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Challenging Lewis’s challenge to the best system account of lawhood


David Lewis has formulated a well-known challenge to his Best System account of lawhood: the content of any system whatever can be formulated very simply if one allows for perverse choices of primitive vocabulary. We show that the challenge is not that dangerous, and that to account for it one need not invoke natural properties (Lewis in Aust J Phil 61: 343–377, 1983) or relativized versions of the Best System account (Cohen and Callender in Phil Stud 145: 1–34, 2009). This way, we help to move towards an even better Best System account. We discuss extensions of our strategy to the discussions about the indexicality of the notion of laws of nature (Roberts in Phil Sci 66: S502–S511, 1999), and to another trivialization argument (Unterhuber in Erkenntnis 79: 1833–1847, 2014).

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  1. 1.

    Thus: “I take a suitable system to be one that has the virtues we aspire to in our own theory-building, and that has them to the greatest extent possible given the way the world is. It must be entirely true; it must be closed under strict implication; it must be as simple in axiomatization as it can be without sacrificing too much information content; and it must have as much information content as it can have without sacrificing too much simplicity. A law is any regularity that earns inclusion in the ideal system. (Or, in case of ties, in every ideal system.)” (Lewis 1983, p. 367)

  2. 2.

    Another well-known acronym is BSA (for Best System Account).

  3. 3.

    Many proponents of the MRL account tend to be unhappy with this appeal to natural properties. See Eddon and Meacham (2015) for an overview of the debate.

  4. 4.

    Perhaps, to be a re-axiomatization, one should also require that the new system shouldn’t be able to prove new things. Since this issue will play no role in our argument, for the sake of simplicity we’ll stick to the weaker requirement.

  5. 5.

    Yet they add that strictly speaking the problem of transcendent comparisons is prior to Lewis’s challenge, since the latter assumes that we have intuitive transcendent measures that allow \(\forall x Fx\) in the first place. (Cohen and Callender 2009, p. 6)

  6. 6.

    Explosive realism is the view that “the world permits possibly infinitely many distinct carvings up into kinds, each equally good from the perspective of nature itself, but differentially congenial and significant to us given the kinds of creatures we are, perceptual apparatus we have, and (potentially variable) matters we care about.” (Cohen and Callender 2009, p. 22)

  7. 7.

    In a more recent paper, Callender and Cohen (2010) still subscribe to this solution to Lewis’s challenge.

  8. 8.

    We would like to thank an anonymous reviewer for raising this point.

  9. 9.

    We would like to thank two anonymous reviewers for pressing us on this issue.

  10. 10.

    Notice that thinking about this trivialization problem not in terms of sets of possible worlds, but rather in terms of what’s implied, is fairly common in the literature. See for example (Unterhuber 2014), where the problem is formulated in terms of implying all facts, or (Loewer 2007), where it is said that the re-axiomatization entails all truths.

  11. 11.

    One may object that in order to be useful for prediction, manipulation, or explanation, theories should not be too complex. This point is covered by Lewis’s simplicity criterion, however.

  12. 12.

    Earman’s target is Lewis’s ‘information content’, but his criticism applies to propositional content (in the sense of exclusion of possible worlds) just as well.

  13. 13.

    The draft of this paper available on Loewer’s website uses a somewhat different phrasing with the same gist: “[...the re-axiomatization] fails to provide information about the world in a way that gives us explanations, predictions, understanding of how the macro supervenes on the micro, and so on in ways that are salient. And the reason for that is even though we know that \(\forall {x}\,\,F(x)\) is true from the way it has been specified we don’t know what proposition it expresses in a way that we can extract information from it ...” (p. 16 of the draft).

  14. 14.

    Note that unless further specifications are added which would define one of the terms involved in Lewis’s criteria of theory choice in terms of possible worlds, this account by no means requires reference to possible worlds. Or at least it is separable from the discourse of possible worlds if one doesn’t define strength and simplicity of a theory in terms of possible worlds. Also, Lewis’s objection doesn’t really hinge on what one thinks about possible worlds, because the phrase “let F be a predicate that applies to all and only things at worlds where S holds” can be replaced with “let F be a predicate that applies to all and only those things which satisfy the property of being an object such that S holds.” As we already pointed out, Lewis (1983, p. 367) explicitly leaves open the question whether we should “take our systems as consisting of propositions (classes of worlds) or as consisting of interpreted sentences”.

  15. 15.

    This worry was raised by an anonymous reviewer.

  16. 16.

    This worry and the two next ones were raised by another anonymous reviewer.

  17. 17.

    For instance, there is no agreed upon standard of simplicity. See Woodward (2015) for a criticism of the role of simplicity in MRL and Wheeler (2016) for a recent proposal to interpret simplicity as ‘compression’ in the algorithmic information theoretic sense. See Eddon and Meacham (2015) for a recent overview of different views on simplicity (and related matters).


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  2. Callender, C., & Cohen, J. (2010). Special sciences, conspiracy and the better best system account of lawhood. Erkenntnis, 73, 427–447.

  3. Cohen, J., & Callender, C. (2009). A better best system account of lawhood. Philosophical Studies, 145(1), 1–34.

  4. Earman, J. (1984). Laws of nature: The empiricist challenge. In R. Bogdan (Ed.), D.M. Armstrong (pp. 191–223). Dordrecht: Reidel.

  5. Eddon, M., & Meacham, C. J. G. (2015). No work for a theory of universals. In B. Loewer & J. Schaffer (Eds.), The Blackwell companion to David Lewis (pp. 116–137). Oxford: Wiley.

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  9. Lewis, D. (1991). Parts of classes. Oxford: Blackwell.

  10. Loewer, B. (2007). Laws and natural properties. Philosophical Topics, 35(1/2), 313–328.

  11. Psillos, S. (2002). Causation and explanation. Chesham: Acumen.

  12. Roberts, J. (1999). Laws of nature as an indexical term: A reinterpretation of Lewis’s best-system analysis. Philosophy of Science, 66, S502–S511.

  13. Turner, T. (1989). The best. In Foreign Affair. Capitol Records, Los Angeles.

  14. Unterhuber, M. (2014). Do ceteris paribus laws exist? A regularity-based best system analysis. Erkenntnis, 79(10), 1833–1847.

  15. Wheeler, B. (2016). Simplicity, language-dependency and the best system account of laws. Theoria, 31(2), 189–206.

  16. Woodward, J. (2015). Simplicity in the best systems account of laws of nature. British Journal for the Philosophy of Science, online first.

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Correspondence to Rafal Urbaniak.

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Urbaniak, R., Leuridan, B. Challenging Lewis’s challenge to the best system account of lawhood. Synthese 195, 1649–1666 (2018). https://doi.org/10.1007/s11229-016-1287-6

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  • Laws of nature
  • Natural kinds
  • Lewis
  • Possible worlds
  • Best system account of lawhood
  • Indexicality of laws of nature
  • Mill-Ramsey-Lewis account of lawhood