In this paper a simple model in particle dynamics of a well-known supertask is constructed (the supertask was introduced by Max Black some years ago). As a consequence, a new and simple result about creation ex nihilo of particles can be proved compatible with classical dynamics. This result cannot be avoided by imposing boundary conditions at spatial infinity, and therefore is really new in the literature. It follows that there is no reason why even a world of rigid spheres should (...) be eternal, as has been erroneously assumed, especially since the time of Newton. (shrink)

In this paper, an example is presented for a dynamic system analysable in the framework of the mechanics of rigid bodies. Interest in the model lies in three fundamental features. First, it leads to a paradox in classical mechanics which does not seem to be explainable with the conceptual resources currently available. Second, it is possible to find a solution to it by extending in a natural way the idea of global interaction in the context of what is called interaction (...) by impenetrability. Third, the solution presented throws light on a problem posed and discussed in the recent literature in connection with the mass conservation principle. (shrink)

In this paper a model in particle dynamics of a well-known supertask is constructed. As a consequence, a new and simple result about the failure of determinism of classical particle dynamics can be proved which is related to the non-existence of boundary conditions at spatial infinity. This result is much more accessible to the non-technical reader than similar ones in the scientific literature.

This paper presents three interesting consequences that follow from admitting an ontology of rigid bodies in classical mechanics. First, it shows that some of the most characteristic properties of supertasks based on binary collisions between particles, such as the possibility of indeterminism or the non-conservation of energy, persist in the presence of gravitational interaction. This makes them gravitational supertasks radically different from those that have appeared in the literature to date. Second, Sect. 6 proves that the role of gravitation in (...) supertasks of this kind may be highly non-trivial. Third,, the gravitational supertasks found in the first part enable us to show that indeterminism of classical mechanics with gravitation is much more general than has been supposed until now. This result is especially interesting from the philosophical viewpoint, as it links the scope of indeterminism in a theory like classical mechanics directly with the nature of its ontological hypotheses. (shrink)

The paper presents a new paradox in the sphere of the classical mechanics of infinite systems. The paradox, which implies the existence of an interaction at a distance as well as gravitation, would seem to require an extension of the concept of mechanical explanation. However, it is not clear how such an extension might be carried out.

The examples of dynamic supertasks analyzed to date in the philosophical literature, in which both determinism and the classical laws of conservation of energy and momentum are violated, all share the important limitation of requiring material systems of infinite mass. This paper demonstrates that this limitation is not necessary. This has important consequences for the scope and meaning of such violations.

The paper presents a new paradox in the sphere of the classical mechanics of infinite systems. The paradox, which implies the existence of an interaction at a distance as well as gravitation, would seem to require an extension of the concept of mechanical explanation. However, it is not clear how such an extension might be carried out.

This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a philosophical discussion of randomness in general, I argue that deterministic interpretations of quantum mechanics are strictly speaking incompatible with the Born rule. I also stress the role of outliers, i.e. measurement outcomes that are not 1-random. Although these occur with low probability, their very existence implies that the no-signaling (...) principle used in proofs of randomness of outcomes of quantum-mechanical measurements should be reinterpreted statistically, like the second law of thermodynamics. In three appendices I discuss the Born rule and its status in both single and repeated experiments, review the notion of 1-randomness that in various guises was investigated by Kolmogorov and others and treat Bell’s Theorem and the Free Will Theorem with their implications for randomness. (shrink)

The merits of David Lewis’s Best System Account of natural law are frequently debated. But to my knowledge, the prospects for extending the BSA to cover meta-laws have never been examined. I shall identify two obstacles facing the most natural way of extending the BSA to cover meta-laws. The BSA’s fans should consider how these obstacles are to be overcome. Meta-laws are laws about laws. For example, Einstein’s special theory of relativity incorporates a meta-law: The content of the [special] relativity (...) theory can … be summarized in one sentence: all natural laws must be so conditioned that they are covariant with respect to Lorentz transformations. [The special theory of relativity] is not a theory in the usual sense but is better regarded as a second-level theory, or a theory of theories that constrains first-level theories. The principle of relativity is an example of a symmetry principle: a principle requiring that the first-order laws be unchanged under a given transformation. Long before Einstein proposed the principle of relativity, other spacetime symmetries were widely believed to be meta-laws: that the first-order laws are covariant under arbitrary spatial displacements, temporal displacements and spatial rotations. These spacetime symmetries require the laws to treat all spatial locations and directions alike and all moments alike. For instance, symmetry under temporal displacements rules out a fundamental force law specifying that a given force declines with the inverse-square of the distance before a given moment but with the inverse-cube of the distance at and after that moment. Wigner characterizes such a symmetry principle as ‘a superprinciple which is in …. (shrink)

