Basic trumping pre-emption

First example (due to Schaffer96): Suppose a major shouts “charge” to the corporal (C), and a sergeant simultaneously shouts “charge” to the corporal as well (A). Suppose the corporal charges (E). The corporal’s charging would have occurred as a result of the major’s orders alone, or the sergeant’s, but when they both occur together, the major’s shouting is the exclusive factor which causes the charging (it ‘trumps’ the sergeant’s orders), given a corporal will always obey the orders of the highest ranking soldier with a rank higher than him.

Example (25):

Second example(also due to Schaffer97): Schaffer observes we can also give ‘trumping’ examples in which the actual cause precedes the trumped cause (as an interesting variation of cases of trumping). Suppose it is a law of magic that the first spell cast on any given day matches the following enchantment at midnight. Merlin casts the first spell that day to turn the prince into a frog (C), Morgana casts the same spell slightly later (A), and at midnight, the prince turns into a frog (E). Schaffer observes that clearly Merlin’s spell, and not Morgana’s, is the exclusive factor which causes the enchantment (it ‘trumps’ Morgana’s spell), because the laws provide for the determination of the enchantment by Merlin’s spell and not by Morgana’s.

Example (26):

96_{Schaffer, p. 59, [2000]} 97_{Schaffer, p. 67, [2000]}

Third example(also due to Schaffer98): Suppose a certain type of particle takes a certain type of curved trajectory (E) when it is subject to a certain type of field (called “black”, “grey”, or “white”) with a certain sort of magnitude. Suppose also that whenever such a particle is subject to multiple fields scattered around the particle, it will take a trajectory as if only subjected to the magnitude of the “darkest” field. Suppose that such a particle is subject to two fields next to one another (one black (C), the other white (A)), such that the particle takes the trajectory (E) as determined by the black field (C), but would have taken the same trajectory had the black field not been there, given the presence of the white field (A).

First of all, what are we to make of cases of trumping? Hall and Paul are two philosophers who reject Schaffer’s view that only C is the cause of E in such cases. They write:

“Although they have attracted a small flurry of interest in the recent literature, cases of trumping turn out on inspection to be nothing more than either cases of symmetric over-determination in disguise, or cases of late pre-emption in disguise; either way, they have nothing new to teach us.”99

98_{Schaffer, p. 67, [2000]} 99_{Hall and Paul, p.3, [2006]}

No clue is given as to why they think this. We might suppose that they think that if they are cases of late pre-emption in disguise, then we can identity some intrinsic properties in the process running from the pre-empted back-up cause that fail to ‘get in touch’ with the effect (as this is characteristic of cases of late pre-emption). This may be the case with the sergeant-major example - perhaps we can indeed identify some physical process from the sergeant’s order that doesn’t ‘get in touch’ with the corporal’s motivating thoughts to charge; but not enough is known about the physics of such cases to make a determinate answer. In any case, the Merlin-Morgana case is clearer on this matter - there seems no process that is physically ‘cut short’ from ‘reaching’ the effect as far as the pre-empted cause (Morgana’s spell) is considered, and so contra Hall and Paul, at least this example isn’t simply a case of late pre-emption.

What about the alternative suggestion, that such cases could be analysed as cases of over- determination? We shall meet these cases later, but for now all we need to know is that if Schaffer’s cases are actually cases of over-determination, then both C and A are to be analysed as causes of E (contra Schaffer’s conclusion that only A is not a cause of E). This suggestion has some weight to it; the conclusion that A is also a cause of E is certainly not as implausible as the suggestion that the pre-empted back-up cause is actually a cause of the effect in the other cases of pre-emption; for starters it seems as if the ‘process’ from Morgana’s spell to the enchantment is intrinsically just like causally efficacious counterparts to her spell. Following this, and as far as brute intuitions are concerned, I would say it would be fortunate if an analysis analysed A as a non cause of E, but not a disaster if it didn’t.

The Humean counterfactual, dependence fixing, and counterfactual chains analyses fail: It’s easy to demonstrate how these three analyses fail, so we shall deal with them in one go; we shall demonstrate this by appeal to the Merlin/Morgana example:

First, the Humean counterfactual analysis fails because the enchantment (E) does not counterfactually depend on Merlin’s spell (C). This is because had Merlin’s spell not occurred, then the enchantment still would have, because Morgana’s spell would have occurred to cause the enchantment.

Secondly, the counterfactual chains analysis fails because there is no chain of events running from the enchantment (E) to Merlin’s spell (C) which constitutes a chain of dependence. This is because Merlin’s spell causes the enchantment directly by appeal to ‘action at a spatio-temporal distance’, without appeal to any intermediary events, and thus there is no event the enchantment depends on which is linked to a chain of dependence ending up with Merlin’s spell.

Thirdly, the dependence fixing analysis fails because there is no event that can be ‘held fixed’ such that if Merlin’s spell hadn’t occurred, the enchantment wouldn’t have; in any such variation of ‘holding fixed’, Morgana’s spell would still have caused the enchantment.

The influence and influence-chains analyses seem to succeed:100 We note that the influence and influence chains analyses seem to analyse Merlin’s spell (C) as a cause of the enchantment (E), and Morgana’s spell as a non cause. To see this in depth, recall the details of the influence analysis; where C and E are distinct actual events, then:

 C causes E iff C influences E, and C and E are distinct actual events.

 C influences E iff there is a substantial range of C1… Cn of different not-

too-distant alterations of C (including the actual alteration of C) and a range of E1… Enof alterations of E, at least some of which differ, such that if C1

had occurred, E1 would have occurred, if Cn had occurred, En would have

occurred.101

We note:

1. Merlin’s spell (C) influences the enchantment of the prince turning into a frog (E). Or, in other words, there is a substantial range of not-too-distant alterations of Merlin’s ‘prince to frog’ spell, which counterfactually implies a range of alterations to the enchantment. As follows: Had Merlin cast the spell ‘prince to newt’ (C1), then the prince would have turned into a newt (E1), had Merlin cast

the spell ‘prince to worm’ (C2), then the prince would have turned into a worm 100_{Demonstrating that the influence analysis succeeds in this case indirectly demonstrates that the influence}

chains analysis succeeds; given it is true that if an event influences another, it influences it via a chain of events.

(E2), had Merlin cast the spell ‘prince to kangaroo’ (C3), then the prince would

have turned into a kangaroo (E3)… etc.

We note here that Morgana’s spell does not influence the enchantment, given that the not-too-distant alterations of her spell (we can consider the range of Merlin’s spells above if we like) do not counterfactually imply a range of alterations to the enchantment. This is simply because in the range of worlds in which Morgana’s spell is not too distantly altered, the law of nature ‘the first spell cast that day matches the enchantment at midnight’ still holds, and thus Merlin’s ‘prince to frog’ spell would still have influenced the prince to turn into a frog.

We should be sufficiently accustomed to variations of ‘modally fragile’ pre-emption to see how the influence analysis can be made to go wrong. For that, we consider an example of Rosen’s: