Hesperus is Bosphorus

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Casting a Shadow on Lewis’s Theory of Causation

with 11 comments

A Shadowy Puzzle:

In the above diagram L is a distant light source, A and B are two opaque rectangular objects with equal width.  If only A had been present, it would have cast the shadow R+S on the ground; and if only B had been present, it would have cast the shadow S.  In the situation above, P is the shadow A casts on B (which coincides with the area of B facing A).

Question: Clearly, the shadows R and P are caused by A.  But which one of A and B is causally responsible for the shadow S?

(1) B cannot be causing S, because B is not receiving any light, as A blocks the light from reaching B.  And an object which doesn’t have any light impinging on it cannot cast any shadow.

(2) A cannot be causing S, because A’s casting S is prevented by A’s casting P on B.  And an object can cast only one shadow in the presence of one light source.  In this case, A’s full shadow due to L is R+P; so we cannot claim that A casts S in addition to casting P.

(3) Since neither A nor B is causally responsible for S, we can’t say A and B overdetermine S.  For in overdetermination situations, there are two or more causes each of which is causally responsible for the same effect.  Nor can we say that one of A and B is preempting the other and itself causing S—for neither is a cause of S.

Then what is causing S?

My answer to this puzzle is that it is A, despite the considerations in (2).  Clearly, A is what is causing the dark region (umbra) behind A, by blocking the light coming from L.  (B has no share in bringing about that dark region, as B doesn’t receive any light.)  The presence of the ground (represented by the long horizontal line in the figure) that intersects with the dark region leads to the casting of the shadow R+S on the ground.  Hence, it is A that is causally responsible for S.

B is a “back-up cause” of S: If A hadn’t been present, B would have cast S.  It follows that we do have a case of preemption here, after all: A preempts B from causing S.

Another interesting feature of the situation in the diagram is that it seems to pose a problem for David Lewis’s well-known counterfactual analysis of causation.1  Although, as I argued, the presence of A is causally responsible for (or is “a cause” of) the shadow portion S, we don’t have a series of actual events running from A to S that constitute a chain of counterfactually dependent events from A to S, which Lewis’s analysis requires.  The presence of B blocks completion of such a chain.  Take, for example, the events:

d1: the presence of the dark region between A and B

d2: the presence of the dark region to the right of B,

and consider the counterfactuals:

If A had not been present, then d1 would not have occurred

If d1 had not occurred, then d2 would not have occurred

If d2 had not occurred, then S would not have been present.

These counterfactuals fail to entail a chain of counterfactually dependent events in Lewis’s sense, because the second counterfactual is false: even if d1 had not occurred, d2 would still have occurred thanks to the presence of B.

Hence the situation above appears to constitute a counterexample to Lewis’s 1973 analysis of causation.  And this case doesn’t seem to be assimilable to the other problematic cases for that analysis, such as “late preemption” and “trumping preemption.”  (To give a name to them, we might call the kind of cases exemplified in the diagram “overshadowing preemption.”)

To illustrate how the improved theory Lewis offered in 20002 works, let me give the example of how this new theory is supposed to take care of trumping preemption cases.  An example of trumping preemption was given by Jonathan Schaffer:

… the major and the sergeant stand before the corporal, [and they] both shout “Charge!” at the same time, and the corporal decides to charge.[.]  Orders from higher-ranking soldiers trump those of lower rank.  I hope you agree that the major’s order, and not the sergeant’s, causes the corporal’s decision to charge….3

Lewis thinks that his improved theory can handle Schaffer’s example.  According to the new criteria Lewis added, first we imagine altering the trumping factor while keeping the trumped factor the same, and see if there will be any change in the effect.  Secondly, we imagine altering the trumped factor while keeping the trumping factor the same, and see if the effect will be any different.  Lewis argues that in the first case there will be a change in the effect (e.g. if the major were to shout “Charge in 5 minutes from now!”, instead), whereas in the second case there will be no change in the effect (e.g. if the sergeant  were to shout “Charge in 5 minutes from now!”, instead).  Thus we can conclude that the major’s shouting, rather than the sergeant’s, is a cause of the soldiers’ charging, according to Lewis.