Joule’s Energy Conservation Law was the first “meta-law”: a general principle that all physical equations must satisfy. It has led to many important and useful physical discoveries. However, a recent analysis seems to indicate that this meta-law is inconsistent with other principles—such as the existence of free will. We show that this conclusion about inconsistency is based on a seemingly reasonable—but simplified—analysis of the situation. We also show that a more detailed mathematical and physical analysis of the situation reveals that (...) not only Joule’s principle remains true—it is actually strengthened: it is no longer a principle that all physical theories should satisfy—it is a principle that all physical theories do satisfy. (shrink)

A recent proposal by Norton (2003) to show that a simple Newtonian system can exhibit stochastic acausal behavior by giving rise to spontaneous movements of a mass on the dome of a certain shape is examined. We discuss the physical significance of an often overlooked and yet important Lipschitz condition the violation of which leads to the existence of anomalous nontrivial solutions in this and similar cases. We show that the Lipschitz condition is closely linked with the time reversibility of (...) certain solutions in Newtonian mechanics and the failure to incorporate this condition within Newtonian mechanics may unsurprisingly lead to physically impossible solutions that have no serious metaphysical implications. ‡I thank Steven Savitt of the Philosophy Department at the University of British Columbia for drawing my attention to the Lipschitz condition, and Alexei Cheviakov of the Mathematics Department at the University of British Columbia for useful discussions. †To contact the author, please write to: Department of Philosophy, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada; e-mail: [email protected]. (shrink)

This paper argues against a standard view that all deterministic and conservative classical mechanical systems are time-reversible, by asking how the temporal evolution of a system modulates parametric imprecision (either ontological or epistemic). It notes that well-behaved systems (e.g. inertial motion) can possess a dynamics which is unstable enough to fail at reversing uncertainties—even though exact values are reliably reversed. A limited (but significant) source of irreversibility is thus displayed in classical mechanics, closely analogous the lack of predictability revealed by (...) unstable chaotic systems. (shrink)

My title is intended to recall Terence Fine's excellent survey, Theories of Probability [1973]. I shall consider some developments that have occurred in the intervening years, and try to place some of the theories he discussed in what is now a slightly longer perspective. Completeness is not something one can reasonably hope to achieve in a journal article, and any selection is bound to reflect a view of what is salient. In a subject as prone to dispute as this, there (...) will inevitably be many who will disagree with any author's views, and I take the opportunity to apologize in advance to all such people for what they will see as the narrowness and distortion of mine. (shrink)

We critically discuss Cleland''s analysis of effective procedures as mundane effective procedures. She argues that Turing machines cannot carry out mundane procedures, since Turing machines are abstract entities and therefore cannot generate the causal processes that are generated by mundane procedures. We argue that if Turing machines cannot enter the physical world, then it is hard to see how Cleland''s mundane procedures can enter the world of numbers. Hence her arguments against versions of the Church-Turing thesis for number theoretic functions (...) miss the mark. (shrink)

Laws of nature have been traditionally thought to express regularities in the systems which they describe, and, via their expression of regularities, to allow us to explain and predict the behavior of these systems. Using the driven simple pendulum as a paradigm, we identify three senses that regularity might have in connection with nonlinear dynamical systems: periodicity, uniqueness, and perturbative stability. Such systems are always regular only in the second of these senses, and that sense is not robust enough to (...) support predictions. We thus illustrate precisely how physical laws in the classical regime of dynamical systems fail to exhibit predictive power. *R. G. Holt gratefully acknowledges the support of the National Center for Physical Acoustics at Oxford, Mississippi, and the Office of Naval Research. (shrink)

The goal of this paper is to sketch and defend a new interpretation or 'theory' of objective chance, one that lets us be sure such chances exist and shows how they can play the roles we traditionally grant them. The account is 'Humean' in claiming that objective chances supervene on the totality of actual events, but does not imply or presuppose a Humean approach to other metaphysical issues such as laws or causation. Like Lewis (1994) I take the Principal Principle (...) (PP) to be the key to understanding objective chance. After describing the main features of Humean objective chance (HOC), I deduce the validity of PP for Humean chances, and end by exploring the limitations of Humean chance. (shrink)

