aa r X i v : . [ phy s i c s . h i s t - ph ] J u l How Humean is Bohumianism?
Tomasz BigajUniversity of Warsaw, Institute of PhilosophyKrakowskie Przedmieście 300-927 WarsawAntonio VassalloInternational Center for Formal OntologyFaculty of Administration and Social SciencesWarsaw University of TechnologyPlac Politechniki 100-661 Warsaw
Accepted for publication in
Foundations of Physics
Abstract
An important part of the influential Humean doctrine in philoso-phy is the supervenience principle (sometimes referred to as the prin-ciple of separability). This principle asserts that the complete stateof the world supervenes on the intrinsic properties of its most funda-mental components and their spatiotemporal relations (the so-calledHumean mosaic). There are well-known arguments in the literaturepurporting to show that in quantum mechanics the Humean superve-nience principle is violated, due to the existence of entangled states.Recently, however, arguments have been presented to the effect thatthe supervenience principle can be defended in Bohmian mechanics.The key element of this strategy lies in the observation that accordingto Bohmian mechanics the fundamental facts about particles are factsabout their spatial locations, and moreover, for any proper subsystem f the world its state may non-trivially depend on the spatial config-uration of the rest of the universe. Thus quantum-mechanical statesof subsystems do not represent their intrinsic properties but rathercharacterize their relations with the environment. In this paper wepoint out the worry that this Bohmian strategy –known as Bohumi-anism – saves the letter but not the spirit of the Humean doctrine ofsupervenience, since it prima facie violates another seemingly impor-tant Humean principle, which we call
Strong Supervenience and whosedenial implies the existence of necessary connections among distinctindividuals. We argue that the best defense for Bohumians is to ques-tion the fundamental existence of complex physical systems and theirstates by treating any reference to them as a convenient descriptionof the underlying collection of Bohmian particles. We consider severalpros and cons of this strategy.
Keywords : Humean supervenience; quantum entanglement; Bohmianmechanics; Bohumianism
The main purpose of this paper is to critically evaluate the latest attemptsto reconcile modern developments in quantum physics with the broad philo-sophical doctrine of Humeanism. It is no secret that the worldview emerg-ing from quantum mechanics turns out to be rather hostile to many vener-ated philosophical views, such as for instance determinism. The doctrine ofHumeanism, with its insistence on separability, non-modality and reduction-ism, seems to be another prime target for an assault inspired by quantumdiscoveries. And yet, given the persistent popularity of Humeanism amongcontemporary philosophers of science, no wonder that this assault is met withpowerful resistance. One recent episode in an ongoing battle between variousphilosophical approaches to quantum mechanics started out with a vigorousattack on Humeanism at the hands of Tim Maudlin in his provocativelytitled piece “Why be Humean?” (Maudlin, 2007). It didn’t take long be-fore defenders of the “greatest denier of necessary connections” responded tothis challenge in various ways. A particularly interesting response has beenbased on a popular in philosophical circles interpretation of quantum me-chanics known as Bohmian mechanics (Miller, 2014; Esfeld, 2014; Callender,2015; Bhogal and Perry, 2017). In our contribution to this debate we will tryto identify some weak points of this strategy, and we will suggest, on behalfof the Bohmians, how to strengthen their defensive position.The plan of this article is as follows. Section 2 is mainly expository, de-2oted to the presentation of the main assumptions and arguments in Maudlin’soriginal polemic with Humeanism, as well as the general strategy of de-fense against Maudlin’s attack. Here we will introduce two pillars of theHumean doctrine: the rejection of modal facts and the elimination of nec-essary connections between separate entities, and we will present the well-known Humean principles of Physical Statism and Separability. Reconstruct-ing Maudlin’s criticism of Separability based on the example of entangledstates (singlet- and triplet-spin states), we will formulate an equivalent ver-sion of Separability that we call Supervenience, and we will show, followingElizabeth Miller, how Supervenience can be defended by denying that thesinglet and triplet-states are intrinsic to the quantum systems. In section3 we will explore the physical details of Bohmian mechanics relevant to theabove-mentioned strategy of defending Humeanism. We will stress the nomo-logical character of the universal wave function (interpreted according to theBest System approach), and we will introduce the concept of an effectivewave function that enables us to make a distinction between physical sys-tems and their environments while still admitting that the states of thesesystems are not intrinsic to them.Section 4 is central to the article. In it we present our main critique ofthe Bohmian defense of Humeanism, which is that Separability (or Superve-nience) by itself does not guarantee that no necessary connections betweenseparate entities will be present. Supervenience ensures the lack of necessaryconnections between fundamental objects, but does not exclude the possi-bility that these connections may emerge at higher levels of complexity. Toclarify this further, we spell out the conditions of Strong Supervenience andBinary Separability that in our opinion should constitute parts of the broaderHumean doctrine, and we argue that Bohmian mechanics refutes them. Insection 5 we discuss one possible way for Bohmians to continue their commit-ment to Humeanism by denying the objective existence of complex entitieson a par with fundamental objects. We explain why this move does not im-ply that objects of our experiences are mere illusions or arbitrary constructs.We end the article with a suggestion for Bohmians to bite the bullet and go“Democritean”, i.e. accept that only fundamental particles (“atoms”) existin the most literal sense of the word.
