Counterfactuals: A Problem for

Interventionists & Mechanists?

Alexander ReutlingerUniversity of Münster

DFG Research GroupCausality, Laws, Dispositions &

Explanations - the Intersection of Science and Metaphysics

2

Contents

• (1) The Problem for interventionists & mechanists: truth conditions of counterfactuals

• (2) Solution I: Lewisian Semantics & some objections

• (3) Solution II: Goodmanian semantics

3

Interventionism• Woodward’s definition of a direct type-level

cause: • ‘A necessary and sufficient condition

for X to be a direct cause of Y with respect to some variable set V is that there be a possible intervention on X that will change Y (or the probability distribution of Y) when all other variables are held fixed at some value by intervention.’ (2003: 55)

4

Interventionist Counterfactuals

• What is the counterfactual involved in this definition of a direct cause?

• It is what one might call an interventionist counterfactual:

• If the value of X were changed to be xi by an intervention, then the value of Y would change to yi.

• That’s why Interventionists claim to advocate a (modified) counterfactual theory of causation, (Hitchcock 2001, Woodward 2003, Halpern & Pearl 2005).

5

Mechanisms

• Machamer, Darden & Craver (2000: 3): Mechanisms are entities and activities organized such that they are productive of regular changes from start or set-up to finish or termination conditions.

• Glennan (2002: S344): A mechanism for a behavior is a complex system that produces that behavior by the interaction of a number of parts, where the interactions between parts can be characterized by direct, invariant, change-relating generalizations.

6

Mechanisms & Counterfactuals

• I agree with Psillos (2004: 314): “Counterfactuals may enter [at least] at two places.

• The first is the activities themselves. Activities, such as bonding, repelling, breaking, dissolving etc., are supposed to embody causal connections. But, one may argue that causal connections are distinguished, at least in part, from non-causal ones by means of counterfactuals. If “x broke y” is meant to capture the claim that “x caused y to brake,” then “x broke y” must issue in a counterfactual of the form “if x hadn’t struck y, then y wouldn’t have broken.” So talk about activities is, in a sense, disguised talk about counterfactuals.

• The second entry-point for counterfactuals is the characterization of interactions within the mechanism.” (See also Glennan 2002: S344; Craver 2007: ch 3.5; Woodward 2002: S375)

7

The Problem

• Although interventionist and mechanist approaches rely on counterfactuals, surprisingly they do not provide an account of truth conditions for counterfactuals.

• This is a severe problem, because any proponent of a counterfactual theory seems to be obligated to provide a semantics for counterfactuals. (Hiddleston 2005 and Psillos 2004, 2007)

• Let me focus on Woodward, because (a) his problems with counterfactuals are representative for most interventionists & mechanists and (b) some mechanists rely on Woodward.

8

The Need for Truth conditions

• Woodward repeatedly stresses that counterfactuals do have (objective) truth values & that science seems to rely on truth values of counterfactuals

• Woodward tells us that there are truth conditions for counterfactuals. But he does not tell us what precisely these truth conditions are.

• Is that a problem?

9

The Need for Truth Conditions

• Woodward himself is ambiguous :• (i) Sometimes it sounds as if he is prepared to

accept the truth conditions as primitive & to engage only in ‘pragmatic considerations’ (Woodward 2003b: 4) of the use of counterfactuals, i.e. (a) their use in conceptual analysis (e.g., of laws and causation), (b) how they can be tested empirically, (c) how we can use them in inferences.

• (ii) sometimes it seems that Woodward (& and other interventionists) bet on a proper interventionist semantics for counterfactuals.

• I will argue that one should opt for (ii)

10

Reason 1

• Woodward actually does attempt to determine truth conditions for counterfactuals. But his attempts are not coherent.

