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Better Best Systems and the Issue of CP-Laws

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Abstract

This paper combines two ideas: (1) That the Lewisian best system analysis of lawhood (BSA) can cope with laws that have exceptions (cf. Braddon-Mitchell in Noûs 35(2):260–277, 2001; Schrenk in The metaphysics of ceteris paribus laws. Ontos, Frankfurt, 2007). (2) That a BSA can be executed not only on the mosaic of perfectly natural properties but also on any set of special science properties (cf., inter alia, Schrenk 2007, Selected papers contributed to the sections of GAP.6, 6th international congress of the society for analytical philosophy. Mentis, Paderborn/Münster, 2008; Cohen and Callender in Philos Stud 145:1–34, 2009, Erkenntnis 73:427–447, 2010). Bringing together (1) and (2) results in an analysis of special science ceteris paribus laws.

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Notes

  1. This paper revises and improves ideas of (Schrenk 2007, 2008). These earlier publications are now obsolete. I wish to thank three anonymous reviewers and also the editors, Matthias Unterhuber and Alexander Reutlinger, for their valuable suggestions how to advance the paper beyond the first draft they have commented.

  2. Section (2.2) refines and makes concise pp. 45–54 and 77–86 of (Schrenk 2007).

  3. For a discussion cf. Earman 1978, for considerations regarding fundamentality and exceptions see (Schrenk 2009).

  4. By “irregular” is not meant “probabilistic”. Footnote 10 shows how to distinguish cp-laws or laws with exceptions from probabilistic laws.

  5. Here, I have Lewis’s specification of intrinsic properties in mind cf. (Lewis 1983b) and (Lewis and Langton 1998).

  6. The non-generality requirement is there because if it were possible to add general exclusion clauses to the antecedent of the respective general statement (‘All Fs that are not also H are Gs’, for example) we would say that that general statement is the (exceptionless!) regularity we should consider.

  7. To signify a region I should write (x0 + Δx, y0 + Δy, z0 + Δz, t0 + Δt); for brevity I stick to (x0, y0, z0, t0).

  8. That is, “@(x0, y0, z0, t0)” is a one-place predicate that stands for being localized at the space–time point with coordinates <x0, y0, z0, t0>. One can easily create further such one-place predicates of the same form: “@(x1, y1, z1, t1)”, etc. for further space–time locations.

  9. More on reference to individuals: (Schrenk 2007: 48).

  10. The probabilistic law, by which I mean laws of the sort P(G|F) = r, would claim that, wherever you are, there is a chance r that Fs are Gs. The index law says instead that, except for the indices where the chance is 0, the probability is 1 to find Fs that are Gs. Cf. also (Schrenk 2007: 50) and Reutlinger (this volume).

  11. The long answer is also “yes”: (cf. Schrenk 2007: 76ff).

  12. David Braddon-Mitchell (Braddon-Mitchell 2001), who has his own version of Lewis laws with exceptions (“Lossy Laws”) and who has greatly influenced my own thoughts on the topic, explicitly allows law statements to lie. That is, unlike me, he opts for recording the law as “∀u (Fu ⊃ Gu)” even if there is an exception at (x0, y0, z0, t0). For the consequences of this difference see (Schrenk 2007: 92ff). My interpretation is, for example, more in line with Lewis: “Take all deductive systems whose theorems are true…” (Lewis 1994, p. 231; my italics). For a valuable critical evaluation of both accounts see (Kowalenko 2011).

  13. In which relation bridge laws stand to the best system is not explicit in Lewis. Clearly, they cannot belong to competing systems from the start because of Lewis’s vocabulary restriction to predicates that refer to perfectly natural properties.

  14. The BBSA style ideas can also be found in (Halpin 2003), (Taylor 1993: 97), (Roberts 1998, see also Roberts in this volume), (Loewer 2007) and (Albert 2000). For important discussions see (Frisch forthcoming), (Weslake forthcoming) and (Reutlinger and Backmann under review). A valuable variant and continuation of the BBSA account is Matthias Unterhuber’s contribution to this volume.

  15. I treat, here, properties innocently as the semantic values of predicates. Where no confusion can result I make smooth transitions from properties talk to predicates talk and vice versa.

  16. See (Schrenk 2008: 126). David Albert uses a similar “audience with god” metaphor (Albert unpublished: chapter 1) as, in fact, does David Lewis (1973: 74). Still, it might be important to underline again that the goddess metaphor is only there to highlight that we are operating from an omniscient, that is, metaphysical standpoint. No theism is implied. Omniscience of the whole mosaic is what Lewis assumed for his best system, too, so there is no difference here except for the one that the respective mosaics we look at come in different colours and tesserea sizes.

