Can causality be analysed satisfactorily
in terms of counterfactual dependence?
In brief, the answer is “No!” But in order to explain why not, I will first have to say a few words on the criteria that constitute a “satisfactory analysis”. Then I will provide a brief description of the counterfactual dependence analysis of causality, sufficient that it can form the basis for my argument that it is fatally flawed in at least two respects.
What is a “satisfactory analysis”?
According to Mautner’s Dictionary of Philosophy(1), a philosophical analysis of causality would be an explanation of the concept of causality that “draws attention to its constituents, its presuppositions, its implications, etc.” and shows how the concept can be “reduced to elements belonging to some basic category”. In other words, a satisfactory analysis of the concept of causation would be one that explained what causality was in terms that
(i) employs concepts (words) that are more ontologically fundamental, and therefore presumably simpler and more easily understood; and
(ii) does not draw upon concepts (words) that themselves could only be analyzed in terms of causality.
For an analysis of causality to be “better” (ie. more “satisfactory”) than the concept of causality itself, it will have to explain just what causality is (and what are its presuppositions, implications, etc.) in terms of concepts whose meanings are more easily understood and explained than is causality itself. Otherwise, there would be no gain, and we might just as well treat the concept of causality as sui generis. An analysis of causality that draws upon concepts whose implications and presuppositions are more obscure than is causality itself would therefore not be a “satisfactory analysis” of causality. Also, obviously, a “satisfactory analysis” of causality cannot be circular – cannot employ concepts that themselves can only be analyzed in terms of causality.
So it will be assumed in the remainder of this essay, that by “analyzed satisfactorily”, the essay’s title question is asking whether the counterfactual dependence analysis of causality is more comprehensible than is causality itself, and whether the counterfactual dependence analysis of causality can be done in terms that do not in turn rely on the concept of causality. And my argument will be that the counterfactual dependence analysis of causality fails on both grounds.
I should also note, in preface, that the concept of causality relates (if indeed it is a relation, there being some debate on the matter) things called “causes” and “effects.” These are things that have variously been called “objects,” “events,” “states of affairs,” “situations,” “facts,” “facta,” “properties,” “tropes,” “propositions,” “statements,” or “conditions”. For ease of exposition, in what follows, I will employ the term “event” to mean any or all of these things.
What is the “counterfactual dependence” analysis of causality?
The first attempt to provide a counterfactual explanation of causality was offered in 1748 by David Hume, who wrote –
“We may define a cause to be 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, where, if the first object had not been, the second never had existed.” [Hume, An Enquiry Concerning Human Understanding, Section VII].
The core notion here is that the meaning of causal propositions can be explained in terms of counterfactual conditionals. The proposition “C causes E” (or “E because C”) is to be analyzed (explained) as –
(1) If C had not occurred, then E would not have occurred.
But Hume, after introducing the idea, never expanded on his counterfactual approach to understanding causality. So it was left to his successors to explore the implications of this formulation. The main difficulty facing his successors was the obscurity of counterfactual conditionals themselves – a direct challenge to the first criterion of a “satisfactory analysis”. Two problems remained to be resolved – understanding the truth conditions of counterfactual conditionals, and their apparent reference to unactualized possibilities.
In 1973, however, David Lewis presented what has become perhaps the best known and most thoroughly elaborated counterfactual theory of causation(2). Lewis defines the notion of counterfactual dependence between events as –
(2) Where C and E are two distinct possible events, E causally depends on C if and only if, if C were to occur E would occur; and if C were not to occur E would not occur.
Whether E occurs or not depends on whether C occurs or not. This dependence is “counterfactual” because it holds whether or not C or E actually occur. It holds even if C or E do (not) actually occur. Strictly speaking, Lewis’s definition differs slightly from what I have presented here, because he talks in terms of chains of causal dependence rather than direct causal dependence. But for the purposes of this essay, we can ignore that refinement.
Lewis argues that the concept of causality is a concept of “Something that makes a difference”, and that counterfactuals are the best way of representing that more fundamental notion.