• One attempt to provide Interventionist Semantics is essentially based on the notion of an intervention:

• “A counterfactual of the form ‘if X were to have the value x, then Y would have the value y’ is true if and only if Y has the value y in the hypothetical situation (or possible world) where (i) the value of X is equal to x; and (ii) all other variables have their actual values with the exception of [the intervention variable] I […].” (Hitchcock & Woodward 2003: 13f)

11

Reason 1

• Another attempt essentially involves laws:

• “[semantics] is done by the use of systems of equations or functional relationships […] If the equations […] are correct, they enable us to determine what would happen under these assumptions.” (Woodward 2003b: 3f)

12

Reason 1

• Unlike interventionist semantics, established Semantics for counterfactuals clearly rely on two essential building blocks: laws & singular facts

• In Interventionist Semantics it remains unclear whether and, if at all, what role laws play.

• With Psillos (2007: 104f) I want to defend the slogan: No laws (& interventions) in, no counterfactuals out

• Note that defending this slogan is supposed to improve the interventionist account

13

Reason 2

• Woodward also indirectly commits himself to the task of providing truth conditions for counterfactuals by criticizing Lewis’ semantics for counterfactuals extensively.

• This critique and the claim that there are truth conditions of (at least interventionist) counterfactuals amounts to the obligation of providing a semantics for counterfactuals which is an alternative to Lewis’ semantics.

14

2 Theories of Truth Conditions

• Lewisian semantics• Goodmanian semantics

(metalinguistic theory)

15

Lewisian Semantics

• Lewis possible world semantics is the orthodox view in many areas of philosophy

• Lewisian Semantics: The counterfactual if were the case, then would be the case is (non-vacuously) true at w if and only if there is some possible world u, where and are both true, and u is closer to w than any possible world v, where is true but is false.

• The closeness of worlds is measured in terms of their overall similarity

16

Lewisian Similarity Heuristic

• One finds out that world u is more similar to world w than v by using the following criteria to order worlds:

• (1) similarity in laws• (2) similarity in particular facts

17

Lewis’s Virtues

• Lewis’s semantics is in accord with our slogan: No laws (& facts/interventions) in, no counterfactuals out

18

Objections

• One might not be delighted to adopt Lewisian Semantics. (Woodward 2003a, 2003b; Bogen 2003; Hitchcock & Woodward 2003; Psillos 2004, 2007; Pearl 2000)

• (1) Problem of Naturalization: The heuristic is arbitrary and vague & it is not clear how science measures ‘small’ and ‘big’ miracles

• (2) Non-Reductive Analysis: Lewisian semantics is reductive with respect to causal notions. But one may have independent arguments for the thesis: it is not possible to give a non-reductive account of causal counterfactuals.

19

Objections

• A more strategic objection could be:• (3) Collapse: For interventionists it

seems unwise to accept Lewisian semantics because interventionism would be in danger to collapse into a Lewisian counterfactual theory of causation.

20

So … ?

… is there an alternative to Lewisian semantics?

21

Goodman

• In Fact, Fiction and Forecast Goodman famously argues for the view that counterfactuals are condensed or hidden arguments. => metalinguistic theory

• In general, these arguments contain a set of law statements and singular statements (most importantly singular statements describing a counterfactual situation expressed by the antecedent proposition of the counterfactual conditional) as its premises. The conclusion, which follows from these premises, is another singular statement.

• If the counterfactual is true, the conclusion of the argument is the consequent proposition of the counterfactual conditional, otherwise it is false.

22

Goodman’s Heritage

• In the recent debate on causation there‘s been a renaissance of Goodmanian semantics (see Pearl 2000, Hüttemann 2004, Loewer 2007, Maudlin 2004 & 2007, Leitgeb 2009).

23

Structural Model Semantics

• Judea Pearl provides a semantics for counterfactual conditionals straightforwardly with respect to a causal model M - M is a triple of <U, V, L>.

• “The sentence ‘Y would be y had X been x’ […] is interpreted to mean ‘the solution for Y in Mx is equal to y under the current conditions U=u’.” (Pearl 2002: 100).

