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Example (12):An example in which it’s the case that a cause of the pre-empted back-up process also causes the effect via the actual process, such that if it didn’t cause the effect by the actual process, it would have caused it by another. Term this type of pre-emption ‘shunting pre-emption’, given the back-up cause would have shunted from one process to another.

SUZY AND BILLY#6: (my own example) Suppose the details of SUZY AND BILLY#1 (example 1), but with the following modifications: Suzy only throws her rock because Billy tells her to. Thus, Billy’s presence (A) causes Suzy’s throw (C), which causes her rock to fly in mid-trajectory (D), which in turn causes the shattering (E). Had Suzy not thrown her rock however, the shattering would still have occurred (E), because Billy would have thrown a rock at the window had Suzy not.85

The would be-dependence analysis fails, as follows:

 It is not the case that there would be a chain of counterfactual dependence linking Suzy’s throw (C), to the shattering (E), had it not been for some pure dependence preventer (Billy’s presence (A)- the only dependence preventer present). This is because had Billy not been present Suzy would not have thrown (she only throws because Billy tells her to!), and thus there would not be a chain of dependence between Suzy’s throw and the shattering, because there simply would not have been a chain of events from her throw to the shattering (E).

 Billy’s presence purely prevents dependence of the shattering (E) on Suzy’s throw (C), because had it not been the case that Billy was present, the shattering (E) would have depended on Suzy’s throw (C).

85_{Here we suppose it is Billy’s presence at some time which is the only pure dependence preventer of the}

The problem here is that sometimes getting rid of the pure dependence preventer gets rid of the chain of events that we wished to analyse as a causal chain in the first place! Not to worry: we can simply revise the would-be dependence analysis to succeed in this case by stating in the analysis that we ‘hold fixed’ the relevant chain, as follows:

 C causes E iff there is a chain of counterfactual dependence linking C to E, or there would be such a chain had it not been for some pure dependence preventer,

and the events of the would-be chain still occurred.

We shall give some additional details about a revised notion of dependence prevention later when we visit cases of late pre-emption; for now we note that the above seems a good first step in revising Collins’ analysis. I conclude this section with some general observations:

Some observations: So far, the basic counterfactual analysis has seen two revisions; ‘holding fixed’ and appealing to chains. The influence analysis has also seen these revisions; that is ‘holding fixed’, and appealing to chains. In both cases, the holding fixed strategy has met with better successes than appealing to chains - and with the additional attraction of not having to buy wholesale into the notion that causation is a transitive relation. We also visited both the quasi-dependence analysis, with its strategy of ‘getting rid of’ some of the background events that made these examples so problematic, and the would-be dependence analysis, along with one revision. We met 6 types of early pre- emption examples in this section:

1. Coarse-grained early pre-emption (examples (1) and (2)) 2. Fine-grained early pre-emption (examples (3) and (4)) 3. Modally fragile early pre-emption (examples (8), (9), (10)) 4. Non local early pre-emption (example (6))

5. Over-generative early pre-emption (example (11)) 6. Shunting early pre-emption (example (12))

Our analyses and revised analyses met these cases with varying success. We have not had space to make explicit how every analysis deals with every case or type of pre-emption, but we can catalogue some of the demonstrated (and the obviously expected) results here of how each analysis deals with each of the types of early pre-emption just mentioned:

 The Humean counterfactual analysis fails in all the examples

 The holding fixed analysis succeeds in all the examples

 Lewis’ counterfactual chains analysis only fails in 6

 Lewis’ influence analysis succeeds in all except 8, 9, 10 & 11

 Lewis’ influence chains analysis succeeds in all except 8, 9, & 11

 The holding fixed influence analysis succeed in all examples except 11

 Lewis’ quasi-dependence analysis succeeds in all the examples

 The would-be dependence analysis succeeds in all cases except 12

Three of the analyses we considered so far have met with good results. The ‘holding fixed strategy’ has proven especially effective as a revision for Hume’s basic analysis, and the ‘getting rid of strategy’ has proven effective for the quasi-dependence analysis and revised would-be dependence analysis. Why have these two strategies prospered so well? The answer comes in their treatment of the troublesome pre-empted back-up causes - in either case, the troublesome pre-empted back-up has either been ‘held fixed’ or ‘got rid of’ in such a way that it no longer interferes with the effect counterfactually depending on the cause in the scenarios required for a successful analysis.

I shall now turn to cases of ‘late pre-emption’. Cases of late pre-emption differ subtly from cases of early pre-emption, but as we shall see, these subtle differences make all the difference with respect to how successful some of our analyses are.