“We think of a cause as something that makes a difference, and the difference it makes must be a difference from what would have happened without it. Had it been absent, its effects — some of them, at least, and usually all — would have been absent as well.” [Lewis, “Causation”, Journal of Philosophy, 70: p.161]
It is worth noting, in passing, that this analysis of causality demands that C and E be distinct and independent events – C and E cannot be identical, overlap, nor logically imply each other. Lewis argued that this restriction is necessary in order to reject “false positives” – pairs of events that our intuitions dictate are clearly non-causally related. Lewis also argues that, for the same reason, backtracking counterfactuals must also be excluded. Only counterfactuals that (typically) hold the past fixed up until the instant the counterfactual antecedent is supposed to obtain are acceptable analyses of causality.
So far so good. But to this point Lewis is merely refining Hume. The challenge remains of understanding the truth conditions of counterfactual conditionals, and their apparent reference to unactualized possibilities. Here is where Lewis applies his “Possible World Semantics”.
Possible Worlds Semantics specifies that the truth conditions for counterfactuals can be analyzed (explained) in terms of similarity relations between possible worlds. A possible world W1 is said to be “closer” to the actual world (W0) than another possible world W2 if and only if W1 “resembles” W0 more than W2 does. This resemblance relation produces what Lewis calls a “weak ordering” of worlds – any two worlds Wi and Wj can be ordered with respect to their “closeness” (measured by the degree of resemblance) to the actual world (ties permitted).
In terms of this similarity relation then, the truth condition for the counterfactual “If C were the case, E would be the case”, is –
(3) “If C were the case, E would be the case” is true in W0 if and only if (i) there are no possible C-worlds; or (ii) some C-world where E holds is closer to W0 than is any C-world where E does not hold.
(I shall ignore the first case, wherein the counterfactual is vacuously true.) Lewis’ basic idea here is that the counterfactual is true just in case it takes less of a departure from actuality to make both the antecedent and the consequent true than it takes to make the antecedent true and the consequent false.
When Lewis first presented this analysis of causality in terms of counterfactual dependence, the generally accepted explanation of causality was in terms of lawful regularities of nature. It was also commonly recognized that such regularity theories faced a number of problematic counterexamples where our intuitions conflicted with the theory. Lewis’ counterfactual analysis is not subject to the same counterexamples. So when first introduced, Lewis’s counterfactual analysis of causality offered considerable explanatory benefits.
Why is the counterfactual analysis flawed?
Deeper analysis since that time, however, has revealed a number of difficulties. Two of these problems I believe disqualify the counterfactual dependence as a “satisfactory analysis” of causality.
The first problem is that possible worlds are not inspectable. Whether they are abstract concepts as many maintain, or real existents as Lewis maintains, they are not causally connected with this, the actual world. We too easily forget that this means that we cannot really inspect any other possible world than our current world. So the question of whether C or E holds in some possible world is not a question of empirical investigation. What in fact holds in any other possible world can have no actual bearing on the answer, regardless of how we choose to express the results of our determination. Given that all we have epistemic access to is the actual world, how could we know anything about these other possible worlds or what holds in them? How, therefore, are we judge whether one world is “closer” than another to the actual world? How could we even guess? Obviously, we can’t. Although Lewis discusses the resemblance relation at considerable length in his Counterfactuals(3), what remains obscure is how we can determine the relative “closeness” of C-worlds wherein E holds and C does not hold. Whether C or E holds must be determined on the basis of factors that are known to us here in this actual world. What we wish to assert about the relative “closeness” of possible worlds can be so only by stipulation. Whatever the judgement, the grounding for our judgements of “closeness” has to be right before us in this actual world. But how we are to make that judgement, remains unexplained.