• In this formulation ‘Mx’ denotes a submodel of M: a model where structural equations (laws) in which X figures X has taken the value x.

24

Structural Model Semantics

• ‘the solution for Y in a submodel MX’ consists three steps according to Pearl (2000: 206):

• Step 1 - Abduction: Update the boundary conditions by evidence e.

• Step 2 - Action: Modify M by action do(A), where A is the antecedent of the counterfactual, to obtain the submodel MA.

• Step 3 - Prediction: Use the submodel to compute the probability of B, the consequent of the counterfactual.

25

Structural Model Semantics

• Note that Pearl argues that• (a) his semantics does not rely on a

similarity heuristic (Pearl 2000: 239f)• (b) that Pearl (2000: 240-243; Galles &

Pearl 1998: section 4) agrees with Lewis‘s logic of counterfactual, i.e. V-logic (see Lewis 1973: 123, 132)

26

Maudlin’s 3-Step-Semantics

• In a first step, determine the actual boundary conditions (i.e. the values of the variables, or ‘magnitudes’) in question.

• In a second step, change the value of the variable, which the antecedent of the counterfactual refers to, to the value that the antecedent assigns to it.

• In a third step, see whether the consequent of the counterfactual follows from the new boundary conditions (as constructed in the second step) and a law that applies to the boundary condition.

• If it follows the counterfactual is true; if it does not follow, then the counterfactual is false. (Maudlin 2007: 23)

27

Modified Goodmanian Semantics

• Here is an attempt to condense the 3-step-approaches into a handy definition:

• Greek letters stand for realizations of a variable (X=x), for X V

• If were the case, then would be the case is true relative to a causal model M= <U, V, L> if and only if

follows from and the values of other variables in U and V and the laws L.

28

2 Modifications

• Modification 1: The semantics I propose differs from Goodman’s reductive spirit. It refers to causal information.

• In a sense Goodman’s major problem of determining the set of relevant conditions does not arise from an interventionist point of view, because (some) relevant conditions are already part of the model as other causes.

• A modest morale could be: Our semantics is model-relative, i.e. a counterfactual is true relative to a set of variables and a set of laws. And more – something non-relative – one cannot say.

29

2 Modifications

• Modification 2: The semantics claims that the consequent of the counterfactual follows from a set of premises. Contrary to Goodman, for counterfactuals in the special sciences this inference is likely to be non-monotonic, because we cannot rely on universal laws of nature.

• Laws are better characterized as ceteris paribus laws or stable generalizations that are limited in scope, stochastic, mechanistically fragile & historically contingent (Craver 2007: 67-69).

30

Conclusion

• We have started with a problem: interventionist and mechanists are committed to counterfactuals but they do not clarify what their truth conditions are.

• I have argued that both should tell a story about truth conditions. There are two options: Lewisian and Goodmanian semantics.

• Interventionists & Mechanists have a common enemy: Lewisian semantics. So, they should bet on Goodmanian semantics.

• The Modified Goodmanian Semantics does not rely on a similarity heuristic. Thus it avoids objections against this heuristic

31

Conclusion

• It supports the slogan: No laws (& interventions) in, no counterfactuals out. Thus, there is a Humean lesson to learn for interventionists and mechanists: laws matter more than one might be willing to admit.

• Adopting Goodmanian semantics also has another advantage for interventionists & mechanists: The profile of their theory becomes more distinguished

• Interventionist and mechanist theories causation, explanation, reduction etc. rely on a different semantics than the orthodox Lewisian counterfactual theory of causation. They employ (something like) Modified Goodmanian Semantics instead of Lewisian Semantics.

32

Thanks for your attention !

Acknowledgements:Many thanks for comments on an earlier version by Michael Baumgartner, Andreas Hüttemann, Marie Kaiser, Beate Krickel &

Wolfgang Spohn & other philosophers in Münster & Konstanz