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The package deal account of laws and properties (PDA)

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This paper develops an account of the metaphysics of fundamental laws I call “the Package Deal Account (PDA)” that is a descendent of Lewis’ BSA but differs from it in a number of significant ways. It also rejects some elements of the metaphysics in which Lewis develops his BSA. First, Lewis proposed a metaphysical thesis about fundamental properties he calls “Humean Supervenience” (HS) according to which all fundamental properties are instantiated by points or point sized individuals and the only fundamental relations are geometrical spatial and temporal relations between these. While the BSA does not require HS Lewis seems to hope that it is true. In contrast, the PDA is not committed to HS or even to the fundamental arena in which fundamental properties are instantiated possessing geometrical structure and thus is able to accommodate relations and structures found in contemporary physics that apparently conflict with HS. Second, although Lewis’ BSA doesn’t require HS his Humeanism does require that fundamental properties are categorical. In contrast, the PDA allows for the possibility that fundamental properties are individuated in terms of laws and so are not categorical. Third, the PDA expands and develops the criteria for what counts in favor of a candidate system with more attention to the criteria employed by physicists in evaluating proposed theories. Fourth and most importantly, unlike Lewis’ BSA, the PDA does not presuppose metaphysically primitive elite properties/quantities that Lewis calls “perfectly natural” properties/quantities or presuppose a metaphysically preferred language whose terms denote such properties/quantities. It replaces Lewis’ account with an account on which natural properties are not metaphysically prior to the laws but are elements of a package that includes a fundamental arena that plays the role of space-time as well as fundamental laws and properties. By doing so it responds to some epistemological and metaphysical issues that have been raised regarding natural properties and their role in the BSA. In sum, the PDA goes further in explicating the notion of laws in terms of the aims and practices of science especially fundamental physics rather than in terms of prior metaphysics. I begin by reviewing Lewis’ account of perfectly natural properties and his Humean BSA of laws.

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  1. “Necessitarian” because these accounts all hold that there are fundamental necessary connections in nature and that laws either account for them or are consequences of them. Governing accounts originated in the Seventeenth century with the idea that laws are the principles by which God governs the motions of bodies (see Harrison). There are also Powers and dispositionalist accounts locate necessary connections in fundamental dispositions and powers of certain properties and laws as due to their activities. These accounts are developments of Aristotelian and medieval accounts of natural necessity. See Cartwright (1999) and Mumford (1998).

  2. A third view on which laws involve necessary connections is Marc Lange’s counterfactual account on which lawful propositions are those that are stable under certain conditions. See Lange (2009).

  3. Two philosophers who do make the connection between theology and governing explicit but for different reasons are John Foster (2004) and Nancy Cartwright (2005). Foster in The Divine Law Maker argues that God’s will is required to make sense of the governing role of laws and Cartwright in “No God No Laws” appeals the connection between laws and theology in her argument that there are no laws of nature and for a return to a more Aristotelian account of science.

  4. This type of account of laws was developed by Armstrong, Dretske and Tooley in the 1980s.

  5. Tim Maudlin (2007) proposes an account along these lines. The account also forges a connection between accounts of laws and accounts of the nature of time. This connection is discussed in Loewer (2012).

  6. On powers accounts laws lawful regularities are metaphysically necessary but whether or not the properties connected by a law are instantiated is contingent.

  7. But properties/quantities instantiated in the same or overlapping locations may be necessarily connected. For example, having a mass of 5 grams necessarily excludes having a mass of 6 grams.

  8. There is controversy concerning Hume’s view. The standard interpretation is that Hume held that since we have no impression of necessary connections between events we cannot form concepts of them and concludes that they don’t exist. Recently some reject this and instead understand Hume as claiming only that we can’t know about them e.g. Strawson (2011).

  9. This is not to say that Humeans must eschew notions of metaphysical and nomological necessity that can be explained in terms that don’t presuppose them e.g. Lewis sees nomologically necessary connections as encapsulating certain patterns among events while others e.g. Blackburn see them as projections by us onto the pattern of events.

  10. Among recent proponents of Humean views are David Lewis, John Earman (1984), Mike Hicks (2018) Stathis Psillos (2014) and Barry Loewer (1996, 2007a).

  11. Lewis first discusses the account in Lewis (1973) and elaborates in Lewis (1986). He attributes the basic idea of the BSA to Mill and Ramsey. The BSA is further developed and defended in Loewer (1996) and Beebee (2000).

  12. Lewis also thinks that there are degrees of naturalness. It may be that the degree of naturalness of a property can be defined in terms of perfect naturalness and complexity, but I don’t know of any account that works. In any case, only perfectly natural properties figure in my discussion.