Complicating this difficulty is the fact that the problem of trans-world identity has not been resolved. Consider a proposition of counterfactual dependence like “If Ann were to throw the ball [at the window], the window would break.” Possible worlds semantics demands that we examine every possible world in which Ann throws the ball to see if any of those worlds in which the window does not break is “closer” to the actual world that worlds in which the window does break. Obviously, from the preceeding argument, we do not do this examination in anything like an empirical sense. Rather we do it conceptually, on the basis of what we stipulate about these possible worlds. But just what is it that (conceptually) picks out an instance of “Ann” or “the ball” or “the window” in any other possible world than this actual world. Some philosophers (Kripke in particular) have suggested that trans-world identity is established only by identical origins. So any existent in some possible world that had the same parents (manufacturing plant?) would be the “same” Ann, ball or window. But this runs into infinite regresses. The hypothesis leaves problematic the question of the identicality of the origins – and so forth with infinite circularity. And if that is the case, then clearly our judgements of resemblance and closeness are prior to, and not dependent upon the possible worlds semantics.
What this means is that Lewis’ notion of “closeness” or “similarity” or “resemblance” between possible worlds is more obscure and less fundamental than is the notion of “causality” that he seeks to explain by their use. This, as I suggested above, disqualifies the counterfactual dependence analysis of causality as a “satisfactory analysis”.
The second problem is related to the first, in that it develops from Lewis’ notion of the kind of “departure” from actuality that would be necessary to make either (or both) the antecedent and/or the consequent true. Suppose we stipulate that W1 is identical to W0 at some time t1 and then there occurs a “departure” necessary to make W1 into a C-world (a possible world wherein C counterfactually holds – say one wherein Ann throws the ball). How do we determine what this “departure” is, and how do we determine whether it takes less of a departure from actuality to make both the antecedent and the consequent true than to make the antecedent true and the consequent false. Obviously, to judge whether any hypothetical departure might make either the antecedent or the consequent true, we must draw upon our understanding of how a possible world would evolve through time, given some change in the status quo. But that understanding is itself an understanding of causality – an understanding of how the actual world reacts to stimulii. In other words, Lewis’ concept of how possible worlds can “differ” from this our actual world, and the relative “closeness” of different possible worlds, is itself dependent on our concept of causality.
What this means is that Lewis’ notion of “closeness” or “similarity” or “resemblance” between possible worlds is fatally circular. This, as I suggested above, also disqualifies the counterfactual dependence analysis of causality as a “satisfactory analysis”.
Given either of these problems individually, but especially given both together, I conclude that causality can not be analyzed satisfactorily in terms of counterfactual dependence.
Notes & References
(1) Mautner, Thomas; The Penguin Dictionary of Philosophy, Penguin Putnam Inc., New York, New York. 1996. ISBN 0-14-051250-0. pg 18-19.
(2) Lewis, David; “Causation”, Journal of Philosophy, 70: 556-67. reprinted in Causation, Ernest Sosa and Michael Tooley, eds. Oxford University Press, Oxford, England, 1993. ISBN 978-0-19-875094-9
(3) Lewis, David; Counterfactuals, Blackwell Publishing, Oxford, England. 1973. ISBN 0-631-22425-4
Anscombe, G.E.M.; “Causality and Determination” in Causation, Ernest Sosa and Michael Tooley, eds. Oxford University Press, Oxford, England, 1993. ISBN 978-0-19-875094-9
Armstrong, D.M.; “Going Through the Open Door Again: Counterfactual versus Singularist Theories of Causation” in Causation and Counterfactuals, Collins, John & Hall, Ned & Paul L.A. (eds.). The MIT Press, Cambridge, Massachusetts, 2004.ISBN 0-262-53256-5.
Bennett, Jonathan: “Event Causation: The Counterfactual Analysis” in Causation, Ernest Sosa and Michael Tooley, eds. Oxford University Press, Oxford, England, 1993. ISBN 978-0-19-875094-9
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(Citations will be given in “Treatise, Book, Part, Section” format.)
Hume, David; An Enquiry Concerning Human Understanding, 1748.Eighteenth-Century Studies, URL = < http://18th.eserver.org/hume-enquiry.html#5>
(Citations will be given in “EUH, Section, Part” format.)
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