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Schaffer on laws of nature


In ‘Quiddistic Knowledge’ (Schaffer in Philos Stud 123:1–32, 2005), Jonathan Schaffer argued influentially against the view that the laws of nature are metaphysically necessary. In this reply I aim to show how a coherent and well-motivated form of necessitarianism can withstand his critique. Modal necessitarianism—the view that the actual laws are the laws of all possible worlds—can do justice to some intuitive motivations for necessitarianism, and it has the resources to respond to all of Schaffer’s objections. It also has certain advantages over contingentism in the domain of modal epistemology. I conclude that necessitarianism about laws remains a live option.

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  1. Schaffer (2005, p. 13).

  2. Non-fundamental properties (like being a river of beer) and determinate properties (like having a mass of exactly 2 100 kg) raise interesting complications which are mostly orthogonal to the question of the modal status of laws. I will set them aside.

  3. This example was introduced by Fine (2002). Despite its dubious physical credentials, it suffices to make the general point.

  4. Schaffer (personal communication) has confirmed that in Schaffer (2005) he presupposed that the actual laws govern only properties instantiated at the actual world. This presupposition is required to make sense of various aspects of his setup, for example: “The nomic and causal necessitarian countenance all the worlds that the modal necessitarian countenances, plus some worlds with alien laws, provided that these alien laws only govern alien properties (properties distinct from the actual ones, and from any conjunctions or composites thereof).” (Schaffer 2005, p. 3.).

  5. Schaffer (2005, p. 3).

  6. Fine (2002) likewise advocates building a specification of the fundamental determinable properties instantiated at any world w into the laws of nature of w. A referee points out that this assumption entails that it cannot be a chancy matter whether some particular fundamental determinable is instantiated. This consequence is interesting, but it doesn’t strike me as terribly problematic.

  7. Few philosophers have expressed sympathy in print with this package of views. The most prominent example is Alexander Bird, who expresses cautious support for it under the label of ‘strong necessitarianism’ (Bird 2004, 2007).

  8. Schaffer (2005, p. 8).

  9. My own view is that the best argument for modal necessitarianism is based on the many-worlds interpretation of quantum mechanics. (See Wilson 2011.) More commonly, necessitarians have attempted to support their view by arguing that it best makes sense of certain features of scientific practice.

  10. Schaffer (2005, p. 7).

  11. Fine (2002).

  12. Sophisticated frequentist attempts like those of Howson and Urbach (1993), Hoefer (2007) and Schwarz (forthcoming) to prove versions of Lewis’ Principal Principle may help the contingentist make progress in this direction, linking chancy laws to subjective expectations about particular events via the chances that the laws assign to those events. See Strevens (1999) and Handfield (2012) chap. 7 for sceptical views of this project.

  13. Of course, the non-modal norm ‘assign credence zero to falsehoods’ subsumes the modal norm ‘assign credence zero to genuine impossibilities’. But it seems like the modal norm is in some real sense easier for us to follow than the non-modal norm, and is thus more explanatory of our epistemic practices. By comparison, ‘apportion your beliefs to the evidence’ is an easier norm to follow than ‘believe all and only the truths’; and thus the former is more explanatory of our epistemic practices than the latter, despite the capacity of the former to produce false beliefs even when followed correctly.

  14. Note that the analysis of epistemic modality as restricted is by no means universally accepted. A consequence of the analysis is that all metaphysically necessary truths are epistemically necessary; but we certainly lack knowledge of many of the metaphysically necessary truths of mathematics and of logic.

  15. It is not clear why this amounts to a serious problem. Although counterfactuals like ‘had I scratched my nose just now, the initial state of the universe would have been different’ seem false, so do counterfactuals like ‘had I scratched my nose just now, a small miracle would have occurred’. We might further suspect that part of the resistance to the former counterfactual derives from the feeling that it incorrectly indicates that my nose-scratching caused the initial state to be different. If we cancel this implication by use of the form ‘had I scratched my nose just now, the initial state of the universe would have had to have been different’, the result no longer seems obviously false (especially if we are explicitly attending to the possibility of determinism). In contrast, ‘had I scratched my nose just now, a small miracle would have had to have occurred’ still seems false. So an alternative possible route for modal necessitarians is to accept unlimited back-tracking; this allows modal necessitarianism to be reconciled with deterministic laws without giving up on widespread counterfactual truth. See Wilson (forthcoming) for further discussion.

  16. Might there turn out to be too few low-chance quantum–mechanical events to play the role of miracles in the Lewisian semantics? While this is perhaps an open empirical question—if something like Robin Hanson’s ‘mangled worlds’ hypothesis (Hanson 2003) turns out to be correct, there may be no quantum possibilities involving extremely unlikely events—I think the evidence is pretty strong that quantum mechanics will allow for analogues of the kind of ‘small miracles’, localized in time and space, which are needed for the Lewisian counterfactual semantics.

  17. An advantage of this approach is that it does not render true counterfactuals like ‘if I had scratched my nose just now, a highly unlikely quantum event would have had occurred’. Other motivations for the approach might include the worries raised by Hawthorne (2005) and Hájek (MS) about the interaction of the Lewisian theory of counterfactuals with indeterministic laws. Some potential responses are canvassed by Williams (2008). But we can set these worries aside here, since they apply to contingentism as much as to modal necessitarianism.

  18. A variant of this argument assumes that we can know that certain counterfactuals have non-trivial truth-conditions even in advance of knowing whether the actual laws are indeterministic, and concludes that non-trivial truth-conditions for counterfactuals must be recoverable under determinism.

  19. The use of these terms is philosophically standard, but grammatically incorrect. See Bennett (2003, §5).

  20. Schaffer (2005, p. 9).

  21. Perhaps like charges attracting is conceivable while mathematical falsehoods aren’t. But to press this point is to change the subject from the argument from propositions to the argument from conceivability, discussed in the next subsection.

  22. Schaffer (2005, p. 12).

  23. Schaffer (2005, p. 26).

  24. Schaffer (2005, p. 12).

  25. Schaffer (2005, p. 12).

  26. Schaffer (2005, p. 27).

  27. Even if an argument of this sort can be provided, the modal necessitarian could fall back on the assumption that the laws are necessarily indeterministic. Wherever there are independent chance events, all combinations of their possible outcomes are possible: this undermines the thought that the world is ‘the essential outpouring of the initial singularity’.


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Discussions with Toby Handfield triggered the writing of this paper; he also made many useful suggestions for improvement. An early version was presented at a Monash work-in-progress seminar, and at an ANU metaphysics workshop in Kioloa. My thanks go to these audiences for their feedback, and in particular to Alexander Bird, Antony Eagle and Jonathan Schaffer for their patient and constructive comments. I am also grateful to an anonymous referee for this journal.

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Correspondence to Alastair Wilson.

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Wilson, A. Schaffer on laws of nature. Philos Stud 164, 653–667 (2013).

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  • Law
  • Property
  • Necessitarianism
  • Modality
  • Determinism
  • Indeterminism
  • Schaffer
  • Counterfactuals