The modern version of Humeanism is based on two intuitions, both of whichcan be traced back to David Hume himself. One of them is skepticism regard-ing irreducible modal facts: facts involving necessity, possibility, dispositions,3owers, counterfactuals etc. The other intuition suggests that there can beno necessary connections between separate entities. The first intuition canbe expressed in the statement that all facts about the world are exhaustedin its total state that tells us what the world is , as opposed to what it could ,or would , or ought to be. All purported modal facts, encompassed for in-stance in laws or tendencies or dispositions or whatever, are to be ultimatelyreducible to the total state of the world (in the sense that there could beno difference in modal facts without the underlying difference in the totalstate).The non-existence of necessary connections between separate individualsgives us more insight into the internal composition of the total state of theworld according to Humeanism. Roughly speaking, the state of the worldshould be decomposable into the states of separate individuals plus their spa-tiotemporal arrangements. The so-called Humean mosaic, consisting of theassignment of intrinsic, natural and non-modal properties to individual ob-jects, together with the spatiotemporal arrangement of these objects, shouldbe sufficient to fix the state of the entire world. Admitting any facts beyondwhat is included in the Humean mosaic would amount to the acceptanceof fundamental correlations between distinct entities that are not reducibleto their intrinsic properties and spatiotemporal relations, and hence wouldinfringe the second Humean intuition.Tim Maudlin’s verbalization of Lewis’s variant of Humeanism has becomethe gold standard in the literature. He spells out two principles he calls Physical Statism and
Separability as follows (Maudlin, 2007, p. 51):(Physical Statism) All facts about a world, including modal andnomological facts, are determined by its total physical state.(Separability) The complete physical state of the world is de-termined by (supervenes on) the intrinsic physical state of eachspacetime point (or each point-like object) and the spatiotempo-ral relations between those points.As Bhogal and Perry (2017, p. 74) point out, Physical Statism and Sep-arability jointly imply that the world is fundamentally non-modal, and thatthere are no necessary connections at the fundamental level. The last suppo-sition is secured by Separability, since Separability ensures that fundamental We are not claiming that these two intuitions are independent from one another. Inparticular, it may be argued that rejecting irreducible modal facts, as per the first intuition,eliminates necessary connections between distinct entities. On the other hand, it is at leastfeasible to reject irreducible modal facts as parts of the world, and still insist that there aresome necessary connections which present themselves in the fact that certain combinationsof fundamental, non-modal properties are not admissible. intrinsic property. From this assumption we can now derive that the We do not wish to enter the intricate debate on the exact meaning of “intrinsic prop-erties”. For our purposes it is sufficient to accept the following partial characteristic: if anintrinsic property of a system X supervenes on any property of an object Y , Y has to bea spatiotemporal part of X . any properties of the fundamental elements of the world(whether or not these elements are parts of the considered system) and theirspatiotemporal arrangements. And because the total state of the world mustcontain the states of its components, Separability is violated.Proceeding slightly more formally, we can first introduce a new principlethat can be simply called Supervenience :(Supervenience) For any physical system S , the intrinsic prop-erties of S supervene on the intrinsic physical states and spa-tiotemporal relations between points and pointlike objects thatare parts of S . Given some reasonable assumptions, it can be proven that Supervenienceis in fact equivalent to Separability. Because trivially all the properties ofthe entire world are intrinsic to it, Separability follows from Supervenience(if we assume that the world constitutes a physical system, which seemsplausible). The entailment in the opposite direction can be shown as follows.If Supervenience were false, some intrinsic properties of a particular system S would not supervene on the Humean mosaic of fundamental, point-likeobjects that are parts of S . But intrinsic properties of system S cannotdepend on any object spatiotemporally external from S , hence the intrinsicproperties of S do not supervene on the fundamental properties of point-likeobjects at all. Provided that the intrinsic properties of any physical systemare parts of the total state of the world, this means that Separability is false.It is clear that the example of the singlet and triplet states directly vi-olates Supervenience, if only these states qualify as intrinsic properties ofappropriate systems. But here one escape route immediately opens up. Wecan namely attempt to save Supervenience (and Separability) by denyingthat the singlet and triplet states represent genuine intrinsic properties ofphysical systems. This is precisely the strategy adopted by Miller in herattempt to defend Humeanism against Maudlin’s argument. If we can arguethat the singlet or triplet states of a system of two particles depend non-trivially on the properties of objects extrinsic from this system, Maudlin’sargument can be repelled. Miller calls the negation of Supervenience
