13 February 2026

Laws and Counterfactuals

The laws of nature have a special counterfactual invariance that distinguishes them from mere accidents. For example, if Earth’s axis had been perpendicular to its orbital plane, all laws of nature would still have been true. But numerous accidents, even ones strictly compatible with the supposition, would have been different. For instance, there would have been no familiar cycle of seasons.¹Lange, M. (2026). ‘Can Pragmatic Humeanism Account for the Counterfactual Invariance of Natural Laws?’, British Journal for the Philosophy of Science, 77, available at . Explaining this difference is especially challenging for Humeans about laws, since they hold that laws are mere patterns in the contingent phenomena and thus lack any inherent necessity.

We,²Loew, C. and Jaag, S. (2020). ‘Humean Laws and (Nested) Counterfactuals’, Philosophical Quarterly, 70, pp. 93–113. along with Dorst,³Dorst, C. (2022). ‘Why Do the Laws Support Counterfactuals?’, Erkenntnis, 87, pp. 545–66. have offered pragmatic accounts of the counterfactual invariance of laws that are compatible with Humeanism. Dorst argues that we use counterfactuals for testing hypotheses. According to Dorst, we can test hypothesis H in light of evidence E by considering the counterfactual ‘if H had been the case, E would have been the case’. If this counterfactual is true, E confirms H. We have argued that we use counterfactuals to make and justify predictions from simplified models.⁴Loew, C. and Jaag, S. (2020). ‘Humean Laws and (Nested) Counterfactuals’, Philosophical Quarterly, 70, pp. 93–113. According to this account, we use counterfactuals both to describe these simplified situations (where certain actual background conditions are presumed absent) and to justify why such simplifications are permissible.

Both uses would explain why we hold the laws fixed. The laws are our best tools for inferring actual truths from other truths. So if we want to find out whether hypothesis H (if true) would lead to E, the laws of nature are the best tool to use. And, similarly, if counterfactuals are used for predictions from simplified models, these predictions are most accurate with the laws held fixed.

Lange objects that both proposals fail as explanations of the laws’ counterfactual invariance. Against Dorst, Lange argues that counterfactuals are generally unsuited for confirming hypotheses. When assessing whether E confirms H, we should hold fixed everything else we know and thus use indicative conditionals. By contrast, when using counterfactuals, we often vary known facts while holding underlying explanatory mechanisms constant. For example, when we counterfactually suppose that a second assassin shot Kennedy, we do not hold fixed that there was just a single bullet wound.⁵Lange, M. (2026). ‘Can Pragmatic Humeanism Account for the Counterfactual Invariance of Natural Laws?’, British Journal for the Philosophy of Science, 77, available at .

Against our account, Lange presents a scenario where, when predicting the trajectory of body B, we can ignore all outside influences except for P’s electric force. He argues that no counterfactual that holds the laws fixed is available in this case, since there is no nomologically possible scenario where P exerts an electric but not a gravitational force on B. Instead, Lange argues that we can simply make these calculations based on the laws without entertaining any counterfactuals.

But if counterfactuals are not needed and sometimes unsuited for hypothesis testing and prediction, then, according to Lange, these purposes cannot explain why the laws are held fixed in counterfactual reasoning.

We offer two replies: First, Lange has not shown that counterfactuals play no role for the relevant purposes. For example, ‘if the Russians had killed Kennedy, they would have used poison’ is a natural way of justifying that the Russians did not kill Kennedy. And ‘if Jones had taken arsenic, he would have shown just exactly those symptoms that he does in fact show’ supports the hypothesis that Jones has taken arsenic.⁶Anderson, A. R. (1951). ‘A Note on Subjunctive and Counterfactual Conditionals’, Analysis, 12, p. 37.

Similarly, Elga uses counterfactuals to justify simplifications when predicting the rough behaviour of a rock on your desk.⁷Elga, A. (2007). ‘Isolation and Folk Physics’, in H. Price and R. Corry (eds), Causation, Physics and the Constitution of Reality: Russell’s Republic Revisited, Oxford University Press, pp. 106–19. He points out that ‘subject to some very weak background conditions (for example, the condition that there will be no gigantic explosions)’, you can ignore what happens on the other side of the Earth. And he assesses the relevance of such going-ons via counterfactuals such as ‘if there were a supernova there right now, that would certainly make a big difference to your rock in less than a second’.⁸Elga, A. (2007). ‘Isolation and Folk Physics’, in H. Price and R. Corry (eds), Causation, Physics, and the Constitution of Reality: Russell’s Republic Revisited, Oxford University Press, p. 108.

Lange might insist that only models, not counterfactuals, are strictly required for deriving and justifying such predictions. But the two are in fact intimately related. Maudlin argues that counterfactuals are a form of model-reasoning,⁹Maudlin, T. (2007). The Metaphysics Within Physics, Oxford University Press, pp. 21–34. while Dohrn proposes to reconstruct scientific modelling in terms of counterfactuals.¹⁰Dohrn, D. (2023). ‘Modals Model Models: Scientific Modeling and Counterfactual Reasoning’, Synthese, 201, available at . This connection is obscured by Lange’s example, which requires a counterlegal supposition.

That we sometimes use counterfactuals for these purposes is enough to explain why we hold the laws fixed in counterfactual reasoning. We hold them fixed because doing so makes them suitable for confirmation and prediction in many cases, even if not in all. Analogously, we put up speed-limit signs to promote travel safety, even though in some circumstances they are not conducive to this purpose or might even have the opposite effect (for example, when they cause motorists to drive at the speed limit despite bad weather conditions).

