Excerpt from paper: Lewis on counterfactuals
David Lewis instances Hume’s outline of causation: “we may define cause to be (1) an object followed by another, and where all the objects, similar to the first, are followed by objects similar to the second. Or, in other words (2) where, if the first object had not been, the second never had existed” (italicized by Lewis, numbered by me). Most of the debate on causation has revolved around the first part of the definition, and although Lewis feels that progress has been made since it was originally penned, he thinks it is time to take a look at it from another perspective.
Lewis outlines causation as it stands when the article was written, “a cause is defined (roughly) as any member of any minimal set of actual conditions that are jointly sufficient, given the laws, for existence of the effect.” This is a regularity theory of causality, and it is saying that all that is required for any given event to take place is that all its antecedent factors be present.
He in turn presents his alternative, a counterfactual analysis of causation, by appealing to the second part of Hume’s definition of causation: that if the cause had not been, there never would have been an effect. To extrapolate on his theory, he invokes a methodology of modality. When we speak of causes, we think of causes having made a difference, or producing events alternative to how they possibly could have been. Thus, possibility is key to any analysis of cause. Counterfactuals are presented at “face value,” as “statements about possible alternatives to the actual situation, somewhat vaguely specified, in which the actual laws may or may not remain intact,” or simply, statements about possible alternatives. By constructing statements about causation as such, Lewis hopes to avoid many of the inconsistencies cited above in conjunction with regularity theories of causation.
To speak of actuality, he introduces his concept of comparative similarity. That is to say, an actual world is a possible world that most closely approximates actuality. Thus one that more closely resembles actuality than another after taking into account all the factors that are similar and different. We might say that we can arrange these possible worlds along a spectrum according to similarity, with the one nearest actuality being the actual world.
Using the above modality, it follows that for any two propositions A and C, we can construct a counterfactual proposition: A->C, where “->” symbolizes counterfactuality, or “if it were the case that a, it would be the case that b”. The operation is demonstrably true accordingly:
Lewis outlines causation as it stands when the article was written, “a cause is defined (roughly) as any member of any minimal set of actual conditions that are jointly sufficient, given the laws, for existence of the effect.” This is a regularity theory of causality, and it is saying that all that is required for any given event to take place is that all its antecedent factors be present.
He in turn presents his alternative, a counterfactual analysis of causation, by appealing to the second part of Hume’s definition of causation: that if the cause had not been, there never would have been an effect. To extrapolate on his theory, he invokes a methodology of modality. When we speak of causes, we think of causes having made a difference, or producing events alternative to how they possibly could have been. Thus, possibility is key to any analysis of cause. Counterfactuals are presented at “face value,” as “statements about possible alternatives to the actual situation, somewhat vaguely specified, in which the actual laws may or may not remain intact,” or simply, statements about possible alternatives. By constructing statements about causation as such, Lewis hopes to avoid many of the inconsistencies cited above in conjunction with regularity theories of causation.
To speak of actuality, he introduces his concept of comparative similarity. That is to say, an actual world is a possible world that most closely approximates actuality. Thus one that more closely resembles actuality than another after taking into account all the factors that are similar and different. We might say that we can arrange these possible worlds along a spectrum according to similarity, with the one nearest actuality being the actual world.
Using the above modality, it follows that for any two propositions A and C, we can construct a counterfactual proposition: A->C, where “->” symbolizes counterfactuality, or “if it were the case that a, it would be the case that b”. The operation is demonstrably true accordingly:
A->C is true [at an actual world] iff either (1) there are no possible A-worlds (in which case A->C is vacuouse), or (2) some A-world where C holds closer (to the actual world) than is any A-world where C does not hold.
That is to say a counterfactual is not vacuously true iff it takes less deviation from actuality to make the consequent true together with the antecedent than it does to make the antecedent true without the consequent (This is a gross paraphrase). Thus A->C implies the material conditional, if A then C at a world approaching actuality. He calls this conditional dependence, (C depends on A: if not A then not C) counterfactual dependence.
Lewis, in turn, adapts the above theory involving propositions to events and constructs his general theory of causation. Presumably events are not propositions, however we can signify events using propositions. Counterfactual dependence applies to events in as much as they correspond to their respective signifying propositions. If proposition E corresponding to event e, counterfactually depends on proposition C corresponding to event c, then it follows that event e counterfactually depends on event c. It translates, that two events causally depend on one another, e on c, at a world approaching actuality iff, “if c had not been, e would never have existed.” So the same conditional dependence described above, counterfactual dependence, can be applied to events, and subsequently used to depict causal dependence. Then e depends causally on c. He expands causation, introducing the concept of causal chains. If e depends causally on c, and c on a, then it follows that e, by virtue of a causal chain, depends causally on a. Causation is ‘transitive’, and thus causation from a to e is possible without direct causal dependence. Finally, “one event is the cause of another iff there exists a causal link leading from the first to the second.”
Lewis, in turn, adapts the above theory involving propositions to events and constructs his general theory of causation. Presumably events are not propositions, however we can signify events using propositions. Counterfactual dependence applies to events in as much as they correspond to their respective signifying propositions. If proposition E corresponding to event e, counterfactually depends on proposition C corresponding to event c, then it follows that event e counterfactually depends on event c. It translates, that two events causally depend on one another, e on c, at a world approaching actuality iff, “if c had not been, e would never have existed.” So the same conditional dependence described above, counterfactual dependence, can be applied to events, and subsequently used to depict causal dependence. Then e depends causally on c. He expands causation, introducing the concept of causal chains. If e depends causally on c, and c on a, then it follows that e, by virtue of a causal chain, depends causally on a. Causation is ‘transitive’, and thus causation from a to e is possible without direct causal dependence. Finally, “one event is the cause of another iff there exists a causal link leading from the first to the second.”
posted by Nicholas @ 1.4.06
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