Abstract
This paper aims to explain why the laws of nature are held fixed in counterfactual reasoning. I begin by highlighting three salient features of counterfactual reasoning: it is conservative, nomically guided, and it uses hindsight. I then present a rationale for our engagement in counterfactual reasoning that aims to make sense of these features. In particular, I argue that counterfactual reasoning helps us evaluate the evidential relations between unanticipated pieces of evidence and various hypotheses of interest about the history of the actual world. Given this goal, it makes a great deal of sense that counterfactual reasoning would have the aforementioned features. Additionally, it turns out that this account of counterfactual reasoning is nicely congruent with Humean views of laws. Specifically, it can explain, in a Humean-friendly way, both why the laws are counterfactually resilient, and why we may be inclined to have anti-Humean intuitions in the first place, even if some form of Humeanism is correct.
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Notes
See also Paul and Hall (2013, pp. 47–53). Maudlin’s recipe bears obvious similarities to Lewis’s (1973, 1979) semantics for counterfactuals. I focus on Maudlin’s proposal partly for ease of exposition, and partly because of some respects in which it differs from Lewis’s––e.g. Maudlin’s theory has the feature of “hindsight” (see below), while Lewis’s does not.
Maudlin talks of selecting a Cauchy surface rather than a time slice, but nothing crucial will hang on the difference here.
David Lewis's semantics for counterfactuals is also conservative, in the sense that we are directed to consider an A-world that is as similar as possible to the actual world (at least before the time of the antecedent).
This example occurs in Slote (1978, p. 27). Slote attributes it to Sidney Morgenbesser.
Actually, Redhead need not be committed to the claim that my actions affect the outcome of the game. That would depend on the further thesis that causation is to be analyzed in terms of counterfactual dependence. (Thanks to Marc Lange for pointing this out.) So strictly speaking, all that Redhead's account commits him to is the claim that if I had turned the television off, the Pirates might have won. This may be slightly less unreasonable than the claim that my actions affect the outcome of the game. But only slightly.
I borrow this terminology, and this way of articulating the method, from Edgington (2004). One worry about this way of articulating the method is that it presupposes a notion of causal independence in its analysis of counterfactual independence, and therefore it looks to preclude our ability to provide a counterfactual analysis of causation. Those who are sympathetic with a counterfactual analysis of causation would therefore have reason to stick with Maudlin’s “infected magnitudes” analysis. (Thanks to Mike Hicks on this point.).
Of course, some counterfactual suppositions are themselves inconsistent with the laws, so there is no way to create an altered state that both (1) makes the antecedent true, and (2) is consistent with the actual laws. It is an important question how to handle such "counterlegals," but that is beyond the scope of this paper.
Note, however, that it is left open here whether the laws are still laws in the counterfactual situation, or whether they are merely still true. The laws figure into the recipe by allowing us to construct models of counterfactual situations that follow, via the laws, from the altered state. All we need to assume for this to work is that the regularities described by the laws still obtain, but that is consistent with them not being laws. So the correctness of the Altered States Recipe does not settle the issue of Nomic Preservation.
To say that the counterfactual facts are an independent domain of facts is not to imply any commitment about their truthmakers, be they possible worlds, actual-world entities, or whatever. It is only to suggest that the counterfactual facts are out there somewhere, and they are totally independent of us and our interests.
See Lange (2019) for a critical evaluation of Wilson’s discussion of these virtual work counterfactuals.
It may be tempting to think that the pragmatic goal conception of counterfactuals implies an objectionable sort of instrumentalism, whereby counterfactual claims are, strictly speaking, neither true nor false. However I follow Wilson in regarding the truth values of counterfactual claims as derivative upon their practical utility: “the ‘truth conditions’ of our [counterfactual] conditionals should be regarded as informationally rooted within the manners in which we decide upon their truth” (2017, p. 317).
Cf. Edgington (2004) for a similar proposal.
Of course, we also want P(H) to be high, and \(P(\neg H)\) to be low, but consideration of these priors is not germane to our present purposes.
Note that this is distinct from the so-called "problem of old evidence" [as posed in Glymour (1980)]. The problem here is not that we have a newly-formulated hypothesis designed to account for previously-known evidence. It is rather that we have newly-acquired, unanticipated evidence, and we want to figure out which hypothesis rendered that evidence most likely.
