Abstract
Among the most important questions in the metaphysics of science are “What are the natures of fundamental laws and chances?” and “What grounds the direction of time?” My aim in this paper is to examine some connections between these questions, discuss two approaches to answering them and argue in favor of one. Along the way I will raise and comment on a number of issues concerning the relationship between physics and metaphysics and consequences for the subject matter and methodology of metaphysics.
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Notes
“Humeanism” regarding laws and chances has no commitment to Hume’s theory of impressions and ideas, his epistemology, or his account of meaning. Where it agrees with the historical Hume as he has been usually understood is in its denial of fundamental necessary connections in nature and in its reductionism regarding laws and causation.
Lewis thinks of Humean Supervenience as a contingent doctrine that may be true of our world. In 1984 he worried that quantum theory is incompatible with HS due to quantum entanglement and he was right to worry. See Lewis (1986), Maudlin (2007) and Loewer (1996a, b, 2007b). However there are modifications that save the basic Humean idea of no necessary connections between distinct existences and the BSA account of laws and chances (Loewer 1996a, b).
The other main metaphysical issues regarding time are between tense and non-tense theories of time (between A-theorists and B theorists) and the issues between so called presentists, growing block theorists, and eternalists. Positions on each of these issues are closely connected to positions on others and in particular with views about the direction of time. Tense theorists take the distinction between past and future as grounded in tensed facts the growing block theory has a built in direction. As will be clear Maudlin’s view makes no appeal to tensed facts or growing blocks.
An M-law has no location in space–time although it governs events in space time and Maudlin has suggested that it is possible that different laws operate in different regions of space–time.
Maudlin says “I find that I am strongly inclined to a view that strikes many of my colleagues as lunacy. I believe that it is a fundamental, irreducible fact about the spatio-temporal structure of the world that time passes.” The view doesn’t strike me as lunatic or unprecedented or even unpopular among philosophers. But, I will argue it is obscure and unexplanatory.
Scholium to Definition 8 of the Principia in Newton (1999).
Although Maudlin isn’t averse to speaking of the rate at which time passes—he says it is “one second per second” he doesn’t literally propose that time is flowing relative to some super time and talk of its rate plays no role in his account.
Some philosophers who speak of time flowing/passing hold that so called “tensed-facts” are fundamental and irreducible to tenseless facts. This is not merely a claim about the irreducibility of tensed propositions to tenseless propositions but the stronger claim that the a fact expressed by a true tensed statement relative to its context fails to supervene on the totality of tenseless facts. The picture that often goes along with this view is that of a moving Now that travels up a tree of possibilities fixing the past as it goes. This is not what Maudlin has in mind when he speaks of time passing. As far as I can tell his view is compatible with a 4-dimensionalist conception of space–time and with the reducibility of tensed statements.
In a relativistic space–time points that lie outside of the light cones of a point are neither in that point’s future nor in its past.
Lewis’ version of the BSA assumes that the language in which candidates for Best System are formulation in a language whose simple predicates/terms denote perfectly natural properties and quantities. He also assumes that in the actual world all fundamental properties are instantiated at points or by point size entities (or fields that have values at points) and that the only fundamental relations are geometrical. As mentioned earlier (footnote 3) HS as Lewis characterizes it is unacceptable in view of quantum entanglement (Maudlin 2007). In Loewer (2007b) I explore the possibility of formulating the BSA without presupposing metaphysically given perfectly natural properties and without assuming that the fundamental properties are categorical.
Lewis says “Take all deductive systems whose theorems are true. Some are simpler better systematized than others. Some are stronger, more informative than others. These virtues compete: An uninformative system can be very simple; an unsystematized compendium of miscellaneous information can be very informative. The best system is the one that strikes as good a balance as truth will allow between simplicity and strength. How good a balance that is will depend on how kind nature is. A regularity is a law iff it is a theorem of the best system.” (1994, p. 478) Lewis imposes the requirement that the candidates for best systematization are formulated in the language of perfectly natural properties in response to a worry that without some such restriction the best system account collapses. In (Loewer 2007b) I argue that the BSA can be formulated without assuming a metaphysically prior category of properties.
This is a rather crude measure since any sentence excludes infinitely many worlds and so only sentences related by entailment can be compared.
Weinberg (1992). It is important to keep in mind that candidates for Best Theory systematize all the fundamental truths not the empirical truths. And if our world does have a best theory, and even if scientists manage to formulate it, it is plausible that they won’t know it is the true theory since it is plausible that there are other empirically equivalent (but false) theories that seem to equally well satisfy all the scientific virtues.
Though there are “fall back” Humean positions should the world fail to have a best theory. If there are ties laws could be identified as generalizations that belong to all best theories or laws could be indexed by best theories.
