The dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein's equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities (...) --qua part of a physical law-- highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature. (shrink)

Laws of nature have various roles in scientific practice. It is widely agreed that an adequate theory of lawhood ought to align with the roles that scientists assign to the laws. But philosophers disagree over whether Humean laws or non-Humean laws are better at filling these roles. In this paper, I provide an argument for settling this dispute. I consider possible situations in which scientists receive conclusive evidence that—according to the non-Humean—falsifies their beliefs about the laws, but which—according to the (...) Humean—does not falsify their beliefs about the laws. I argue that, in these possible scenarios, all law-related aspects of scientific practice would remain unchanged. In other words, scientists would treat the regularities “preferred” by the Humean as the laws of nature. On this basis, I conclude that non-Humean laws fail to align with scientific practice. (shrink)

Symposium review of Richard Healey, Gauging What’s Real: The Conceptual Foundations of Contemporary Gauge Theories. Oxford: Oxford University Press, 2007. Pp. 297. $99.00 HB.

In the recent philosophy of explanation, a growing attention to and discussion of non-causal explanations has emerged, as there seem to be compelling examples of non-causal explanations in the sciences, in pure mathematics, and in metaphysics. I defend the claim that the counterfactual theory of explanation (CTE) captures the explanatory character of both non-causal scientific and metaphysical explanations. According to the CTE, scientific and metaphysical explanations are explanatory by virtue of revealing counterfactual dependencies between the explanandum and the explanans. I (...) support this claim by illustrating that CTE is applicable to Euler’s explanation (an example of a non-causal scientific explanation) and Loewer’s explanation (an example of a non-causal metaphysical explanation). (shrink)

Humeans take reality to be devoid of ‘necessary connections’: things just happen. Laws of nature are to be understood in terms of what ‘just happens’, not vice versa. Here the Humean needs some conception of what it is that ‘just happens’ – a conception of the Humean mosaic. Lewis’s Humeanism incorporates such a conception in the form of a Lewis-style metaphysics of objects, properties, and modality. Newer versions of Humeanism about laws of nature, such as the Better Best Systems approach, (...) typically reject such a Lewisian metaphysics, but it remains unclear what they can offer in its place. By exploring different candidate conceptions, this paper sheds light on the limits of Humeanism about laws of nature: not all conceptions of the Humean mosaic form a suitable basis for a Humean theory of laws. In fact, only a metaphysics roughly in line with Lewis’s will do. The paper ends with a tentative generalization of this result, thus pointing to the ‘limit’ of Humeanism in general: taking the Humean way of thinking to its limit results in a rejection of the whole idea of such a mosaic – and hence of Humean mosaic-based accounts of anything. (shrink)

In this paper, I argue against John Beatty’s position in his paper “The Evolutionary Contingency Thesis” by counterexample. Beatty argues that there are no distinctly biological laws because the outcomes of the evolutionary processes are contingent. I argue that the heart of the Caspar–Klug theory of virus structure—that spherical virus capsids consist of 60T subunits (where T = k 2 + hk + h 2 and h and k are integers)—is a distinctly biological law even if the existence of spherical (...) viruses is evolutionarily contingent. (shrink)

Many philosophers argue that explanatoriness plays no special role in confirmation – that “inference to the best explanation” (IBE) incorrectly demands giving hypotheses extra credit for their potential explanatory qualities beyond the credit they already deserve for their predictive successes. This paper argues against one common strategy for responding to this thought – that is, for trying to fit IBE within a Bayesian framework. That strategy argues that a hypothesis’ explanatory quality (its “loveliness”) contributes either to its prior probability or (...) to its likelihood. This paper argues that this strategy fails because it must give different treatments to two hypotheses that are unlovely for the very same reason. The strategy therefore loses the insight into scientific reasoning that its reconstruction in terms of IBE is supposed to provide. The paper then provides a Bayesian account of the confirmatory role of explanatoriness that represents explanatory quality as having an impact in the same place for two hypotheses that are unlovely for the very same reason. This approach works by “putting explanation back into IBE” – that is, by invoking hypotheses that refer explicitly to scientific explanation and by invoking the agent's background opinions regarding the kind of explanation that the evidence is liable to have. On this approach, there is no list of “explanatory virtues” the possession of which always helps to make an explanation better. Rather, for different facts, there are different characteristics that our background knowledge of other explanations gives us some reason to expect the given fact's explanation to possess. (shrink)