My argument here owes a great deal to Edgington (2004), which lays out a similar explanation for why our counterfactual reasoning uses hindsight.
For the sake of simplicity, I am supposing that all of the models in each set agree on the length of the tire tracks.
Of course, if Wilson (2017) is right, there are some contexts in which alternative practical factors motivate reasoning about counterfactuals using a different recipe. One might then wonder why the ASR strikes us as the “usual” method, rather than the other methods than Wilson entertains. I suspect that this can be traced to the fact that the ASR is useful in a much wider range of circumstances than the more localized applications that Wilson considers.
Woodward (2003, p. 10) maintains a similar position with respect to causal explanation: “…our interest in causal relationships and explanation initially grows out of a highly practical interest human beings have in manipulation and control; it is then extended to contexts in which manipulation is no longer a practical possibility.”.
Strictly speaking, on Lange's view the explanation runs in the other direction: the fact that the laws are held fixed in counterfactuals is what accounts for their necessity.
Lewis's theory of counterfactuals is a prime example of this, though that theory only requires that the laws be held mostly fixed, as it allows for certain sorts of violations of actual law.
See, e.g., Lewis (1986, 1994). The characterization of Lewisian laws as “efficient summaries” can be found in, e.g., Albert (2015, pp. 23–24) and Beebee (2000, p. 574). There are also a variety of developments of Lewis's view that leave the basic picture of laws as efficient summaries intact. See, for example, Loewer (1996), Cohen and Callendar (2009), and Demarest (2017).
See Dorst (2018) for a more comprehensive discussion of this point.
If it turns out that the laws are still laws under any counterfactual supposition that is consistent with them, then the Humean might be in trouble. For the reasons given above, Nomic Preservation looks to be incompatible with Humeanism, and even if this incompatibility can be avoided, the Humean is still going to face some pretty difficult motivational questions about why the lawhood of the laws, and not just their truth, is held fixed. Though see both Bhogal (forthcoming) and Loew and Jaag (2020) for some illuminating suggestions about how the Humean could secure and motivate Nomic Preservation.
See, for example, Hall’s “Humean Reductionism about Laws of Nature” (ms, p. 25).
See Mill (1956), bk. III ch. VIII, sec. 2.
One possible exception is grounding facts, which may figure into a Humean metaphysics as well; see Bhogal (forthcoming) and Dorst (2019) for further discussion about how the Humean might approach grounding facts.
See Hall (ms) for a similar line of argument. I hasten to add here that the Humean need not think that we have no reason to try to identify facts about what explains what. Rather, my suggestion is that the point of discovering these facts must be reconstrued. For the Humean, discovering facts about what explains what is not plausibly taken to be the end goal of scientific inquiry.
As an anonymous referee points out, since the Humean metaphysics posits no necessary connections, there is a serious question for the Humean about how we could be justified in using either the laws, or counterfactual reasoning that relies on the laws, to ascertain previously unknown facts about the mosaic from the known parts of the mosaic. This is especially worrisome given that, before we have seen the entirety of the mosaic, we cannot be sure that we know the laws. Of course, this worry is essentially just the problem of induction, and the crucial question is whether the Humean is in any worse of a position here than the anti-Humean is. Beebee (2011) argues that no particular advantage is gained in this regard by adding anti-Humean necessary connections to one’s ontology; if the Humean cannot justify induction, then neither can the anti-Humean. Conversely, see Armstrong (1983) and Bhogal (ms) for dissenting opinions. Clearly this is an important issue, and it deserves more attention than I can give it in the current paper.
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I owe many thanks to Marc Lange, Ned Hall, John Roberts, Matt Kotzen, Laurie Paul, Alison Fernandes, Mike Hicks, Kevin Dorst, and the participants at the Society for the Metaphysics of Science Annual Conference in August 2018.
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Dorst, C. Why do the Laws Support Counterfactuals?. Erkenn 87, 545–566 (2022). https://doi.org/10.1007/s10670-019-00207-1
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DOI: https://doi.org/10.1007/s10670-019-00207-1