  17. I should say: I no longer assume that natural properties exist. In (Schrenk 2007) I did, now I am agnostic.

  18. It would be very interesting to engage in the question how BBSA laws for less than perfectly natural properties would compare to the non-fundamental laws an original Lewis BSA would generate (via bridge principles) if there were natural properties. This question can, however, not be targeted here.

    Note also that the vocabulary choices are not as straightforward as I made it seem above. The reason is that many biological laws will also essentially refer to physical and/or chemical properties. Think of the bio-medical law that humans cannot survive much longer than 10 days without water, i.e., H 2 O+ certain dissolved isotonic salts. I discuss this problem at length in (Schrenk Manuscript).

  19. For further challenges and how to meet them see (Schrenk Manuscript).

  20. I thank Alexander Reutlinger for helping me to disentangle these two types of objectivity.

  21. The vocabulary sets of the sciences suggest themselves as the canonical selections if the system winners are to be called “laws of nature”. This to limits the abundance of useful vocabularies.

  22. While not being their central concern Cohen and Callender also have a view on cp-laws (cf. their 2009: 25–26; 2010: 433). As they explicitly say, what they have to contribute depends partially on existing accounts of what cp, when attached to a regularity statement, could mean (Cohen and Callender 2009: 25), and they are positive that acceptable solutions exist (they list some options, including Schrenk 2008). Once such a theory is in place, so they continue, BBSAs can easily cope with cp-regularities/laws. Their argument is, like mine, very similar to Braddon-Mitchell’s. It says, in essence, that generalisations with exceptions can be subjected to best systematisations, checking strength and simplicity, just as this can be done with strict generalisations (ibid. 25–26). How Cohen and Callender’s and my account differs thus depends entirely on which additional theory for the cp-clause they adopt. If mine, there is no difference at all.

  23. “Naming” in the sense of “singling them out”. What she can’t do is give them proper names that would then be mentioned in the exclusion clauses, for proper names do not belong to the scientific vocabulary we handed over. Yet, that is no major hurdle because the divine helper has the resources to pick out individuals simply as the space time worms they occupy and we can safely assume that space–time vocabulary is allowed in any science. (I wish to thank Jenann Ismael for the observation that proper names mustn’t appear.)

  24. I thank an anonymous referee for pointing out this difficulty.

  25. My BBSAcp account shares with so called “completer accounts“(cf. Reutlinger et al. (2011: §5)) that the antecedent of the respective law statements is expanded so that the statement is strictified, yet, it differs from those accounts in that the addenda are not general but individual (cf. the section about indices) and appended only under idealized conditions (omniscience) and not within scientific practice.

  26. Of course, nothing speaks against excluding at least some “exceptional” individuals from the antecedent of scientific law candidates (the ones we are certain of to be exceptions). Also, nothing counts against scientists trying to find a systematic account for the exceptions. The account here given is for those exception ridden laws for which this cannot be successfully done.

    In Schurz (this volume) Gerhard Schurz introduces the important distinction Ceteris Paribus versus Ceteris Rectis Laws. A classification of kinds of exceptions is thereby made. Michael Strevens (also this volume) explains why higher-level laws have exceptions. My own pure enumeration of exceptional individuals comes without any classificatory (Schurz) or explanatory (Strevens) judgement and is, therefore, orthogonal to and coherent with both Schurz’ and Strevens’ accounts.

  27. How the BBSA ceteris paribus solution here offered can be paired with Pietroski and Rey’s well known account of cp-laws (Pietroski and Rey 1995) is discussed in (Schrenk 2008). By such a maneuver a problem of the latter account is solved and the BBSA gains a valuable epistemic supplement. An equally promising supplement (next to Pietroski and Rey’s) would be, at least for physical cp-laws, Andreas Hüttemann’s dispositional account (this volume) and, alternatively for laws in general, Nancy Cartwright’s and John Pemperton’s nomological machine account (this volume).

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Acknowledgments

Thanks are due to the audiences at the GAP8 conference, Konstanz (2012), at Matthias Frisch’s Laws of Nature workshop in Munich (2012), and at the Pittsburgh Lunchtime Seminar (2013). I am especially grateful to Marius Backmann, Jenann Ismael, Siegfried Jaag, Andreas Hüttemann, Alexander Reutlinger, Charlotte Matheson, Thomas Müller, Stephen Mumford, Jesse Mulder, Emma Tobin, Matthew Tugby, Matthias Unterhuber and Brad Weslake for many valuable discussions and/or advice and comments on earlier drafts of this paper. I wish to thank Bastian Walter who helped me with editorial issues regarding the manuscript. The paper was finalized within the context of the Causation and Explanation Research Group funded by the Deutsche Forschungsgemeinschaft (DFG).

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    Markus Schrenk

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Schrenk, M. Better Best Systems and the Issue of CP-Laws. Erkenn 79 (Suppl 10), 1787–1799 (2014). https://doi.org/10.1007/s10670-014-9642-9

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