  13. Because no individual can have distinct values of mass, charge, etc. Ned Hall suggest calling them “magnitudes”. See Hall (ms). But I will continue to refer to them as “natural properties” with the understanding that a natural property may have many values.

  14. In Lewisian metaphysics individuals are world bound, i.e. no individual exists at more than one point. Points in a world’s space-time are fundamental individuals and certain regions in a space-time may also be fundamental although Lewis doesn’t say what makes a region of points a fundamental individual.

  15. For an account of how probabilistic laws systematize by conveying information in terms of degrees of belief see Loewer (2004).

  16. As described for example in Albert (2000) and Loewer (2020).

  17. See Loewer (2001) and (2020).

  18. Lewis doesn’t say exactly what further features a proposition entailed by the best system are needed to earn the title ‘law’ although he seems to think that laws must be generalizations and dynamical. I don’t think this is right since there may restrictions on initial conditions and propositions like symmetry principles that may be entailed by the best system and play the role of laws and so should be considered to be laws.

  19. Lewis’ proposal counts propositions as laws that are generally not regarded to be such. While gruesome predicates don’t refer to perfectly natural properties generalizations composed of them e.g. “all emerubies are gred” may still be entailed by the best theory. This doesn’t seem to me to be a serious problem since such generalizations are nomologically necessary and further conditions (e.g. predicates refer to properties that are near natural) can be added to weed out generalizations like “all emerubies are gred” which would not be considered to express laws.

  20. Lewis shows how to extend the account to probabilistic laws and proposes a principle for how probabilities should guide rational belief in (1994). His approach is modified, argued for, and extended in Hall (1994), Loewer (2004), Schwarz (2014), and Hoefer (2019). Lewis says that he can “see dimly but well enough” why Humean probabilities should guide credence. Loewer and Hoefer provide arguments for this.

  21. Armstrong (1983), Maudlin (2007), Foster (2004), Lange (2009).

  22. This complaint is made by many non-Humeans e.g. Foster (2004). It is especially forcefully presented by Lazarovici (ms.) Of course, to a Humean this complaint appears question begging.

  23. Loewer (1996, 2012, 2020), Beebee (2000), Hicks and Elswyk (2015), Hicks (2020), Miller (2015).

  24. The initial formulation of the PDA is in Loewer (2007a). The account of the PDA developed in this paper goes considerably beyond its initial formulation. Callender and Cohen (2009) develop a version of the BSA for special science laws that also doesn’t rely on Lewis’ perfectly natural properties.

  25. See, for example, Butterfield and Isham (1999).

  26. French and McKenzie (2012).

  27. Lewis (1999) p. 226.

  28. For discussions of ways of understanding the ontology of QM wave functions see Albert and Ney (2013). Michael Esfeld (forthcoming), Eddy Chen (2020) and others have proposed versions of Bohmian mechanics whose ontology consist solely of point particles while the wave function is construed as a device for systematizing particle trajectories. This account is arguably compatible with Humean Supervenience but conflicts with certain well-established features of fundamental theories.

  29. Lewis (2009).

  30. Black (2000, p. 94).

  31. The example is suggested by Ned Hall’s discussion in (Hall ms, p. 41). He thinks this is just a skeptical problem. But it seems to me very damaging to the role of perfectly natural properties in Lewis’ account since it shows that perfectly natural and so laws characterized in terms of them are disconnected from the physicist’s interest of finding regularities describing particle motions.

  32. The mismatch problem is discussed by van Frassen (1989) and Demarest (2015) who suggested its name.

  33. Lewis suggested this response to me in conversation.

  34. Ted Sider suggested this in conversation.

  35. Even if Lewis’ very intriguing suggestion can be made to work it doesn’t touch the other problems that motivate the PDA.

  36. Dasgupta (2018).

  37. Dasgupta observes that it is ironic that Lewis raises exactly the missing value problem to accounts of objective probabilities which take them to be metaphysically fundamental propensities. Objective probabilities are supposed to be credence guiding via Lewis’ Principal Principle and its ilk, but Lewis thinks that there is no explanation of why a metaphysically primitive propensity should guide credence. P.5 I just paraphrased Lewis’ famous objection to anti-Humean conceptions of objective chance, because my objection to realism is exactly analogous. Ironic, then, that the problem with realism can be found in the writings of someone I take to be an arch realist! But ironies aside, let us review Lewis’ argument so as to use it as a guide.

