Evaluating counterfactuals in worlds with deterministic laws poses a puzzle. In a wide array of cases, it does not seem plausible that if a non-actual event were to occur that either the past would be different or that the laws would be different. But it’s also difficult to see how we can avoid this result. Some philosophers have argued that we can avoid this dilemma by allowing that a proposition can be a law even though it has violations. On this view, for the relevant cases, the past and the laws would still hold, but the laws would have a violation. In this paper, I raise a problem for the claim that the laws and the past are preserved for all of the relevant counterfactual antecedents. I further argue that this problem undermines motivating the possibility of violations on the grounds that they allow us to hold that the past and the laws are typically counterfactually preserved, even if they are not always preserved.
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Braddon-Mitchell (2001, p. 267) also considers a nearby variant where the laws of nature take the following form: ‘the generalization L is part of the best system of laws,’ where L can be false.
As Lewis (1979, pp. 462–463) points out, there may be a small transition time before the event in which the past can differ. For simplicity, I set this consideration aside.
The believer in Violations may strengthen this by holding that all laws could be violated, but that is an extra commitment that I do not assume the believer in Violations must take on.
The classic case is Cartwright (1980).
For a useful recent discussion, see Roberts (2008, pp. 48–50).
For independent reasons, Lange (2000, p. 177) does not think these sorts of counterfactuals are always true, but near enough to being ‘correct’ to assert. I set aside this qualification in what follows.
There are also so-called ‘back-tracking’ contexts where it is uncontroversial that the past is not preserved when evaluating counterfactuals. For present purposes, we set aside contexts that are uncontroversially back-tracking. For more discussion, see Lewis (1979, pp. 456–458).
The defender of Violations may wish to further strengthen their view and hold that (3) and (4) are metaphysically necessary, rather than simply nomologically necessary. However, we will only consider nomologically possible antecedents, so this extra strengthening is unnecessary.
I thank an anonymous referee for helpful comments on this issue.
Note that since the claim that all Fs are Gs is logically equivalent to the claim that all non-Gs are non-Fs, I require a fairly fine-grained notion of laws of nature, so that the law that all Fs are Gs is not identical with the law that all non-Gs are non-Fs. Those inclined to reject this assumption should replace my talk of laws with talk of law statements, as the statement that all Fs are Gs is not identical with the statement that all non-Gs are non-Fs. As far as I can see, my argument is not affected by this substitution.
While Braddon-Mitchell (2001, pp. 270–272), Kment (2014, p. 216), and Lange (2000, pp. 76–77) do not commit themselves to the claim that the laws and the past are counterfactually robust in full generality, they do aim to support Violations on the grounds that it allows us to hold that the laws and the past are at least generally counterfactually preserved.
Note that if The Conjunction counterfactually implies that L would no longer be a law, that does not show that The Conjunction is nomologically impossible. It could be that if the past were different then The Conjunction could be true and L would still be a law.
Are we guaranteed that there is such an antecedent? If A1 simply says that the instance of L doesn’t obtain and (3) and (4) hold, then we are guaranteed a violation, given the assumption of determinism, but we aren’t guaranteed that it is L that is violated rather than some other law. However, we can add to the antecedent to ensure that at least L is violated. If L is not violated because some other law L* is violated, then we can add to the antecedent so that L* is not violated at the relevant time and place.
I am grateful to a referee for pointing this out.
I thank an anonymous referee for bringing this possibility to my attention.
Perhaps this doesn’t guarantee that the right law is violated, maybe some other law would be violated instead. But, as noted in footnote 14, we can avoid this problem by changing the antecedent to also state that this other law is not violated.
To get a sense for how this could work, we can think of the structure of the densely-ordered instances along the lines of the positive rational numbers, for between any two rational numbers there is another. We can now take a non-densely-ordered series of regions that contain these instances. This could be done by thinking of the regions as collections of rational numbers. For example, we have a collection of all rational numbers greater than 0 and less than 1, a collection of all rational numbers at least as great as 1 but less than 2, and so on. Thought of in this way, there is no challenge to taking a non-densely-ordered series of spacetime regions that contains the instances of the law.
Of course, on an epistemicist view of vagueness, there will be a sharp point at which the laws change and are not counterfactually preserved, but we are unable to know where that point is. But since it is implausible that there is a sharp point at which the laws are no longer counterfactually preserved, the combination of Violations, Humeanism about the laws, and epistemicism about vagueness does not produce a very attractive package.
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Thanks to Phillip Bricker, Troy Cross, Patrick Grafton-Cardwell, Justis Koon, Chris Meacham, Alejandro Pérez Carballo, and two anonymous referees for very helpful comments and discussion.
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Gibbs, C. Counterfactuals and laws with violations. Synthese (2020). https://doi.org/10.1007/s11229-020-02740-x
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