One of the traditional desiderata for a metaphysical theory of laws of nature is that it be able to explain natural regularities. Some philosophers have postulated governing laws to fill this explanatory role. Recently, however, many have attempted to explain natural regularities without appealing to governing laws. Suppose that some fundamental properties are bare dispositions. In virtue of their dispositional nature, these properties must be (or are likely to be) distributed in regular patterns. Thus it would appear that an ontology (...) including bare dispositions can dispense with governing laws of nature. I believe that there is a problem with this line of reasoning. In this essay, I’ll argue that governing laws are indispensable for the explanation of a special sort of natural regularity: those holding among categorical properties (or, as I’ll call them, categorical regularities). This has the potential to be a serious objection to the denial of governing laws, since there may be good reasons to believe that observed regularities are categorical regularities. (shrink)

Humean accounts of laws of nature fail to distinguish between dynamic laws and static initial conditions. But this distinction plays a central role in scientific theorizing and explanation. I motivate the claim that this distinction should matter for the Humean, and show that current views lack the resources to explain it. I then develop a regularity theory that captures this distinction. My view takes empirical accessibility to be one of the primary features of laws, and I identify features laws must (...) have to be empirically accessible. I then argue that laws with these features tend to be dynamic. _1_ The Best System _1.1_ Orthodox Humeanism _2_ The Best Is Not Good Enough _2.1_ Laws and boundary conditions _2.2_ Laws and scientific practice _2.3_ An illustrative example _3_ Laws and Epistemic Roles _3.1_ The epistemic criterion _3.2_ The epistemic role account _3.3_ Scientific virtues _3.4_ Applying the epistemic role account _4_ Conclusion. (shrink)

Do the laws of nature supervene on ordinary, non-nomic matters of fact? Lange's criticism of Humean supervenience (HS) plays a key role in his account of natural laws. Though we are sympathetic to his account, we remain unconvinced by his criticism. We focus on his thought experiment involving a world containing nothing but a lone proton and argue that it does not cast sufficient doubt on HS. In addition, we express some concern about locating the lawmakers in an ontology of (...) primitive subjunctive facts and suggest that a 'mixed' metaphysics to the lawmaker question might be attractive. (shrink)

Given its importance in modern physics, philosophers of science have paid surprisingly little attention to the subject of symmetries and invariances, and they have largely neglected the subtopic of symmetry breaking. I illustrate how the topic of laws and symmetries brings into fruitful interaction technical issues in physics and mathematics with both methodological issues in philosophy of science, such as the status of laws of physics, and metaphysical issues, such as the nature of objectivity.

Perhaps the most significant contemporary theory of lawhood is the Best System (/MRL) view on which laws are true generalizations that best systematize knowledge. Our question in this paper will be how best to formulate a theory of this kind. We’ll argue that an acceptable MRL should (i) avoid inter-system comparisons of simplicity, strength, and balance, (ii) make lawhood epistemically accessible, and (iii) allow for laws in the special sciences. Attention to these problems will bring into focus a useful menu (...) of novel MRL theories, some of which solve problems the original MRL theory could not. Hence we conceive of the paper as moving toward a better Best System theory of laws. (shrink)

David Lewis’s ‘Humean Supervenience’ (henceforth ‘HS’) combines realism about laws, chances, and dispositions with a sparse ontology according to which everything supervenes on the overall spatiotemporal distribution of non-dispositional properties (Lewis 1986a, Philosophical papers: Volume II, pp. ix–xvii, New York: Oxford Univesity Press, 1994, Mind 103:473–490). HS faces a serious problem—a “big bad bug” (Lewis 1986a, p. xiv): it contradicts the Principal Principle, a seemingly obvious norm of rational credence. Two authors have tried to rescue Lewis’s ontology from the ‘big (...) bad bug’ (henceforth ‘the Bug’) by rejecting realism about laws, chances, and dispositions (Halpin 1994, Aust J Phil 72:317–338, 1998, Phil Sci 65:349–360; Ward 2005, Phil Sci 71:241–261). I will argue that this strategy cannot possibly work: it is the ontology, not the realist thesis, that lies at the root of the problem. (shrink)