But this ploy wouldn’t work in our case.  In our example, suppose we lowered the height of A, while we kept B unaltered.  The effect S wouldn’t change.  Secondly, suppose we increased the height of B while A remained unaltered.  The effect S would thereby change—it would become a taller shadow.  Consequently, we must conclude that the presence of A isn’t a cause of S, contrary to our verdict above.

——————————–

1 David Lewis, “Causation,” Journal of Philosophy, 70(1973), pp.556-567.

2 David Lewis, “Causation as Influence,” Journal of Philosophy, 97(2000), pp.182-197.

3 Jonathan Schaffer, “Trumping Preemption,” Journal of Philosophy, 97(2000), pp.165-181; see p.175.

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Written by Erdinç Sayan

August 12, 2012 at 1:31 am

Posted in Metaphysics

11 Responses

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  1. Hi Erdinc,
    Interesting post. What would you say if instead of two opaque objects there was a single opaque solid, C, with A and B forming it’s left and right sides? In such a case would you say the whole object was the cause of the shadow, or merely A, its left hand side?

    Lucas Thorpe

    August 13, 2012 at 2:24 pm

    • Hmm… I think, strictly speaking, shadows are caused by surfaces of opaque objects blocking the light that fall on those surfaces. But instead of referring to surfaces as causers of shadows, we ordinarily talk about the objects that have those surfaces as causers of shadows.

      So, in your scenario, I’d say C is causing the shadow S.

      Let me add though that the issue of shadows is no superficial matter…

      Erdinç Sayan

      August 15, 2012 at 1:46 am

  2. I would say S is overdetermined by A and B, based on causation as influence. See my related paper, “The nature of shadows, from Yale to Bilkent, available here:

    http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7637344

    and here:

    http://istvanaranyosi.net/resources/Shadows.pdf

    István Aranyosi

    August 13, 2012 at 2:43 pm

  3. This bit does not seem right to me: “But this ploy wouldn’t work in our case. In our example, suppose we lowered the height of A, while we kept B unaltered. The effect S wouldn’t change. Secondly, suppose we increased the height of B while A remained unaltered. The effect S would thereby change—it would become a taller shadow. Consequently, we must conclude that the presence of A isn’t a cause of S, contrary to our verdict above.”

    What matters in causation as influence is for there to be a series of small changes in the cause event corresponding to a series of small changes in the effect event, such that each slight alteration of the effect is counterfactually dependent on an alteration of the cause. We have this in our example in both the relation between A and S and that between B and S, namely the series of size alterations upwards (i.e.keeping either of them fixed in size while raising the size of the other would change the size of the shadow), and the series of location alterations from left to right. (i.e. keeping either of them fixed and moving the other to the right would change the size of the shadow).

    It doesn’t matter that there also are alterations that don’t have such effects, if I understood the theory correctly :)

    István Aranyosi

    August 13, 2012 at 3:26 pm

    • Hi Istvan,

      Thanks for the challenging comments.

      As Lewis notes, it is very hard to come by genuine examples of overdetermination. Let me confess that I gave the set-up in my post as an impeccable example of overdetermination to my students in my causation classes. But I realized lately that it can’t be a case of overdetermination at all.

      You know, in overdetermination of an effect there are two or more causes from each of which there is an actual causal pathway from the cause to the effect. Thus, imagine a light bulb which is connected to two separate battery-and-switch sets in such a way that when both switches are closed the bulb lights. It lights in exactly the same way and to the same amount if only either one of the switches is turned on. When both switches are turned on there are two separate, parallel causal pathways both ending at the very same effect—the lighting of the bulb.

      Now, in my scenerio, there is no separate causal pathway from B to S, because the causal pathway from B to S, which would have existed had A not been present there, is thwarted by the presence of A. So, A preempts B from causally connecting to S. I don’t know about you, but I don’t see any actual causal pathway (even the beginning of such a pathway) that runs from B to S—in any respectable sense of the notion of ‘causal pathway’—which is parallel to the causal pathway that runs from A to S. The reason of course is that A eliminates one necessary condition for B to produce any shadow: there is no light impinging on (any portion of) B thanks to the blockage of the light by A. B’s situation is very similar to that of the bird that fails to cast any shadow in the Yale Puzzle: B doesn’t cast any shadow either, and hence cannot be a co-caster of S. Hence my scenario cannot be considered as a case of overdetermination. It is a case of preemption where S is being caused by A only.