There is a widely extended viewpoint about physical possibility, what we will call Standard Approach, which holds that the physically possible is delimited by the nomological structure of physical theories: to be physically possible is to be in accordance with the physical laws, to be physically impossible is to be prohibited by physical laws and to be physically necessary is to be demanded by the physical laws. However, it is possible to show that this approach is too relaxed and permissive (...) when it comes to collecting and systematizing many of the modal intuitions present in the physical community. In this work we will argue, on the one hand, that the notion of physical possibility is more complex and richer than suggested by the standard approach and, on the other hand, that it is necessary to add some extra elements to the characterization of physical possibility in order to that it is adequate in scientific contexts. (shrink)

In this paper, I defend a theory of local temporality, sometimes referred to as a point-present theory. This theory has the great advantage that it allows for the possibility of an open future without requiring any alterations to our standard understanding of special relativity. Such theories, however, have regularly been rejected out of hand as metaphysically incoherent. After surveying the debate, I argue that such a transformation of temporal concepts (i) is suggested by the indexical semantics of tense in a (...) relativistic universe, (ii) when properly understood easily withstands the usual accusations of metaphysical incoherence and (iii) leads naturally to a meta-philosophical position from which we can understand and escape the increasing sterility of debates between radical Parmenideans and radical Heracliteans in the philosophy of time. (shrink)

Discussion of Alvin Plantinga's book, "Where the Conflict Really Lies".

David Malament (1996) has recently argued that there can be no relativistic quantum theory of (localizable) particles. We consider and rebut several objections that have been made against the soundness of Malament’s argument. We then consider some further objections that might be made against the generality of Malament’s conclusion, and we supply three no‐go theorems to counter these objections. Finally, we dispel potential worries about the counterintuitive nature of these results by showing that relativistic quantum field theory itself explains the (...) appearance of “particle detections.”. (shrink)

The hole argument purportedly shows that spacetime substantivalism implies a pernicious form of indeterminism. We show that the argument is seductive only because it mistakes a trivial claim (viz. there are isomorphic models) for a significant claim (viz. there are hole isomorphisms). We prove that the latter claim is false -- thereby closing the debate about whether substantivalism implies indeterminism.

We call attention to different formulations of how physical laws relate to what is physically possible in the philosophical literature, and argue that it may be the case that determinism fails under one formulation but reigns under the other. Whether this is so depends on our view on the nature of laws, and may also depend on the inter-theoretical relationships among our best physical theories, or so shall we argue.

Difficulties over probability have often been considered fatal to the Everett interpretation of quantum mechanics. Here I argue that the Everettian can have everything she needs from `probability' without recourse to indeterminism, ignorance, primitive identity over time or subjective uncertainty: all she needs is a particular *rationality principle*. The decision-theoretic approach recently developed by Deutsch and Wallace claims to provide just such a principle. But, according to Wallace, decision theory is itself applicable only if the correct attitude to a future (...) Everettian measurement outcome is subjective uncertainty. I argue that subjective uncertainty is not to be had, but I offer an alternative interpretation that enables the Everettian to live without uncertainty: we can justify Everettian decision theory on the basis that an Everettian should *care about* all her future branches. The probabilities appearing in the decision-theoretic representation theorem can then be interpreted as the degrees to which the rational agent cares about each future branch. This reinterpretation, however, reduces the intuitive plausibility of one of the Deutsch -Wallace axioms. (shrink)

While agreeing with Fischborn’s (2018) contention that, according to one traditional definition of compatibilism, my position should be classified as that of a libertarian incompatibilist, I argue here for a different view of compatibilism. This view involves, on the one hand, local probabilistic causation of decisions (rather than universal strict determinism) and, on the other, free will conceived as involving decisions generated by a decision-making process carried out by the brain, which consciously contemplates different alternatives and could in principle have (...) been different from what it was, implying that the agent could in normal conditions have done otherwise in the same circumstances. After discussing different views of causation (including determinism) and of free will, I make a revision of some passages from my earlier work, quoted by Fischborn. I conclude that what is crucial in the question of (in)compatibilism is the (in)compatibility between freedom of decisions and natural causation of human actions. According to this looser and, I argue, more pertinent view of compatibilism, I maintain my previous classification of my position on the matter as compatibilist. (shrink)