Metaphysical holism (Miller, 2014, p. 568). Another strategy of how to deal with Maudlin’s challenge to Humeanism has beenconsidered by George Darby (Darby, 2012). The idea is roughly to include in the superve-nience basis irreducible relations between particles occupying the singlet or triplet state,
6n order to provide a philosophically clear discussion of this strategy,we will focus on the so-called “primitive ontology” approach to quantumphysics (see Allori et al., 2008, for a technical discussion of the framework),In particular, we will follow Miller in framing the discussion in the contextof non-relativistic Bohmian mechanics. Bohmian mechanics, in rough outline, is based on the assumption that theworld consists of fundamental particles which have well-defined trajectories.The modern version of the theory, as set out in Dürr et al. (2013), is in factthe simplest non-local Galilean-invariant theory of N moving particles. Thedynamics of the theory is given by: i ~ ∂∂t Ψ( Q , t ) = ˆ H Ψ( Q , t ); (1a) d Q dt = ~ m − Im h Ψ , ∇ Ψ ih Ψ , Ψ i ( Q , t ) . (1b) Q = q · · · q N ∈ R N represents an instantaneous configuration of N parti-cles, ∇ = ∇ · · · ∇ N is the “gradient vector”, m is the N × N diagonal “massmatrix” { δ ij m i } , and h· , ·i is an appropriate inner product defined over thespace of wave functions. thus expanding the Humean mosaic. Darby claims that this move saves the reductive spiritof Humeanism, but he himself admits that some form of holism has to be accepted, whichmay be seen as departing from the Humean idea that everything that is is the local mat-ters of particular fact. To that we would like to add that admitting irreducible, externalrelations between distinct individuals violates the intuition of no necessary connections.Clearly, the holding of the relation of anticorrelation between electrons in the singlet spinstate implies that there is a necessary connection between the values of the spin of bothelectrons. We stress the fact that here we are adopting a primitive ontology approach just as aworking hypothesis that lets us exemplify the issues at stake, being fully aware that noteverybody would agree with this choice (see Ney and Philips, 2013, for a critical discussionof the primitive ontology approach). The roots of the theory can be traced back to the work of Louis de Broglie (seede Broglie, 1928).
7o sum up, (1b) is a concise way to write N coupled equations of theform: d q k dt = ~ m k Im h Ψ , ∇ k Ψ ih Ψ , Ψ i ( Q , t ) . (2)Formally, (1b) depicts a vector field on R N depending on Ψ, whose inte-gral curves Q = Q ( t ) can each be “unpacked” as collections of N continuoustrajectories { q i = q i ( t ) } i =1 ,...,N . The dynamics encoded in (1) is determin-istic: once provided a set of initial conditions (Ψ , Q ) at a fixed time t , thedynamics singles out a unique dynamical evolution at earlier and later times.Moreover, it can be shown that (1) recovers Born’s rule of standard quantummechanics, thus matching all the empirical predictions of this latter theory(Dürr et al., 1992, provide a detailed justification of this claim).The above formalism establishes that Bohmian mechanics is a theory of N point-like particles with definite positions q k = ( x k , y k , z k ) in Euclidean3-space at all times. The non-locality of the theory is evident in (2), thevelocity of the k -th particle particle being instantaneously dependent on thepositions of all the other N − any type of wave function, includingspinor states (of which singlet/triplet states represent a particular case).Put in these terms, a natural interpretation of the wave function as alaw-like element of the formalism suggests itself. To see this, we can fol-low (as people like Miller and Esfeld do) the well-trodden path taken bymany Humeans with respect to the laws of nature. According to the BestSystem Approach (known also as the Mill-Ramsey-Lewis theory) laws areaxioms systematizing our knowledge of individual facts that achieve the bestbalance between strength and simplicity (see Hall, 2015, for an exhaustive in-troduction to the subject). In other words, laws ultimately supervene on thecollection of individual facts. In the same vein, the universal wave functioncan be treated as a law that gives us the best description of the behaviorof individual particles. In this sense, the Humean treatment of quantum People like David Albert (see, e.g., Albert, 1996) would deny the need for this last step.For them, the real dynamics literally unfolds in a higher dimensional space, where a single“world-particle” is pushed around by a “Ψ-field”. We will not consider this controversialreading of (1) here. However, see Dewar (2018) for a recent critique of the Best System approach toBohmian mechanics. We do not wish to take a stand on whether this critique is se-rious enough to undermine Bohumianism independently of our objections developed in over time and their mutual spatiotem-poral relations, of which the wave function (or, say, the Hamiltonian, in theclassical case) represent just (a part of) the simplest and most informativedescription. In this context, all the physical properties usually encoded inthe wave function can be reduced to the mutual arrangement of particlesthroughout the entire history of the universe, spin being one of such proper-ties. It is important to