      Here’s another similar situation. In the example of the bulb with the two circuits, suppose that when you turn on one of the switches in one circuit, this action knocks off the battery in the other circuit, thus preventing any causal pathway from the second battery to the bulb to take off. We can call these kinds of preemption “very early preemption” or “thwarting preemption” (if my earlier term “overshadowing preemption” sounds too example-specific).

      Moreover, your own “material exstitution view” of shadows that you propose in the paper that you refer to in your comment seems to imply—correctly to my mind—that it is A but not B that is causally responsible for the shadow segment S. (By the way, even if we grant to you that portions or regions of shadows are not themselves shadows, I think we can still talk about causes of portions of shadows, such as S.) According to that view, “… shadows are spatially determined … by extraneous light, that is, by the configuration of light that delimits the region occupied by … a … collection of materially occupied regions.” If I understand your theory right, the extraneous light L does the delimiting around A first. Once A performs that function, there is no role left for B to help or contribute to that process. Hence B plays no role in the determination of S.

      On a second thought (and a better understanding of Lewis’s revised theory, hopefully), you seem right: Lewis’s influence view makes both A and B independently cause, i.e. overdetermine, S. But if I am right about my contentions above, this is a serious minus for Lewis’s account.

      Erdinç Sayan

      August 16, 2012 at 11:32 am

  4. It seems intuitively right to me, without having an account of causation as influence or some other account in mind, that we have a case of causal overdetermination here. A’s being located at the point it is located in the example is individually (taking the presence of the light source as it is for granted) causally sufficent for the occurence of the shadow, and B’s being located at the point it is located in the example is individually causally sufficient for the ocurrence of the shadow. In this case, we have both.

    Erhan Demircioglu

    August 13, 2012 at 7:09 pm

    • Hi Erhan,

      It is very tempting to take my set-up as an example of causal overdetermination, but as I explained at length in my reply to Istvan’s comments above, we should resist that temptation.

      Erdinç Sayan

      August 16, 2012 at 11:54 am

  5. [...] This is a very clever objection to David Lewis’ theory of causation, but an interesting puzzle on all on it’s own. The author of the post, Erdinç Sayan, is to be commended for expositing the puzzle with such clarity. It reminds me of a similar puzzle I thought of years ago, which I’ll post about soon. Share this:TwitterFacebookLike this:LikeBe the first to like this. Leave a Comment [...]

    • Thanks for the kind words. I’d be very interested to read your post.

      Erdinç Sayan

      August 27, 2012 at 8:01 pm

      • A very interesting puzzle! Here is a new twist to it. No one asks “what is the distance between A and B?”. Why not? One good reason is because we believe that it is irrelevant.If that is the case, let us suppose that the distance between them is zero, in which case the two walls would be exactly the same size. Further suppose that they have negligible thickness like two sheets of black paper glued to one another. In that case the argument for overdetermination sounds very implausible. If we initially have only paper A with its shadow, then gluing another paper to its right hand side (from our perspective) should make no difference. That supports Erdinc’s position. But suppose that we initially had only paper B,with its shadow. Now if we were to glue paper A to its left face, then are we willing to say that now it is A which is responsible for the shadow? Perhaps that should be the correct answer. If we deny that, then we should have to conclude that the answer to our question depends on which wall was put up first, which sounds very odd.

        ilhan inan

        September 13, 2012 at 12:18 pm

        • Thanks for your supportive comment Ilhan hoca.

          … if we were to glue paper A to its left face, then are we willing to say that now it is A which is responsible for the shadow? Perhaps that should be the correct answer. If we deny that, then we should have to conclude that the answer to our question depends on which wall was put up first, which sounds very odd.

          I agree totally. Assuming that we still have two distinct objects, A and B, after the gluing, I’d say A is the one that blocks the light and hence causes the shadow on the ground. Now, if we fuse A to B, so that we now want to regard them as a single thing, C, I think my reply would be along the lines of my reply to Lucas’s August 13 comment above.

          Erdinç Sayan

          September 13, 2012 at 10:07 pm


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