  38. By Loewer (2007a), Eddon and Meacham (2015), Dorr and Hawthorne (2013).

  39. The idea of developing a Humean account of laws as a package deal in which the best system determines both laws and the properties that figure in them was proposed in Loewer (2007a) and somewhat differently in Cohen and Callender (2009). The former invoke this approach to fundamental laws and properties while the latter apply it as well to special science laws and properties.

  40. Richard Feynman put the point this way “If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis…that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.” (Feynman 1963, 1–2, emphasis in original).

  41. Although Newtonian mechanics is not true illustrates what a TOE might look like. In Newtonian mechanics physical objects (planets etc.), gases. liquids and light are composed of elementary particles and their motions are systematized by dynamical laws that specify the evolution of an isolated system’s state. When supplemented with laws specifying the statistical mechanical probability distribution and the low entropy macro state of the very early universe this package is arguably (Albert 2000 and Loewer 2020) able to account for most macro phenomena (at least if one does not look too closely).

  42. Although two systems may disagree on which generalizations are laws since laws must be true the generalizations must be mutually consistent.

  43. Jaag and Loew (2018).

  44. For example, Dave Chalmers (2012) thinks the connections as a priori discoverable by conceptual analysis while Jonathan Schaffer (2017) construes them as substantive grounding principles. The issue of the metaphysical and epistemological status of the principles that connect the fundamental to the non-fundamental is important and difficult. My own view is that understanding theoretical terms e.g. “atom” involves understanding the role it plays in a theory that explains antecedently understood phenomena. On this view connecting principles are epistemologically but not metaphysically substantive.

  45. By “systematic” I mean that they systematically connect arrangements of fundamental with less fundamental in terms of the properties of each. For example, arrangements and motions of gas molecules are connecting with gasses at various temperatures and pressures. The requirement that connecting principles are simple and systematic excludes the proposal that the fundamental system is simple and informative while the connecting principles are complicated and unsystematic.

  46. Ned Hall (ms) and Craig Callender and Cohen (2009) also make the point that Lewis’ criteria of “simplicity and informativeness” need to be clarified and added to. Hall mentions that to apply laws we typically need a distinction between dynamical laws and initial conditions, Callender mentions some of the other criteria on my list, Jaag and Loew (2018) focus on the importance of a system being usable by us, and Dorst (2017) on its role in predictions.

  47. Albert (2000).

  48. Loewer (2007b).

  49. A consequence is that the PDA’s fundamental properties may not satisfy recombination and so can’t be used to characterize possible worlds. Also, it is plausible that it is possible that there are alien properties that are not references of fundamental terms of $(L) and so possibilities not captured by recombination applied to these properties even if they are all categorical.

  50. If the fundamental predicates of the optimal system’s language are interpreted as referring to properties whose instantiations possess necessary connections then the account of laws looks a lot like Heather Demarest’s Potency-Best System Account of Laws (Demarest 2017). But it is quite different since on that account the laws are entailments of the theory that best systematizes properties that are potencies that antecedently possess necessary connections while on the PDA necessary connections have nothing to do with what makes a proposition express a law.

  51. Hall (2015, p. 28, fn. 14) and Demarest (2019, p. 393).

  52. Michael Esfeld’s “Super-Humeanism” also avoids quiddities (Esfeld forthcoming). It accomplishes this by proposing an ontology that consists only of permanent point particles related by distances. This account’s ontology is compatible with the PDA since it could turn out that its ontology is the optimal arena and ontology for the actual world but it also may turn out that the optimal ontology has no primitive point particles but concerns fields occupying a manifold that lacks primitive distance relations. Further, it fails to satisfy some of the criteria required of the optimal system, in particular (iii).

  53. This is suggested by Ned Hall in his (ms) pp. 15–17.

  54. See Peter Harrison (2019) for a discussion on the theological origin of the idea of laws of nature in the Seventeenth century.

  55. The view that laws are primitive entities that enforce regularities is forcefully argued for by Maudlin (2007).

  56. Intuitions regarding the role of laws in explanation are a mix of anti-Humean and Humean views. For an anti-Humean laws explain by governing or constraining. Humeans reject this since for them the HM determines (constrains) the laws rather than the reverse. So Humeans need to develop an account of the role of laws in explanation perhaps along the line of Kitcher’s unificationist account (Kitcher 1989).

  57. Schaffer (2010) and (2019).

  58. Putnam, Hilary (1982).


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Thanks for comments and discussion to David Albert, Harjit Bhogal, Eddy Chen, Heather Demarest, Denise Dykstra, Michael Esfeld, Alison Fernandes, Michael Hicks, Jenann Ismael, Isaac Wilhelm and two anonymous referees for Synthese.

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Loewer, B. The package deal account of laws and properties (PDA). Synthese 199, 1065–1089 (2021).

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