stress the fact that this story makes sense becauseBohmian mechanics by construction accords a metaphysically privileged sta-tus to positions , otherwise one could wonder why, among the many physicallypossible bases onto which the quantum state could be projected, we just focuson the position basis. Hence, if we adopt this perspective, then the entangle-ment encoded in the wave function does not represent anymore a threat to aHumean reading of Bohmian mechanics. In fact, it seems that Bohmianismmay be argued to satisfy Separability. To emphasize the Humean characterof Bohmian mechanics, Miller even coins the term “Bohumianism”.It is enlightening to see how Bohumianism concretely defuses Maudlin’schallenge. Let’s start from the trivial case in which the two-particle system isall there is to the world. In this case, the mosaic would be too meager to bedescribable in terms of singlet/triplet states. Particles’ relative motion mightinstead allow for, e.g., a description in terms of simple Coulomb interactions.In this case, Maudlin’s challenge is dodged rather than defused. The mostinteresting case involves, of course, the actual world.The first question to be answered, then, is how Bohmian mechanics is ableto describe the behavior of our pair of entangled particles, given that theyrepresent just a small portion of the universal N -particle configuration. Let’scall q the two-particle subsystem and Q the rest of the configuration. Clearly,( q , Q ) = Q . Now, in general there is no physically interesting case in whichthe universal wave function Ψ can be written as a simple product state ofthe form Ψ( Q ) = ψ ( q ) φ ( Q ). However, there are more physically interestingcases in which it can be written as Ψ( Q ) = ψ ( q ) φ ( Q ) + Ψ ⊥ ( Q ) and the section 4. Standard Humeans would add some natural intrinsic properties, such as mass andcharge, on top of positions. However, it is now clear that nothing over and above particles’(relative) positions and change thereof is needed in order to make sense of the Humeanapproach to laws of physics. See Esfeld et al. (2018) for a presentation of this “Super-Humean” stance. Such a construction is not immune to criticism. For example, Matarese (2018), ar-gues that purging the mosaic of all natural properties makes it impossible to establishwhich description among the many possible is in fact the simplest and most informative.Simpson (2019), goes as far as arguing that a mosaic consisting only of material particles’trajectories is untenable. ⊥ ( Q ) remains empty throughout the dynamical evolution (i.e.it never gets to “guide” any particle). This happens when the followingconditions are met:1. ψφ and Ψ ⊥ do not substantially overlap in configuration space.2. Q always lies in a region of configuration space where Ψ ⊥ is close tozero but φ is not.In this case, we recover the orthodox picture in which system and envi-ronment are assigned an effective wave function, ψ and φ respectively, eachof which is subjected to a Schrödinger-like dynamics. From this point on, wecan give the standard quantum description of ψ ( q ) and φ ( Q ) in terms of a“subsystem” and its “environment” (see, Dürr et al. (1992), section 5, for afar more rigorous presentation of this topic).The above story makes it manifest why there is strictly speaking nothingin the effective wave function ψ that is intrinsic to the two-particle system.Indeed, ψ is just the tip of the iceberg of a more complex description involvingalso the particles in the environment. In other words, we say that the two-particle subsystem is in a singlet or triplet state just in virtue of how thetrajectories of the two particles are related to those of the particles makingup, say, a Stern-Gerlach apparatus. In this sense, the appropriate ontologicalpicture is not that of an initially isolated subsystem that gets mixed withthe environment as a result of the dynamical evolution but, rather, that ofa global mosaic of trajectories to which we attach a simple and informativedescription in terms of subsystem/environment. The important point is thatall the relevant information to account for, say, the detection of a two-particlesystem in a singlet or triplet state is crafted, so to speak, in the mosaic:nothing more is needed. In this sense, there is no question whether quantumphysics is compatible with Humeanism.Does all of this mean that Humeanism is fully vindicated in Bohmianmechanics? Well, not so fast! The key point of our critique of the above-described strategy is the obser-vation that while Separability reflects strong Humean sentiments, it by nomeans exhausts the entire Humean doctrine, as encompassed in the two basic The reader interested in nonstandard approaches to quantum measurements (espe-cially those dispensing with decoherence), can take a look at, e.g., Drossel and Ellis (2018). P is an intrinsic property of S , then P supervenes onthe properties and spatiotemporal relations of S ’s parts. But what if S hasno interesting intrinsic properties (i.e. its physical state turns out to be anextrinsic property)? Then the conditional is true, but its truth follows simplyfrom the falsity of the antecedent. There is no genuine supervenience here,because there is no property to which the supervenience could be attributedin the first place.The distinction we’ve made immediately suggests a natural strengthen-ing of the Supervenience principle: rather than limiting the supervenienceproperty to the intrinsic features of physical systems, we