Lewis says “Consider deductive systems that pertain not only to what happens in history, but also to what the chances are of various outcomes in various situations - for instance the decay probabilities for atoms of various isotopes. Require these systems to be true in what they say about history….Require also that these systems aren't in the business of guessing the outcomes of what, by their own lights, are chance events; they never say that A without also saying that A never had any chance of not coming about” (1994, p. 480). Lewis proposes evaluating the informativeness of a probabilistic theory in terms of the “fit” of the world on the theory i.e. the likelihood of the world on the theory. This is problematic since it is plausible that the likelihood of the actual world on any plausible candidate theory is infinitesimal. See Elga (2004) and Loewer (2001) for some discussion of this point.
Lewis’ also assumes that the actual world conforms to a thesis he calls “Humean Supervenience.” HS says that the natural properties of our world are instantiated at points of space–time or by point size entities and that the only natural relations are geometrical. The existence of so-called “quantum entangled states” seems incompatible with HS (Loewer 1996b; Maudlin 2007). Fortunately, BSA can be developed without assuming HS (Loewer 2007b).
The entropy of a macro condition M is given by S B (M(X)) = k log |Γ M | where |Γ M | is the volume (on the measure) in Γ associated with the macro state M, and k is Boltzmann's constant. S B provides a relative measure of the amount of Γ corresponding to each M. Given a partition into macro states the entropy of a micro state relative to this partition is the entropy of the macro state which it realizes.
So the second law should not have been stated in the first place as an absolute prohibition on the entropy of a system decreasing but rather as being enormously unlikely.
If the Boltzmann probability posit is applied to the macro condition of the universe at t since it implies that it is likely that this macro condition arose out higher entropy states and in particular this means that the “records” in books etc. likely arose out of chaos and not as accurate recording of previous events. This undermines the claim that there is evidence reported in those books that support the truth of the dynamical laws and so results in an unstable epistemological situation.
Also, the prescription will prescribe incompatible probabilities at different times since the uniform distribution over the macro state at t will differ from the uniform distribution over the macro state at other times.
See Sklar (1995) for a discussion of some proposals for responding to the reversibility paradox.
Although there are issues concerning how to think of entropy in the very early universe it is generally held that cosmology supports the claim that right after the big bang the entropy of the universe was very tiny. This may strike one as counterintuitive since at the big bang the universe was enormously tiny and dense with matter/energy uniformly distributed in space. But because gravitation acts to clump matter this is a very low entropy condition. For a discussion see Callender (2011), Penrose (2004), Greene (2004), Carroll (2010).
This idea isn’t original with Albert. For example, it is explicit in a lecture by Feynman (1994).
While the account is developed on the assumption of a classical mechanics ontology of particles and deterministic dynamical laws pretty much the same considerations carry over to deterministic versions of quantum mechanics (e.g. Bohmian mechanics, and Everettian QM). If the dynamical laws are probabilistic (as on GRW theory) then while the initial probability distribution no longer needs to be part of the account although the past hypothesis still plays the role it plays in the account that I sketch. See Albert (2000) for a discussion.
Maudlin suggested in discussion that if the uniform probability distribution accomplishes all Albert claims for it then infinitely many other distributions will do as well. This may be so. If so and if probabilities are understood objectively in the way I discuss later then there may be empirical discernable differences among these distributions or it may be a case of massive under determination. It is reasonable to posit the uniform distribution since it is the simplest until evidence is adduced against it.
The name “Mentaculus” comes from the Coen brothers’ movie “Serious Man” in which a character is working on “the probability map of the universe” which he calls “the Mentaculus.”
It is thought that the length of time it would take for entropy to increase to equilibrium is far greater that the approximately 14 billion years that have passed since the Big Bang.
See Albert (2000) for a discussion of how a Maxwell demon may prepare a system so that its entropy likely decreases.
Popper and Lewis both seem to agree that if determinism is true then there are no chances different from 0 and 1. “…if classical physics is deterministic, it must be incompatible with an objective interpretation of classical statistical mechanics” Popper, Quantum Theory and the Schism in Physics (Popper 1992). “To the question of how chance can be reconciled with determinism….my answer is it can’t be done….There is no chance without chance. If our world is deterministic there is no chance in save chances of zero and one. Likewise if our world somehow contains deterministic enclaves, there are no chances in those enclaves”. Lewis in Postscript to “A Subjectivist’s Guide to Objective Chance” (Lewis 1986). In Loewer (2001) I argue that Lewis was wrong about his own account.
I am not claiming that the Mentaculus requires a Lewisian or Humean account of laws. Its truth is compatible with non-Humean accounts and even with Maudlin’s account.
For example Woodward (2003).
There is a very nice discussion of these points as regards our intuitions about time’s passage in a paper by Paul (2010).
Van Frassen (1989) urges an objection like this against a non-Humean account.
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Loewer, B. Two accounts of laws and time. Philos Stud 160, 115–137 (2012). https://doi.org/10.1007/s11098-012-9911-x
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DOI: https://doi.org/10.1007/s11098-012-9911-x