In the epistemological tradition, there are two main interpretations of the semantic relation that an empirical theory may bear to the real world. According to realism, the theory-world relationship should be conceived as truth; according to instrumentalism, instead, it should be limited to empirical adequacy. Then, depending on how empirical theories are conceived, either syntactically as a class of sentences, or semantically as a class of models, the concepts of truth and empirical adequacy assume different and specific forms. In this (...) paper, we review two main conceptions of truth (one sentence-based and one model-based) and two of empirical adequacy (one sentence-based and one model-based), we point out their respective difficulties, and we give a first formulation of a new general view of the theory-world relationship, which we call Methodological Constructive Realism (MCR). We then show how the content of MCR can be further specified and expressed in a definite and precise form. The bulk of the paper shows in detail how it is possible to accomplish this goal for the special case of deterministic dynamical phenomena and their correlated deterministic models. This special version of MCR is formulated as an axiomatic extension of set theory, whose specific axioms constitute a formal ontology that provides an adequate framework for analyzing the two semantic relations of truth and empirical correctness, as well as their connections. (shrink)

Does the brain behave indeterministically? I argue that accounting for ion channels, key functional units in the brain, requires indeterministic models. These models are probabilistic, so the brain does behave indeterministically in a weak sense. I explore the implications of this point for a stronger sense of indeterminism. Ultimately I argue that it is not possible, either empirically or through philosophical argument, to show that the brain is indeterministic in that stronger sense.

Special divine action is an integral part of the Christian worldview. In fact, the plausibility of the Christian worldview depends on and is grounded in the putative reality, and therefore possibility, of special divine action. Without special divine action, Scripture does not make sense, and without Scripture, Christianity neither. However, the possibility of special divine action is highly contested in almost every field of human enquiry. In what follows, I briefly suggest a minimal definition of special divine action and show (...) its indispensability for the internal plausibility of Christian faith. I then argue against the very possibility of special divine action. I end by way of identifying ways in which Christian theologians can respond to the arguments in order to justify the possibility of special divine action. It turns out that special divine action neither contradicts science nor metaphysics. (shrink)

I start by way of clarifying briefly the problem of special divine intervention. Once this is done, I argue that laws of nature are generalizations that derive from the dispositional behaviour of natural kinds. Based on this conception of laws of nature I provide a metaphysical model according to which God can realize acts of special divine providence by way of temporarily changing the dispositions of natural entities. I show that this model does not contradict scientific practice and is consistent (...) with the assumption that the physical realm is causally closed. I then argue that prima facie any putative candidate for an act of God could also be seen as a random event or as indicating that there is something wrong with our formulation of the corresponding law of nature. While there is no sufficient philosophical or scientific reason to prefer one of these models, I argue that there are sufficient and legitimate theological reasons to endorse a framework in which at least the obtaining of some anomic states of affairs is seen as the effect of special divine intervention. Doing so, theology has the hermeneutic resources to uncover a dimension of meaningful reality, which without faith could not be seen. (shrink)

A common type of argument against the existence of God is to argue that certain essential features associated with the existence of God are inconsistent with certain other features to be found in the actual world. for an analysis of the different ways to deploy the term “God” in philosophical and theological discourse and for an analysis of the logical form of arguments for and against the existence of God.) A recent example of this type of argument against the existence (...) of God is based on the assumption that there are random processes or chancy states of affairs in the actual world that contradict God being absolute sovereign over his creation: Chancy states of affairs are said to entail a denial of divine providence or omniscience. argues that “classical Big Bang cosmology is inconsistent with theism due to the unpredictable nature of the Big Bang singularity.”) More often than not, however, this apparent conflict is formulated only intuitively and lacks sufficient conceptual clarification of the crucial terms involved. As a consequence, it is seldom clear where the conflict really lies. In what follows, I first provide a brief analysis of chance and randomness before I turn to cosmological and evolutionary arguments against the existence of God that in some way or other are based on chance and randomness. I end by way of comparing three popular conceptions of God as regards their ability to deal with God’s relation to a world of chance and randomness. Neither classical theism, nor open theism, nor indeed process panentheism has difficulties in accounting for God’s relation to a world of chance and randomness. (shrink)

Lewis’s original Best Systems Account of laws was not motivated much by pragmatics. But recent commentary on his general approach to laws has taken a ‘pragmatic turn’. This was initiated by Hall’s defence against the charge of ‘ratbag idealism’ which maintained that best systems accounts should be admired rather than criticised for the inherent pragmatism behind their choice of desiderata for what counts as ‘best’. Emboldened by Hall’s pragmatic turn, recent commentators have proposed the addition of pragmatically motivated desiderata to (...) complement or replace the canonical desiderata of strength and simplicity. This, they hope, will allow their revisionary BSAs to respond better to various counterexamples against the original account. While the pragmatic turn itself is well taken, here I problematise these revisionary approaches. First, there are reasonable responses to the counterexamples from within the canonical BSA. Second, while actual laws may satisfy the newly proposed desiderata, there are reasons to think these desiderata cannot be constitutive of laws. By comparison, the canonical desiderata appear to be relevant to explaining why and when the revisionary desiderata will reflect pragmatic features of the laws and better reflect the motives behind practitioners of fundamental physics. (shrink)

