Abstract
The Great Divide in metaphysical debates about laws of nature is between Humeans, who think that laws merely describe the distribution of matter, and non-Humeans, who think that laws govern it. The metaphysics can place demands on the proper formulations of physical theories. It is sometimes assumed that the governing view requires a fundamental/intrinsic direction of time: to govern, laws must be dynamical, producing later states of the world from earlier ones, in accord with the fundamental direction of time in the universe. In this paper, we propose a minimal primitivism about laws of nature (MinP) according to which there is no such requirement. On our view, laws govern by constraining the physical possibilities. Our view captures the essence of the governing view without taking on extraneous commitments about the direction of time or dynamic production. Moreover, as a version of primitivism, our view requires no reduction/analysis of laws in terms of universals, powers, or dispositions. Our view accommodates several potential candidates for fundamental laws, including the principle of least action, the Past Hypothesis, the Einstein equation of general relativity, and even controversial examples found in the Wheeler-Feynman theory of electrodynamics and retrocausal theories of quantum mechanics. By understanding governing as constraining, non-Humeans who accept MinP have the same freedom to contemplate a wide variety of candidate fundamental laws as Humeans do.
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Notes
- 1.
In this paper, we use “fundamental laws” and “laws” interchangeably unless noted otherwise.
- 2.
This is an oversimplification as there are some non-Humeans, such as Aristotelian Reductionists, who do not think that laws govern. See Sect. 2.3.
- 3.
Throughout this paper, for simplicity, we assume that spacetime is fundamental. This assumption is not essential to MinP. One can consider non-spatio-temporal worlds governed by minimal primitivist laws. For those worlds, one can understand MinP as suggesting that laws constrain the physical possibilities of the world, whatever non-spatio-temporal structure it may have. Indeed, if one regards time itself as emergent, one may find it natural to understand governing in an atemporal and direction-less sense.
- 4.
Causal fundamentalism does not imply that everyday causality is metaphysically fundamental. For example, Maudlin’s notion of dynamic production is different from everyday causality (Maudlin 2007, ch.5). For some recent works on causal fundamentalism, physics, and everyday causality, see Blanchard (2016) and Weaver (2019).
- 5.
This survey is by no means exhaustive of the rich literature on laws. For example, against the view that there are fundamental laws that are universally true, Cartwright (1994a) advocates a patchwork view of laws where they are, at most, true ceteris paribus. Van Fraassen (1989) advocates a view where there are no laws of nature. See Carroll (2020), Hildebrand (2020), Bhogal (2020) for more detailed surveys.
- 6.
Whether contemporary Humean position in the metaphysics of science represents the historical Hume has been debated. See for example Strawson (2015).
- 7.
For example, the regularity that all uranium spheres are less than one mile in diameter may be a law or a consequence of some law, but the regularity that all gold spheres are less than one mile in diameter is not a law or a consequence of a law.
- 8.
Another issue concerning theoretical virtues is how we should use them to compare different systems. As noted earlier, simplicity is language relative. Cohen and Callender (2009) suggest that the comparisons should be relativized to languages. Their relativized account (called the Better Best System Account) perhaps can be used to support Fodor (1974)’s vision of the autonomy of the special sciences (e.g. biology, psychology, economics) from fundamental physics.
- 9.
For an overview of Plato’s theory of forms, see Kraut (2017).
- 10.
In the literature it is sometimes called the DTA account of laws or the Universalist account of laws. Calling it Platonic reductionism may be controversial. But see the discussion in (Carroll 1994, appendix A1).
- 11.
We note that this example about F = ma does not exactly fit in Armstrong’s schema of “All F’s are G.” See (Armstrong 1983, ch.7) for a proposal for accommodating “functional laws.”
- 12.
In a famous passage, Lewis (1983) raises this objection: “Whatever N may be, I cannot see how it could be absolutely impossible to have N(F,G) and Fa without Ga…The mystery is somewhat hidden by Armstrong’s terminology. He uses ‘necessitates’ as a name for the lawmaking universal N; and who would be surprised to hear that if F ‘necessitates’ G and a has F, then a must have G? But I say that N deserves the name of ‘necessitation’ only if, somehow, it really can enter into the requisite necessary connections. It can’t enter into them just by bearing a name, any more than one can have mighty biceps just by being called ‘Armstrong’ ” (p. 366).
- 13.
For an overview of the metaphysics of dispositions, see Choi and Fara (2021).
- 14.
- 15.
Many defenders of this view suggest that even though it has roots in Aristotle, it is not committed to many aspects of Aristotelianism.
- 16.
In contrast, Vetter (2015) is open to a temporally symmetric metaphysics but assumes temporal asymmetry in her account of dispositions (which she calls potentialities).
- 17.
- 18.
This reading of Maudlin is supported by the earlier passages as well as this one: “It was perhaps already clear when I wrote ‘A Modest Proposal…’ that the issue of time and the issue of natural laws were deeply intertwined: I noted in that essay that the fundamental laws of nature appear to be laws of temporal evolution: they specify how the state of the universe will, or might, evolve from a given initial state” (emphasis original, p. 172).
- 19.
Bhogal (2017) proposes a “minimal anti-Humeanism” on which laws are ungrounded (true) universal generalizations. It is compatible with primitivism, but it is less minimalist than MinP. For example, on Bhogal’s view, laws cannot be singular facts about particular times or places. However, Bhogal (p. 447, fn.1) seems open to relax the requirement that laws have to be universal generalizations. It would be interesting to see how to extend Bhogal’s view to do so. In an arXiv preprint posted shortly after our paper, Adlam (2021) independently proposes an account that is, in certain aspects, similar to MinP; she also suggests we take seriously laws that do not have a time-evolution form. However, her account is not committed to primitivism and seems more at home in a structural realist framework. Moreover, simplicity does not seem essential to her account of nomic explanations.