An important part of the influential Humean doctrine in philosophy is the supervenience principle (sometimes referred to as the principle of separability). This principle asserts that the complete state of the world supervenes on the intrinsic properties of its most fundamental components and their spatiotemporal relations (the so-called Humean mosaic). There are well-known arguments in the literature purporting to show that in quantum mechanics the Humean supervenience principle is violated, due to the existence of entangled states. Recently, however, arguments have (...) been presented to the effect that the supervenience principle can be defended in Bohmian mechanics. The key element of this strategy lies in the observation that according to Bohmian mechanics the fundamental facts about particles are facts about their spatial locations, and moreover, for any proper subsystem of the world its state may non-trivially depend on the spatial configuration of the rest of the universe. Thus quantum-mechanical states of subsystems do not represent their intrinsic properties but rather characterize their relations with the environment. In this paper we point out the worry that this Bohmian strategy --known as Bohumianism-- saves the letter but not the spirit of the Humean doctrine of supervenience, since it prima facie violates another seemingly important Humean principle, which we call Strong Supervenience and whose denial implies the existence of necessary connections among distinct individuals. We argue that the best defense for Bohumians is to question the fundamental existence of complex physical systems and their states by treating any reference to them as a convenient description of the underlying collection of Bohmian particles. We consider several pros and cons of this strategy. (shrink)

Humeanism about laws of nature is, roughly, the view that the laws of nature are just patterns, or ways of describing patterns, in the mosaic of events. In this paper I survey some of the (many!) objections that have been raised to Humeanism, considering how the Humean might respond. And I consider how we might make a positive case for Humeanism. The common thread running through all this is that the viability of the Humean view relies on the Humean having (...) an importantly different conception of explanation to the anti-Humean. (shrink)

Some patterns call out for explanation, in the sense that we have a pro tanto reason to reject theories that do not give them an appropriate explanation. I argue that certain modal patterns call out for explanation in this way—and this provides a reason to reject certain theories of modality that fail to explain such patterns. However, I also consider a response to this argument, which claims that the modal patterns do not need explanation. This response might be viable but (...) it involves some substantial commitments about the nature of explanation. (shrink)

Despite its apparent complexity, our world seems to be governed by simple laws of physics. This volume provides a philosophical introduction to such laws. I explain how they are connected to some of the central issues in philosophy, such as ontology, possibility, explanation, induction, counterfactuals, time, determinism, and fundamentality. I suggest that laws are fundamental facts that govern the world by constraining its physical possibilities. I examine three hallmarks of laws--simplicity, exactness, and objectivity--and discuss whether and how they may be (...) associated with laws of physics. (shrink)

I argue against the claim, advanced by David Albert and Barry Loewer, that all non-fundamental laws can be derived from those required to underwrite the second law of thermodynamics.

Humeanism about laws of nature — the view that the laws reduce to the Humean mosaic — is a popular view, but currently existing versions face powerful objections. The non-supervenience objection, the non-fundamentality objection and the explanatory circularity objection have all been thought to cause problems for the Humean. However, these objections share a guiding thought — they are all based on the idea that there is a certain kind of divergence between the practice of science and the metaphysical picture (...) suggested by Humeanism. -/- I suggest that the Humean can respond to these objections not by rejecting this divergence, but by arguing that is appropriate. In particular the Humean can, in the spirit of Loewer (2012), distinguish between scientific and metaphysical explanation — this is motivated by differing aims of explanation in science and metaphysics. And they can further leverage this into distinctions between scientific and metaphysical fundamentality and scientific and metaphysical possibility. We can use these distinctions to respond to the objections that the Humean faces. (shrink)

We argue that the truth of determinism is not an interpretation-free fact and we systematically overview relevant interpretational choices that are less known in the philosophical literature. After bypassing the well known interpretational problem that arises in quantum mechanics we identify three further questions about the representational role of the mathematical structures employed by physical theories. Finally we point out that even if we settle all representational issues the received view of physical possibility may also allow the truth of determinism (...) to depend on prior philosophical convictions, notably on one's philosophical account of the nature of laws. (shrink)

On April 1, 2016, at the Annual Meeting of the Pacific Division of the American Philosophical Association, a book symposium, organized by Alyssa Ney, was held in honor of David Albert’s After Physics. All participants agreed that it was a valuable and enlightening session. We have decided that it would be useful, for those who weren’t present, to make our remarks publicly available. Please bear in mind that what follows are remarks prepared for the session, and that on some points (...) participants may have changed their minds in light of the ensuing discussion. (shrink)