Determinación de coliformes en alimentos

Example (19) SUZY AND BILLY#4* (a case of my own): A case in which the cause causes the pre-empted back-up cause; call such a case a case of ‘strengthened late pre- emption’.

Suppose Billy and Suzy both throw rocks at a window in a world in which strong determinism is true (see introduction for the overview of the notion of strong determinism); Suzy throws her rock (C), and smashes the window (E), just before Billy’s throw (A) was able to. Suppose, also, that Billy’s throw was sufficiently determined, given the deterministic laws, by Suzy’s throw (so suppose Billy is very impressionable, and always participates in those mischievous acts which his sister does). Suppose also that Billy’s throw was independently and sufficiently determined, given the laws, by his mischievous nature, such that if Suzy hadn’t thrown her rock, he would have thrown his rock anyway. We suppose (in this strongly deterministic example) that the following laws are true; i) Whenever Suzy throws a rock at a window, so does Billy, ii) Whenever Suzy or Billy throws a rock, there is a window shattering.

The strict quasi-dependence analysis fails: It is easy to see how the strict quasi- dependence analysis fails to analyse the cause of the shattering (E) as Suzy’s throw (C). This is because any isonomic duplicate of C and E, and the process running from C to E, will not elicit counterfactual dependence, given any isonomic duplicate must also contain the pre-empted back-up (A). This is because Suzy’s throw (C) nomologically determines the presence of the pre-empted back-up cause (A) of the shattering; Billy’s throw (A), and thus the shattering (E), will not counterfactually depend on (C) in such an isonomic duplicate.

The general problem then is that if we insist on our isonomic duplicates having exactly

the same laws and events with respect to what the isonomic duplicate is an isonomic duplicate of, and there are cases in which a cause of an effect nomologically determines the presence of pre-empted back-up causes, then in such cases there will be no way to analyse such causes as causes of the effect given the effect won’t be counterfactually dependent on the cause in any isonomic duplicate.

We are now in a dilemma - if we accept the loose Lewisian criteria for isonomic duplication then we face the problem of ‘all too similar pre-emption’, which generates spurious causes by appeal to all too similar cases in which causation actually holds. On the other hand, if we accept the strict criteria for isonomic duplication then we face the problem of ‘background nomological determiners’, where causes are not analysed as causes by the analysis in cases in which the cause nomologically determines the presence of background pre-empted causes. Is there a way out of the dilemma for Lewis?

Solution: Maybe one way to avoid the dilemma would be to tighten the constraint of what events may feature in isonomic duplicates (strict duplicate events), but loosen what laws we allow to feature (i.e. we say ‘similar enough laws’) - but this has the dangerous risk of over-generating spurious causes, given it might just take a minor revision of some nomological relations to generate new causal relations; so we should preferably avoid this strategy.

A better solution might be to analyse isonomic duplication as follows:

 X is an isonomic duplicate of Y iff X and Y have exactly the same events, and the samegoverninglaws.

 Two duplicate sets of events X and Y have the same governing laws iff it’s the case that events A and B are in X and A nomologically determines B iff events A’ and B’ are in Y and A’ nomologically determines B’.

How might this proposed re-analysis of isonomic duplication circumvent the dilemma? Recall, the ‘problem of all too similar pre-emption’ was that giving way to anything other than strict duplication of events between isonomic duplicates had the potential to generate spurious causes - we avoid the problem by maintaining that the isonomic duplicates must indeed have strictly identical events. How does the analysis circumvent the second horn of the dilemma? Recall, the ‘problem of background determiners’ was located in the fact that the actual cause nomologically determined the presence of pre-empted back-up causes - we avoid this by not requiring that the isonomic duplicates have all the same laws, but merely the ones that maintain the structure of nomological determinacy within the two sets of events; problematic laws that determine pre-empted back-up causes outside the set of the isonomic duplicates are then not required to feature. Thus the dilemma seems to be circumvented; the solution comes from the fact that isonomic duplicates must contain strict duplicates of events, but only the samegoverninglaws (i.e. the laws that arerelevantto the causal structure of the case).

We should now visit how the revised would be dependence analysis treats cases of late pre-emption.

The revised would-be dependence analysis succeeds: Recall the details of the revised would-be dependence analysis; where C and E are distinct actual events, then:

 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 would-be chain still occurred

 An event P purely prevents dependence of E on C iff P is a dependence preventer on a chain of events E on C, and P prevents no event in the chain of events that would form a counterfactual chain linking E to C had P not occurred.

 P is a dependence preventer of E on C iff had P not occurred and the C-E chain of events still had, then E would counterfactually depend on C.

The would-be dependence analysis analyses all cases of late pre-emption correctly. Consider a Billy and Suzy late pre-emption case to see this:

 There would be a chain of counterfactual dependence between actual events linking Suzy’s throw (C), to the shattering (E), had it not been for some pure dependence preventer (Billy’s throw (A)), and the would-be chain still occurred.

 Billy’s throw purely prevents dependence of the shattering (E) on Suzy’s throw (C), because had Billy’s throw not occurred, and the would-be chain still had, the shattering (E) would have depended on Suzy’s throw (C).

More revisions shall come for would-be chains later on. For now we note the success of the would-be dependence analysis in analysing Suzy’s throw as a cause of the shattering, and also its success in not analysing Billy’s throw as a cause of the shattering. Billy’s throw is analysed as not a cause of the shattering because the dependence of the shattering on Billy’s throw is not purely prevented - the dependence preventer (Suzy’s throw) of the shattering on Billy’s throw prevents an actual event in the would-be chain between the shattering and Billy’s throw (i.e. the event in which Billy’s rock actually reaches the window). We conclude this section with some general observations:

Some observations: We visited the following different types of late pre-emption in this section:

1. Coarse-grained late pre-emption (examples (13) and (14)) 2. Fine-grained late pre-emption (examples (15) and (16)) 3. Modally fragile late pre-emption (example (17))

4. Over-generative late pre-emption (example (18)) 5. Strengthened late pre-emption (example (19))

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 ofearlypre-emption just mentioned:

 The basic Humean counterfactual analysis fails in all the examples

 The Humean counterfactual analysis fails in all the examples

 The holding fixed analysis fails in all the examples

 The fine-grained holding fixed analysis succeeds in all examples

 Lewis’ counterfactual chains analysis fails in all examples

 Lewis’ influence, influence fixing, and influence chains analyses succeed in all examples except 17 and 18

 Lewis’ quasi-dependence analysis succeeds in all examples except 18 & 19

 The revised quasi-dependence analysis (by appeal to ‘relevant governing laws’) and revised would-be dependence analyses succeed in all cases

We note here that late pre-emption cases are harder to analyse than early pre-emption cases overall. Nonetheless, three analyses still stand out as successful; the revised quasi/would-be dependence analyses, and the revised holding fixed analysis. Once again, it has been the analyses that appeal to strategies of ‘getting rid’ and ‘holding fixed’ that have proved the most successful. We now move on to cases of middle pre-emption.