Second, along with Dorst, we (perhaps unwisely) committed ourselves to particular hypotheses about the role of counterfactuals, namely, confirmation and justifying simplified predictions, respectively. But the more general argumentative strategy is simply to argue that counterfactuals play some distinctive evidential role and that holding the laws fixed is conducive to playing this role. Even if Lange had shown that counterfactuals were not needed for confirmation and prediction, there are other candidates for what practical purposes counterfactuals serve that would equally justify holding the laws fixed.¹¹See, for example, Fernandes, A. (forthcoming). ‘The Branchpoint Proposal and the Role of Counterfactuals’, Journal of Philosophy.

Lange would have to argue that counterfactuals play no distinctive role in our evidential reasoning. But this claim does not seem very plausible. Non-Humeans may think that the primary purpose of counterfactual reasoning is to limn some sui generis modal structure. But even they will typically think that in describing this structure, counterfactuals also track evidential relations between actual events. Humeans can argue that tracking these evidential relations itself justifies why we hold the laws fixed and so any appeal to underlying modal structure is explanatorily inert.

In sum, Humeans can appeal to the evidential role of counterfactuals (whatever it may be exactly), plus the predictive utility of laws of nature, to justify why we hold fixed the laws of nature in counterfactual reasoning.

Christian Loew & Siegfried Jaag

26 February 2026

Laws and Counterfactuals: Reply by the Author

I will briefly reply to Loew and Jaag’s comments about my paper. Although I disagree with Loew and Jaag, I very much admire their work on pragmatic Humean approaches to lawhood (which is why I wrote about their paper in the first place) and I am happy to have this opportunity to say so.

According to Loew and Jaag, ‘Lange has not shown that counterfactuals play no role’ in prediction and hypothesis testing. ‘For example, “if the Russians had killed Kennedy, they would have used poison” is a natural way of justifying that the Russians did not kill Kennedy”’. But equally natural is reasoning that uses an indicative conditional (‘if the Russians murdered Kennedy, then the murder wasn’t by gunshot, but as we all saw, the murder was by gunshot’).). More generally, I argued in the target paper that our background knowledge concerning a given case plays a role in our testing hypotheses about that case. Those background facts can fail to be preserved under a counterfactual antecedent, whereas they persist under an indicative antecedent. This makes indicatives generally more suitable than counterfactuals for hypothesis testing. (Of course, indicatives are not truth-functional conditionals.) But although indicatives are more suitable than counterfactuals for hypothesis testing in cases like those I discussed in the target paper, I admit that in some cases of hypothesis testing, counterfactuals are as suitable as indicatives; it does not matter which we use. A detective could reason, ‘If the butler is the murderer, then evidently the butler’s fingers make loop-shaped fingerprints (since there are loop fingerprints on the murder weapon), but his fingers don’t do that…’ (since they have whorls, not loops) just as well as the detective could reason, ‘If the butler had done it, then (since his fingerprints are whorls) there would have been whorl fingerprints on the murder weapon, but there aren’t’.

I also insist that examples where confirmation and prediction require counterlegal antecedents (if this work is done by counterfactuals, as Loew and Jaag maintain) do not ‘obscure’ what is really going on (as Loew and Jaag allege). Many hypotheses in science are recognized as concerning what the laws are. These cases should be understood in the same way as the rest.

Loew and Jaag say, ‘That we sometimes use counterfactuals for [confirmation and prediction—or some other “evidential role”] is enough to explain why we hold the laws fixed in counterfactual reasoning’. But it is not enough (whatever the evidential role may be). As I said in the target paper, an account like Loew and Jaag’s needs to explain ‘why the laws’ truth is preserved under counterfactuals being entertained for some reason other than to discover subnomic facts’. (As I mentioned in the target paper, Dorst¹²Dorst, C. (2022). ‘Why Do the Laws Support Counterfactuals?’, Erkenntnis, 87, pp. 557–58. recognizes the need for such an explanation in the case of his pragmatic Humean account; he floats several possibilities.) Loew and Jaag say that ‘analogously’ it can be true that we post speed-limit signs to promote travel safety, even though we know that ‘in some circumstances they are not conducive to this purpose’. But then (unless our instrumental reasoning is poor) there must be an explanation of why we post speed-limit signs despite knowing that they sometimes fail to contribute (or even are detrimental) to our purposes. Loew and Jaag’s pragmatic Humeanism owes us an analogous explanation.

Loew and Jaag maintain that one important goal of counterfactual reasoning is confirmation and prediction—enough so that the need for laws to be preserved under counterfactual reasoning performed for these particular purposes explains a feature of all counterfactual reasoning. But why should we think that this is indeed an important goal of counterfactual reasoning if indicative conditionals (or mere calculation without any conditionals involved, as I discussed in the target paper) do these jobs at least as well as (or even better than) counterfactuals? To explain why the laws are preserved under all subnomic counterfactual antecedents with which the laws (taken together) are logically consistent, a pragmatic Humean would be better off appealing to an application for which counterfactuals are indispensable.

Finally, Loew and Jaag’s reply does not seem to address one of my chief concerns in the target paper. If their account is correct about why the laws’ truth is preserved in various counterfactuals (even nested counterfactuals and counterfactuals with consequents concerning causal and explanatory relations), then their account also underwrites the preservation of the laws’ lawhood under these counterfactual antecedents. But Loew and Jaag do not accept that lawhood is preserved. Notice that I have just used indicatives to express this case of (philosophical) hypothesis testing.

Marc Lange