- 20.
For those metaphysically inclined, here are some formal details. Consider w, the complete history of a possible world describable in terms of matter in spacetime. Let Ω w be the non-empty set of worlds that are physically possible (from the perspective of w). It is a priori that w ∈ Ω w. Consider fact L, which may be Newton’s equation of motion with Newtonian gravitation. Let Ω L be the set of models generated by L. Now, suppose L governs w. Then the following is true:
- Equivalence :
-
Ω L = Ω w
Equivalence makes precise the idea that on MinP governing laws limit the physical possibilities. Since w ∈ Ω w, it follows that:
- Constraint :
-
w ∈ Ω L
If we let w = α, the actual world, then Constraint makes precise the idea that, on MinP, laws constrain the actual world. For MinP, we postulate that the above notions and derivations make sense. A natural idea is to reduce or analyze physical possibilities and necessities in terms of fundamental laws and a notion of mathematical consistency. This makes physical possibilities a derivative notion rather than a fundamental one. However, we do not insist on it here. A few epistemological remarks: the fact that Ω L = Ω w is knowable a posteriori; consequently, the fact that w ∈ Ω L is also knowable a posteriori. A careful reader might raise a consistency worry here: what if a single world (history) w is compatible with two different laws L and L′ with non-empty overlap in their solution spaces, such that \(w\in \varOmega ^L \cap \varOmega ^{L'}\)? The worry is handled by the earlier postulates. Having \(w\in \varOmega ^{L'}\) is not sufficient for L′ to be the governing law or for \(\varOmega ^{L'}\) to be the set of physical possibilities. MinP assumes that, from the perspective each world, there is a single set of physical possibilities, given by the governing law(s). Hence, for w, if Ω L and \( \varOmega ^{L'}\) are different sets, then at most one of them is equivalent to Ω w. Moreover, since Ω w is non-empty, the laws that govern w must be consistent with each other.
- 21.
If one prefers the representation where the set of physical possibilities contains each possibility exactly once, one can derive a quotient set \(\varOmega _{\alpha }^\ast \) from Ω α with the equivalence relation given by the time-reversal map.
- 22.
It is an interesting question, on MinP, what more is required and how to understand the equivalence of physical laws. Perhaps their equivalence is related to simplicity and explanations. In any case, we do not provide such an account as it is orthogonal to our main concerns in the paper. For a survey of the related topic of theoretical equivalence, see Weatherall (2019a, 2019b).
- 23.
Humeans face a similar issue, as their account raises the worry as to why the fundamental Humean mosaic is so nice that it can be summarized in a simple way after all.
- 24.
This type of explanation, sometimes called “constraint explanation,” has been explored in the causation literature by Ben-Menahem (2018) and non-causal explanation literature by Lange (2016). Their accounts, with suitable modifications, may apply here. See Hildebrand (2013) for a critical discussion of primitive laws and explanations.
- 25.
Christopher Dorst raised a similar point in personal communication. See also Dorst (2021).
- 26.
Making a similar point, Callender (2017, p. 139) writes: “[The] ten vacuum Einstein field equations separate into six “evolution” equations G ij = 0 and four “constraint equations,” G 00 = 0 and G 0i = 0, with i = 1, 2, 3. The latter impose nomic conditions across a spacelike slice. To decree that four of the ten equations that constitute Einstein’s field equations are not nomic without good reason is unacceptable.”
- 27.
However, see Roberts (2008) for a Humean account of laws based on a contextualist semantics that may alleviate this worry.
- 28.
See also Gordon Belot’s paper on ratbag idealism in this volume.
- 29.
However, Bird (2007) talks about laws supervening on dispositions and allows that laws can still govern in a weaker sense.
- 30.
In a recent book, Vetter (2015) is open to the idea that there can be past-directed dispositions but still suggests that there is a temporal asymmetry: past-directed dispositions are trivial.
- 31.
In personal communication, Maudlin suggests that he now regards (3) as expressing a metaphysical analysis or a definition of ρ in terms of the divergence of E.
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Acknowledgements
For helpful discussions, we thank David Albert, Jeff Barrett, Yemima Ben-Menahem, Craig Callender, Claudio Calosi, Lorenzo Cocco, Maaneli Derakhshani, Christopher Dorst, Joshua Eisenthal, Nina Emery, Veronica Gomez, Mara Harrell, Tyler Hildebrand, Christopher Hitchcock, Mario Hubert, Jenann Ismael, Marc Lange, Federico Laudisa, Dustin Lazarovici, Baptiste Le Bihan, Barry Loewer, Tim Maudlin, Giovanni Merlo, Kerry McKenzie, Jill North, Elias Okon, Ezra Rubenstein, David Schroeren, Charles Sebens, Ted Sider, Shelly Yiran Shi, Isaac Wilhelm, Ken Wharton, Christian Wüthrich, Nino Zanghì, audiences at California Institute of Technology, University of Geneva, Rutgers University, Metro Area Philosophers of Science, 2021 Annual Meeting of the California Quantum Interpretation Network, and participants in the graduate seminar “Rethinking Laws of Nature” at the University of California San Diego in spring 2021. EKC received research assistance from Shelly Yiran Shi and was supported by an Academic Senate Grant from the University of California San Diego.
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Chen, E.K., Goldstein, S. (2022). Governing Without a Fundamental Direction of Time: Minimal Primitivism About Laws of Nature. In: Ben-Menahem, Y. (eds) Rethinking the Concept of Law of Nature . Jerusalem Studies in Philosophy and History of Science. Springer, Cham. https://doi.org/10.1007/978-3-030-96775-8_2
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