may extend it toall their physical states. Thus a stronger Supervenience presents itself:(Strong Supervenience) For any physical system S , the completephysical state of S supervenes on the intrinsic physical statesand spatiotemporal relations between points and pointlike objectsthat are parts of S . It should be noted that the only difference between Strong Supervenienceand Supervenience is that the former drops the condition of intrinsicalitywith respect to the complete physical state of S . However, this differencehas some dramatic consequences. In particular, Bohmian mechanics vio-lates Strong Supervenience, since the singlet/triplet states of two electronsdo not supervene on the properties of the individual electrons and their spa-tiotemporal arrangements, as we have explained in the previous section. Butis Strong Supervenience a necessary part of any Humean doctrine? Can aHumean accept a situation in which the total physical state of a systemcontains an irreducible reference to objects spatiotemporally separated fromthis system? We believe not, since such a scenario clearly flies in the faceof the second Humean intuition regarding the lack of necessary connectionsbetween separate entities. It seems that a committed Humean should sub- Bhogal and Perry (2017) call this principle
Strong Separability . Binary Separability ,which entails Strong Supervenience:(Binary Separability) For any physical system S equipped withits own physical state, the complete state of the world super-venes on the intrinsic properties of S , intrinsic properties of itsenvironment E , and the spatiotemporal relations between S and E .According to Separability, the supervenience basis for the total state ofthe world consists of the most fundamental elements of reality (points orpoint-like objects). Binary Separability, on the other hand, insists that a su-pervenience basis can be also found on non-fundamental levels. This strongerprinciple ensures that each time when we identify a physical system that isa proper part of the world (but does not have to be a simple element withno further proper parts), we can split the state of the world into two compo-nents: one that is associated with the selected system, and the other charac-terizing its environment (plus the requisite spatiotemporal relations betweenthe two). In other words, physical systems do not enter into any relationswith their environments that would not be already included in their intrinsicproperties plus spatiotemporal arrangements.That Binary Separability implies Strong Supervenience can be proven asfollows. First, we can observe that Binary Separability implies Separability,since Binary Separability can be applied to fundamental systems (points orpoint-like objects), which proves that these systems and their intrinsic statesbelong to the supervenience basis for the entire world. Next, assume thatBinary Separability is true and take any physical system S . Since the physicalstate of S is part of the total state of the universe, by Separability it mustsupervene on the Humean mosaic of fundamental objects and properties.But if the state of S supervened on fundamental objects that are not partsof S , this would violate Binary Separability, since the state of S would nolonger be an intrinsic property of S . Thus Strong Supervenience has to betrue as well. Hence, if we can argue that Humeans should accept BinarySeparability, they should also commit themselves to Strong Supervenience.In order to help the reader keep track of the logical relations amongthe array of metaphysical claims introduced and discussed in this paper, wepresent the following diagram of mutual logical dependencies among theseclaims, where arrows indicate the relation of logical entailment:Binary Separability Strong SupervenienceSeparability Supervenience12ur assertion is that the committed Humean should accept Binary Separabil-ity and thus all the remaining theses as well. However, even though Bohmianmechanics is compatible with Separability and Supervenience, it violates Bi-nary Separability and Strong Supervenience, which poses a challenge to theBohmians who want to subscribe to Humeanism.Why isn’t simple Separability enough for a Humean? Why do we need astronger assumption regarding the supervenience of the whole on its parts?One reason may be the intuition that the relation of supervenience should“mesh” naturally with the intuitive mereological structure of the world. Suppose that Binary Separability is false while Separability remains true.This means that the supervenience basis for the entire Humean mosaic forthe world consisting of the fundamental objects and their properties cannotbe divided up into the smaller supervenience bases for the objects composedof the corresponding elements of the fundamental mosaic. Let us choosea subset P of the set of all fundamental (point-like) objects that composea particular physical system S . Even though the entire mosaic of point-like objects constitutes the supervenience basis for the world, the subset P does not analogously ground the state of system S . The state of system S supervenes not only on P but on some elements outside of P as well. Thusthe part-whole relation is not compatible with the supervenience relation.Still, this argument may not convince all Humeans. For example, Bhogal and Perry(2017) defend the view that Separability is all the Humean could ever want,and that introducing any stronger principle, such as Binary Separability orStrong