Basic middle pre-emption

Example (20):

SYLVIA AND BRUNO#1 (an example due to Strevens [2003]): Suppose Sylvia and Bruno both throw an intrinsically identical steel ball each at the same time, but that Bruno is aiming at a glass bottle, and Sylvia is aiming at a different target beyond Bruno and the bottle. Suppose Sylvia throws her ball (C) at time t-1 and her ball shatters the glass bottle (E) at t+1 after colliding with Bruno’s ball (D) at t. Suppose Bruno throws his ball (A) at the same time as Sylvia throws her ball (C), but that his ball does not shatter the glass

bottle, because it collides with Sylvia’s ball at a mid air collision (D) at time t, and bounces away from otherwise causing the shattering (E).91

This is quite a tricky example, and probably easier to understand with diagrams than with words: The following is a topographical diagram representing the trajectories of the two balls. The black line represents the trajectory of Sylvia’s ball, and the dotted line represents the trajectory of Bruno’s ball; the time line is plotted on an x axis below the diagram.

Sylvia’s ball Glass Bottle

Bruno’s ball

T – 1 T T + 1

We add some further details to toughen up the example: Suppose in the range of not-too- distant possible worlds that no alteration of Sylvia’s throw, or Sylvia’s ball in flight towards the collision, would have resulted in an alteration of the shattering of the bottle,

91_{Note that the events to do with a ball flying after the collision up to the shattering would have been}

exactly the same had Sylvia not thrown her ball, given Bruno’s ball is intrinsically identical and would have assumed the same trajectory had Sylvia not thrown.

because even the smallest alteration in Sylvia’s throw, or to Sylvia’s ball in flight towards the collision, would make it relatively impossible for the collision to occur, and so Bruno’s ball would have taken the trajectory of Sylvia’s ball after time t, and caused the shattering of the glass bottle (E) in exactly the same time and manner as it actually did occur. Thus, had any one of the steps of the events involved in the flight of Sylvia’s ball before the collision (D) been altered or not occurred, the shattering would still have occurred thanks to Bruno’s throw.

The Humean counterfactual analysis fails: Recall the details of the Humean counterfactual analysis; where C and E are distinct actual events, then:

 C causes E iff E counterfactually depends on C.

The analysis fails to analyse Sylvia’s throw as a cause of the shattering (E), as follows:

 The shattering (E) does not counterfactually depend on Sylvia’s throw (C). Or in other words, if Sylvia’s throw had not occurred (C), then the shattering still would have occurred (E), because Bruno’s ball would have caused an exact same shattering (E).

We note that the Humean analysis analyses Bruno’s throw as a cause; if Bruno’s throw (A) had not occurred, then there would have been no shattering (E), given there would

then have been no collision (D), Sylvia’s ball would have landed near her intended target (something that wasn’t the bottle), and the bottle would not have been shattered.

We can see that the strategy of appealing to ‘fine-grained-ness’ of the effect won’t help us here as regards the Humean analysis, given that the shattering which Bruno’s ball would havecaused, had Sylvia not thrown, would have been exactly the same as the shattering Sylvia’s throw actually caused (we supposed this in the example above). How do Lewis’ strategies fare?

The counterfactual-chains analysis fails: We have supposed that any alteration to Sylvia’s throw would have made the collision impossible, and that if Sylvia had not thrown, the shattering would still have occurred in the exact same fragile fashion as it actually did. Might there be a way to appeal to chains of dependence to fix the problem? Recall the details of Lewis’ counterfactual chains analysis:

 C causes E iff there is a counterfactual chain of dependence leading from E to C.

 There is a counterfactual chain of dependence from E to C iff there is a set of actual events E, D, D1 etc… C, such that E counterfactually depends on D, D on

D1etc…. C.

Strevens observes that no appeal to chains will help us in this example. He observes that no event to do with Sylvia’s ball’s passage after the collision counterfactually depends on any event to do with Sylvia’s ball flying toward the collision or the collision itself. The

observation is correct; had any event of the trajectory of Sylvia’s ball before or including the collision not occurred, an intrinsically identical set of events would have occurred after the collision up to the shattering, courtesy of Bruno’s throw. Thus the counterfactual chains analysis fails to analyse Sylvia’s throw as a cause.

The dependence fixing analysis succeeds: Recall the details of the dependence fixing analysis: Where C, E, and F are distinct actual events, then:

 C causes E iff there is some event F such that if F had still occurred and C not, then E would not have occurred.

The analysis succeeds in analysing our example, as follows:

 There is some event F (i.e. the events which constitute the trajectory of Bruno’s ball), such that if F had still occurred and Sylvia’s throw (C) not, then the shattering (E) would not have occurred.

Admittedly, the dependence fixing analysis achieves its goal in a strange way. That is, the counterfactual worlds we appeal to in order to achieve our analysis are worlds in which Bruno’s ball seems to take a very unnatural trajectory, Bruno’s ball takes a right turn in mid-air and without apparent cause (given Sylvia’s ball is no longer present)! This shouldn’t worry us too much, given Lewis’ similarity relation allows for ‘local violations’ of laws in such a way as not to damage the overall layout of laws in that

world; and we can confirm this by direct inspection of Lewis’ similarity relation (it is only our second last priority to maintain local non violations of laws, but our first priority to maintain global non violations of laws).

The dependence fixing analysis fails with appeal to a revised example: the dependence- fixing analysis doesn’t seem to analyse some strengthened versions of the Sylvia and Bruno example. To see this, consider the following revised example: