values of M

_{1}.

Here are two situations that have the structure of Figures 4.6 and 4.7. Let M_{1} represent the color of a traffic light, with *m*_{11} being the value for green, and *m*_{12} for red. Let M_{2} represent the state of a car passing the traffic light, with *m*_{21} being the value for the car moving and *m*_{22} for the car stopping.

Let N_{1} represent the state of the electric circuit in the traffic light, where *n*_{11} and *n*_{12} are two states where current flows through the green lamp, and *n*_{13} and *n*_{14} states where current flows through the red lamp. Moreover *n*_{11 }and n_{13} also activate a sound for blind people, something neither n_{12} nor *n*_{14} do. N_{2} represents the state of the engine of the car: values *n*_{21} and *n*_{22 }represent states where it makes the car move, where *n*_{21} makes the car move in automatic mode.

If the driver respects the rules, the situation that has the structure of Figure 4.6: There is downward causal influence from the color of the traffic light to the motion of the car: green light makes the car move (*n*_{21} or *n*_{22}), whereas red light makes it stop (n_{23} or n_{24}).

If the driver is colorblind or inattentive, the situation may have the structure of Figure 4.7: Both states of the traffic light make the car move. But let us furthermore suppose that, to compensate for the driver’s distraction or poor discrimination of colors, the car has a mechanism that puts the engine in automatic mode if and only if it receives the sound emitted by a traffic light. Then there is no downward causation: the color of the traffic light makes no difference to the state of motion of the car. However, there is lower-level causation (just as in the situation corresponding to Figure 4.6): With the colorblind driver, the difference between states of the traffic light that produce a sound (n_{11} and n_{13}) and those that do not (n_{12} and n_{14}) makes a difference to the state of the engine of the car, between the automatic and the non automatic mode.

The existence of these two types of situation, sketched in Figures 4.6 and 4.7, shows that the statement of downward causal influence M^N_{2} has its own specific empirical content, distinct from the statement of lower- level causal influence N_{1}^N_{2}. For the same reason as in the case of higher- level causal statements, it can be difficult to find out whether there is *no downward* causal influence. In certain situations, the absence of downward causation can be justified only inductively (lower-level causation being presupposed). This is the case if either not all values of M_{1} are known or if the causal influence M^N_{2} is probabilistic. In such circumstances, it can be the case that no downward influence has been observed although it objectively exists.

To sum up, supervenience guarantees that there can be neither higher- level causation nor downward causation without lower-level causation. However, there is no “upward exclusion”: The presence of causal influence at some level (e.g. physical) N_{1}^N_{2} leaves the question open whether there is also higher-level causal influence between variables that supervene on N_{1} and N_{2}, and whether there is downward causation M_{1}^N_{2} or not. Given N_{1}^N_{2}, there may be and there may not be higher-level influence M^M_{2}, and there may be, or there may not be, downward influence M^N_{2}. The difference between situations where there is and where there is not higher-level or downward influence has empirical content because it corresponds to different patterns of difference-making.