Supervenience, does not add anything of value to the Humean. Theybelieve that Separability already satisfies the requirements of no modal ir-reducible facts and of no necessary connections, so why bother? To thatwe can repeat what has already been said earlier that Separability assuresonly the non-existence of necessary connections between fundamental en-tities, but does not guarantee that such connections will not appear at ahigher level. Without Binary Separability a complex physical system maydisplay irreducible connections with its environment due to the fact that thesupervenience basis for its state extends beyond its spatiotemporal parts. In response to the above argument one may object that Humeans can Some might object that such a (standard) mereological structure is compatible witha classical world. We are going to discuss this point in the next section. Miller (2016) acknowledges that the acceptance of such connections amounts to thereinstatement of the anti-Humean doctrine of holism. She writes « [S]uppose it turns outthat we can distinguish singlet and triplet pairs on the basis of differing relations theirmembers bear to other elemental parts of the universe. We again might think this globalinterdependence itself indicates some kind of holism [...] regardless of whether entangledwholes bear any non-supervenient intrinsic properties» (p. 512). Take forinstance the Humean regularity analysis of causation. Considering a singleinstance of causal interaction, for instance a stone smashing a window, theHumean will insist that this individual causal fact actually supervenes onthe totality of similar cases in which a breakage of a fragile object followsa collision with a fast-moving projectile. If the supervenience basis for asingular causal fact contains states of affairs external with respect to thisfact, why can’t the same apply to the case of the state of a physical system?To that we reply that there is a fundamental ontological difference be-tween purported causal facts and physical states of systems. Causality is aninherently modal notion, and as such is the subject of a reductionist analysisby Humean standards. Providing such a reductionist analysis in terms ofglobal regularities does not show that a genuine local state of affairs super-venes on some extrinsic facts. Rather, Humeans would insist that singularcausal facts are not local to begin with –they necessarily involve facts regard-ing external objects and systems. To put it differently, the Humean analysisof causation amounts to an elimination of causal connections between par-ticular events, if we interpret such connections as modal facts intrinsic toappropriate pairs of events. But physical states of systems are supposed tobe genuinely non-modal, so prima facie there is no reason why the Humeanshould reduce them to more fundamental properties and their distributions.A similar response can be provided with respect to other purported coun-terexamples to the Humean prohibition of necessary connections betweendistinct entities and their properties. There is an undeniable necessary linkbetween the value associated with a ten-dollar bill in my wallet and thedecision of the Federal Reserve to increase the budget deficit by printingmore money. Similarly, there a necessary connection linking the death of ahusband to the change of the marital status of his wife from being marriedto being a widow. However, in both examples the properties involved (thepurchasing power of a currency, the marital status of a person) are, to putit loosely, “conventional" or “human-dependent". And as such they are un-likely to be part of the most fundamental description of the world (they failto “carve nature at its joints”, using David Lewis’ famous characterizationof natural properties vis-à-vis non-natural ones; see e.g. Lewis, 1999). Ina sense, there is no objective, physical fact of the matter as to whether aperson is married, divorced or widowed – all there is here is a certain social We owe this objection to Michael Esfeld (private communication). Another reductive analysis of that kind concerns individual chances of events which forHumeans are analyzable in terms of frequencies of occurrences of similar events throughoutthe history of the universe. This po-sition, akin to mereological nihilism, rejects the existence of necessary con-nections between complex entities simply by rejecting the existence of theentities in question. We may note that Bhogal and Perry do not subscribeto this view, since they explicitly include in the total state of the world whatthey call the L-state, i.e. the collection of physical states attributed to spa-tiotemporal regions that do not supervene on the states of their subregions(Bhogal and Perry, 2017, p. 77). Hence they have to assume the existenceof objects (regions) that are neither point-like nor identical with the entireuniverse. This move can be seen as conflicting with the ontologically reduc-tionist spirit of the Humean framework. However, at this point, it looks likethe only way the committed Humean could abandon Strong Superveniencewithout reneging on the intuition of no necessary connections is by denying We cannot offer any precise definition of the term “literal existence” (or “fundamentalexistence”) other than that it is meant to refer to the irreducible ontological commitmentsof our best theories when expressed in a most parsimonious and simplest language possible,stripped of all metaphors and unnecessary vocabulary.
