Abstract
Humean reductionism about laws of nature appears to leave a central aspect of scientific practice unmotivated: If the world’s fundamental structure is exhausted by the actual distribution of non-modal properties and the laws of nature are merely efficient summaries of this distribution, then why does science posit laws that cover a wide range of non-actual circumstances? In this paper, we develop a new version of the Humean best systems account of laws based on the idea that laws need to organize information in a way that maximizes their cognitive usefulness for creature like us. We argue that this account motivates scientific practice because the laws’ applicability to non-actual circumstances falls right out of their cognitive usefulness.
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Notes
Lewis proposes that the fundamental properties are perfectly natural and intrinsic (Lewis 1983). This definition of Humean supervenience might be in tension with fundamental physics, especially quantum physics (see Maudlin 2007). See Lewis (1986a, p. xi, 1994, p. 474) for important qualifications. Nothing in what follows hinges on these qualifications.
See Lewis (1988, pp. 30–31, fn. 15). If we talk about laws (of nature) in the following, we mean the fundamental laws of physics, as opposed to the so-called laws of the special sciences.
See Lewis (1973, p. 73). Lewis (1994) introduces the further condition of ‘fit’ to cover chancy laws. Roughly put, a system that assigns the actual history of events a higher chance of happening has a better fit than one that assigns it a lower chance. For our purposes, however, addressing non-chancy laws is sufficient.
For instance, Armstrong (1983) identifies laws with instantiations of an irreducible higher-order necessitation relation between first order universals. Maudlin (2007) regards the fundamental (dynamical) laws as sui generis entities. Bird (2007) argues that the laws originate in primitive facts about the dispositional natures of fundamental properties. And Lange (2009) traces back lawhood to primitive subjunctive facts.
For example, Lange’s (2009) non-Humean account according to which, roughly put, what makes something a law is that it is invariant under a wide range of counterfactual perturbations seems to be tailor-made to capture the modal latitude of laws. We are skeptical, however, that non-Humeans accounts, in general, offer satisfying explanations of the modal features of laws (cf. Jaag 2014).
There is one outstanding worry for this proposal. The epistemic standards that science uses to discover laws may be tied. That is, two or more systems may satisfy these criteria equally well. If Humeans then take these epistemic standards as constitutive of laws, it would, in this hypothetical case, be metaphysically indeterminate what the laws of nature are. But this consequence is implausible. This worry seems to be at the heart of the two hypothetical scenarios that Hall (2015: ch. 17.7) discusses as further challenges for Humean reductionism in the conclusion of his article. Discussing this challenge is a topic for another paper.
You may worry that CU is objectionably anthropocentric, but we will argue below that the ensuing anthropocentricity is unproblematic.
Ismael (2015, p. 197) proposes that laws are “partially prepared solutions to frequently encountered problems.” Our account can be seen as a development of this idea. (Ismael herself does not wholeheartedly endorse Humeanism about laws.).
For chaotic systems, however, small inaccuracies in the data do lead to big inaccuracies in the solutions even if dependence is continuous.
What if there are alien scientists who, like Gods or Laplacean demons, can know the world’s state with complete precision and have no limitations in their processing power? We contend that these agents, if they have a concept of a law of nature at all, would have a different concept from ours such that our laws would not be of particular interest to them.
Lewis’s effort to make his version of the BSA non-anthropocentric, by contrast, comes at the cost of positing perfectly natural properties (Lewis 1983, pp. 367–368) and objective standards of strength and simplicity (Lewis 1994, p. 479). However, it is then not clear that scientists should accommodate this structure when discovering laws. See Cohen and Callender (2009: Sect. 2.1) and van Fraassen (1989, p. 53) for criticisms along these lines.
Thanks to David Glick for discussion of this point.
Thanks to Mike Hicks for discussion of this point. See also our discussion of Elga in Sect. 3.
CU also solves a famous problem for Lewis’s version of the BSA. Take a maximally strong system S and “[l]et F be a predicate that applies to all and only things at worlds where S holds. Take F as primitive, and axiomatize S (or an equivalent thereof) by the single axiom ∀x Fx” (Lewis 1983, p. 367). Since ∀x Fx is maximally informative and simple, Lewis’s BSA has the absurd consequence that all regularities whatsoever come out as laws. Lewis evades this problem by restricting predicates to ones referring to perfectly natural properties. Our account requires no such objective joints, since ∀x Fx does not provide information that is storable or computable by resource-bounded creatures and so is cognitively useless. Our account, thus, incorporates the central insight of the so-called ‘Better Best System Account’, viz., that Humeans need not (and should not) posit a naturalness constraint on the language the best system is couched in (see Cohen and Callender 2009).
You may worry that the above considerations also rule out certain bona fide laws. Suppose (as may well be the case) that weak nuclear force is completely irrelevant to most of the approximate truths that we derive from the laws. Why then should there be a force law for that force? What is the difference between that force law and a fact about the approximate mass of the universe? In reply, we argue that we still would need a force law to tell us that weak nuclear force can be ignored in almost all situations. With regard to the approximate mass of the universe, the gravitational laws tell us that we can ignore it in most cases. But without a law for weak nuclear force, we would have no idea whether in any given situation, we could ignore weak nuclear force or have to take it into account after all.
We suspect that something similar applies to other candidates for fundamental physical laws that decrease modal latitude, such as force laws and other laws of coexistence.
This “if,” however, is a big “if.” It is controversial both whether the past hypothesis and the statistical postulate really provide the required information and whether they do so in the most efficient way. See Albert (2015, p. 6, fn. 2) and Callender (2011) plus the references therein for discussion.
Hicks calls the corresponding constraints “local strength” and “breadth.” He proposes other interesting constraints on laws, but these are not relevant for the discussion at hand.
More recently, Callender and Cohen (2010) argue that each science employs its own standards, based on the goals of systematizing their particular domain. Callender (2017) defends a version of the BSA that is similar to our account. According to this version, a set of laws needs to allow for “well-posed Cauchy Problems,” which is closely related to what we have above called ‘error-tolerance’. Neither of these accounts, however, is proposed as a solution to the challenge for Humeans outlined in Sect. 2.
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Acknowledgements
Both authors contributed equally to the paper. For helpful comments and suggestions, we would like to thank Chris Dorst, David Glick, Ned Hall, Andreas Hüttemann, Michael T. Hicks, Catherine Jo, Marc Lange, Markus Schrenk, three anonymous referees for this journal, as well as audiences in Cologne and Oxford.
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Jaag, S., Loew, C. Making best systems best for us. Synthese 197, 2525–2550 (2020). https://doi.org/10.1007/s11229-018-1829-1
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DOI: https://doi.org/10.1007/s11229-018-1829-1