So it seems that now the Bohumian is cornered. Either she accepts thatStrong Supervenience is vacuously equivalent to Supervenience because thereare no physical systems other than individual points (or point-like objects)and the universe, or she altogether abandons Strong Supervenience under-stood as a principle that is genuinely stronger than Supervenience, thus let-ting her framework be haunted by a ghost of necessity.At this point, the Bohumian might be tempted to buy into the secondhorn of the dilemma, and just accept as a bare fact of the matter that somephysical systems may display mutual irreducible connections that do not de-pend on their spatial separations. After all, Hume’s tenets are a heritage froma pre-quantum era, so there would be nothing unreasonable in seeking to rad-ically revise the doctrine under the light of modern physics. The Bohumianmight further point out that the problem of necessary connections betweendistant systems plagues also Best System Approaches to classical mechanics(see in particular Huggett, 2006, section 5). In that case, the problem isroughly that the way regularities in a small region A of the mosaic determineinertial frames is so strong that it automatically fixes all the other inertialframes throughout the universe, including a far distant region B . Indeed, theconstruction makes automatically true the counterfactual “had the regulari-ties been different in A , the inertial frames in B would have been different”. Going back to the quantum case, the Bohumian can furthermore point outthat the existence of such irreducible necessary connections do not affectthe way physics is done in the lab. It is in fact clear that for all practicalpurposes the effective wave function is insensitive to the exact configurationof the environment as long as no measurement-like interaction happens. SoBohumians may be tempted to downplay the ontological significance of thenecessary connection between a given system and its environment. How-ever, it is quite obvious why this FAPP approach fails. If we can convinceourselves that the quantum state of a system is practically intrinsic to thissystem, then Maudlin’s original argument against Separability returns in fullforce!In our opinion, the most promising way out of the impasse is to go for the Huggett is very careful to attach the notion of frame to that of a reference body (seeHuggett, 2006, page 46, second paragraph), so the talk of frames here is just a shorthandfor referring to elements of the mosaic. by us , but may be argued to be unnecessary for Bohmianmechanics in order to be empirically adequate. All Bohmian mechanicsneeds in order to fit into the physical practice is presented in section 3. But, ifthat is the case, why do we in fact make such a categorization? Because of the role that these objects play in the lab (or in our lives). Thus we call a thing“chair” because it has such and such shape and it sustains our weight when wesit on it. Note that it is extremely simple to argue that the previous sentenceis nothing but a shorthand description of how a bunch of particles trajectoriesrelate to another bunch of particles trajectories throughout spacetime. Ofcourse, it has to be stressed that what individuates a chair is its functionalrole, not just its shape, otherwise we could have cases in which a bunchof particles coalesce into ethereal chairs floating around. This is not to saythat complex subsystems are mere arbitrary constructs. It is still the particletrajectories that determine which sub-configurations are salient and which arenot. However, as already said, this salience boils down to the way particle We do not wish to enter the debate on the exact meaning of empirical adequacy andits relation to perception and scientific practice. A proper analysis of these topics wouldrequire at least a separate article. Here the word “lab” is intended in the broadest sense possible, including, e.g., astro-physical systems. That being said, it is also possible togo further and argue that our perception of a chair sustaining our weightcan be given in terms of correlations between trajectories of “chair” particlesand those of our “brain” particles. For those still skeptical that Bohmianmechanics supports such a functionalist-like reduction of subsystems we canpoint out that the procedure to define an effective wave function literallyis a functional definition of a subsystem. Hence we submit that, by goingfor a functionalist-like account of subsystems, we can defend a minimalistHumean primitive ontology without claiming that such subsystems, includingmacroscopic objects, are mere illusions or arbitrary constructs. From what we have said so far, still it is not clear why Strong Superve-nience and Binary Separability seem so compelling principles to our intuitionswhen, in fact, they cut no metaphysical ice. In other words, even grantedthat everything can be ontologically reduced in a strong sense to an under-lying universal dance of particles, still there is no convincing explanation forthe fact that it is totally natural to think (i) that all that can be predicatedof a chair is reducible to facts happening in the spacetime region where the“chair” particles’ trajectories are located, and (ii) that a coarse-grained ver-sion of the mosaic still represents a legitimate Humean supervenience basis.The answer to these doubts lies in the quantum-to-classical transition. Actu-ally, the classical limit of Bohmian mechanics is still largely work-in-progress(see, e.g., Allori et al., 2002), so a full answer is still to come. Very roughlyspeaking, because of the decoherence mechanism, effective Bohmian states( ψ, q ) evolve at large spatiotemporal scales as classical states ( p , q ), thuswashing away the non-local dependencies at a macroscopic level. This givesthe appearance of having a situation in which Strong Supervenience holds,that is, where non-fundamental levels have the same ontological “dignity” asthe fundamental one. Of course, overlooking this fact, and thus consideringcoarse-grained classical states in parallel with the fine-grained Bohmian dy-namics would muddle the ontological waters enough to create the problemsintroduced in the previous section.To sum up, the suggested strategy for Bohumians is to question the funda-mental ontological reality of complex physical systems other than the entireuniverse. This move solves all the problems described earlier at one boldstroke. The theses of Separability and Supervenience become trivially equiv- But not only humans, of course: a chair can sustain, say, a pile of books, not just aperson! This line of reasoning is adopted by Dickson (2000) as a reply to the challenge inBedard (1999).
Austere
Bohumianism, depends primarily on the plausibility of the aforementionedstory that purports to explain the appearances of complex structures, in-cluding but not limited to the macroscopic objects of our experience. Evenif we accept that austere Bohumians can offer a convincing explanation ofhow such objects emerge from the underlying reality of swarming elementalparticles, still one ontological price to be paid is the rejection of the principlesof mereology. Humeanism is definitely not a free lunch.
In this paper we have tried to assess the compatibility of the Humean tenetswith Bohmian mechanics. While we side with Miller, Esfeld, Bhogal, andPerry in claiming, pace Maudlin, that quantum mechanics does not put the reductionist core of the Humean doctrine in serious jeopardy, we nonethelesssubmit that the literature on the subject has so far glossed over a seriousconsequence that salvaging Humeanism in a Bohmian framework implies. Infact, if we want to repel Maudlin’s challenge, we basically need to abandonthe intuitive –and scientifically successful– picture of the world as having astandard, well behaved mereological structure ((in the sense of displayinga part-whole structure that meshes with the relation of supervenience, asexplained in section 4). The point, then, is to decide how much of theHumean doctrine actually rests upon the assumption of such a structure,that is, how much of the strong supervenience principle is dispensable withoutperverting the nature of Humean supervenience thesis. And even if StrongSupervenience can be salvaged in its entirety, the question remains whatother concessions have to be made in order to preserve the main tenets ofHumeanism.In order to forestall possible objections, we would like to stress that wedo not insist that there is one, well-defined view that can be properly called“Humeanism”. On that issue we side with Earman and Roberts (2005) whowrote: “[“Humean Supervenience”] is a name shared by many different the-ses, differing from one another in subtle ways, though they are all intendedto capture the same general view of the world” (p. 2), and then added evenmore forcefully “Thus, HS [i.e. Humean Supervenience] has acquired a statuslike the one that doctrines like materialism, dualism, and empiricism oftenappear to have: there seems to be an idea there, that one can be determi-19ately for or against, even while it remains an open question exactly how theidea should be formulated” (p. 3). As we have explained above, we believethat one legitimate way to formulate the idea of Humean Supervenience isin terms of the principles we call Strong Supervenience or Binary Separabil-ity, even though we acknowledge that some philosophers who subscribe tothe broad doctrine of Humeanism may be unwilling to accept these princi-ples. By showing that Bohumianism does not respect Strong Supervenienceor Binary Separability we do not commit a straw man fallacy against thosephilosophers, but rather bring to the surface a potentially troubling con-sequence of their position (the existence of necessary connections betweencomplex physical systems), which in our opinion has been ignored in recentdebates. If they are happy with a version of Humeanism that accepts thisconsequence, we have nothing to say against that, other than that there areother variants of Humeanism on the market. The doctrine we call Austere Bohumianism restores the Humean orderat the fundamental level of reality. It dispenses altogether with glaringlyanti-Humean phenomena such as holism and non-separability that, as we arebeing told, permeate the quantum world. Yet this victory has its price, as wehave already conceded. The complex systems emerging from the underlyingdance of particles must be interpreted as ontologically secondary (in com-parison to the full-fledged reality of Bohmian particles), lest they become athreat to Humeanism either by exhibiting holistic, irreducible features, or bydisplaying suspicious necessary connections with their environments. It israther interesting to observe that while the Bohumians gladly accept that forall practical purposes the world behaves as if consisting of isolated and well-individualized systems equipped with their own quantum states, they are notso keen to admit that for all practical purposes the world at the micro-levelbut not limited to fundamental particles looks decidedly anti-Humean, as ev-idenced by the cases of singlet- and triplet-spin states of composite systemsof particles. This “illusion of anti-Humeanism” evaporates when we move tothe fundamental level of reality, but so does the familiar picture of chairs,trees, and many-particle systems of textbook quantum mechanics. It seems Incidentally, it is worth pointing out that Earman and Roberts themselves argue fora variant of Humeanism that seems to be very close to our interpretation based on BinarySeparability. They namely interpret the Humean base to which all the facts should bereducible as consisting of non-nomic facts that can be outcomes of spatiotemporally finiteobservation or measurement procedures (p. 17), and they add that their formulation doesnot make reference to point-like entities (p. 20 ft. 29). So it seems that on their approachstates of composite physical systems can be included in the Humean base. It is interesting to note that this provides the proponents of mereological nihilism witha new argument based on the foundations of physics, aside from the usual arguments frommetaphysics.
Acknowledgements
Tomasz Bigaj acknowledges financial support of grant No.2017/25/B/HS1/00620 from the National Science Centre, Poland.Antonio Vassallo worked on the first draft of this paper while being at theUniversity of Barcelona as a Juan de la Cierva Fellow. Hence, he gratefullyacknowledges financial support from the Spanish Ministry of Science, Inno-vation and Universities, fellowship IJCI-2015-23321. The rest of his workon the paper has been carried out at the Warsaw University of Technologywith financial support from the Polish National Science Centre, grant No.2019/33/B/HS1/01772.
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