Classical statistical mechanics posits probabilities for various events to occur, and these probabilities seem to be objective chances. This does not seem to sit well with the fact that the theory’s time evolution is deterministic. We argue that the tension between the two is only apparent. We present a theory of Humean objective chance and show that chances thus understood are compatible with underlying determinism and provide an interpretation of the probabilities we find in Boltzmannian statistical mechanics.

in Dirac's classical theory of the electron—is causally non-local. I distinguish two distinct causal locality principles and argue, using Dirac's theory as my main case study, that neither can be reduced to a non-causal principle of local determinism.

The sensitive dependence on initial conditions (SDIC) associated with nonlinear models imposes limitations on the models’ predictive power. We draw attention to an additional limitation than has been underappreciated, namely, structural model error (SME). A model has SME if the model dynamics differ from the dynamics in the target system. If a nonlinear model has only the slightest SME, then its ability to generate decision-relevant predictions is compromised. Given a perfect model, we can take the effects of SDIC into account (...) by substituting probabilistic predictions for point predictions. This route is foreclosed in the case of SME, which puts us in a worse epistemic situation than SDIC. (shrink)

On an influential account, chaos is explained in terms of random behaviour; and random behaviour in turn is explained in terms of having positive Kolmogorov-Sinai entropy (KSE). Though intuitively plausible, the association of the KSE with random behaviour needs justification since the definition of the KSE does not make reference to any notion that is connected to randomness. I provide this justification for the case of Hamiltonian systems by proving that the KSE is equivalent to a generalized version of Shannon's (...) communication-theoretic entropy under certain plausible assumptions. I then discuss consequences of this equivalence for randomness in chaotic dynamical systems. Introduction Elements of dynamical systems theory Entropy in communication theory Entropy in dynamical systems theory Comparison with other accounts Product versus process randomness. (shrink)

I have argued that the standard ways of modeling classical particle-field interactions rely on a set of inconsistent assumptions. This claim has been criticized in (Muller forthcoming). In this paper I respond to some of Muller's criticism.

Nearly all defences of the agent-causal theory of free will portray the theory as a distinctively libertarian one — a theory that only libertarians have reason to accept. According to what I call ‘the standard argument for the agent-causal theory of free will’, the reason to embrace agent-causal libertarianism is that libertarians can solve the problem of enhanced control only if they furnish agents with the agent-causal power. In this way it is assumed that there is only reason to accept (...) the agent-causal theory if there is reason to accept libertarianism. I aim to refute this claim. I will argue that the reasons we have for endorsing the agent-causal theory of free will are nonpartisan. The real reason for going agent-causal has nothing to do with determinism or indeterminism, but rather with avoiding reductionism about agency and the self. As we will see, if there is reason for libertarians to accept the agent-causal theory, there is just as much reason for compatibilists to accept it. It is in this sense that I contend that if anyone should be an agent-causalist, then everyone should be an agent-causalist. (shrink)

We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum spacetimes; the status of singularity theorems; the non-existence of a Newtonian limit; the status of the cosmological constant; and the character of matter fields, including perfect fluids and electromagnetic fields. We conclude with a discussion of what constrains our understanding of physics in different dimensions.

If one is interested in reasoning counterfactually within a physical theory, one cannot adequately use the standard possible world semantics. As developed by Lewis and others, this semantics depends on entertaining possible worlds with miracles, worlds in which laws of nature, as described by physical theory, are violated. Van Fraassen suggested instead to use the models of a theory as worlds, but gave up on determining the needed comparative similarity relation for the semantics objectively. I present a third way, in (...) which this similarity relation is determined from properties of the models contextually relevant to the truth of the counterfactual under evaluation. After illustrating this with a simple example from thermodynamics, I draw some implications for future work, including a renewed possibility for a viable deflationary account of laws of nature. (shrink)

Interest in the computational aspects of modeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rational reconstruction of scientific practice. To this end, we first characterize the role and nature of modeling error in relation to a recipe for model construction known as Euler’s recipe. We then describe a general model (...) that allows us to assess the quality of numerical solutions in terms of measures of computational errors that are completely interpretable in terms of modeling error. Finally, we emphasize that this type of error analysis involves forms of perturbation analysis that go beyond the basic model-theoretical and statistical/probabilistic tools typically used to characterize the scientific method; this demands that we revise and complement our reconstructive toolbox in a way that can affect our normative image of science. (shrink)

If the laws of nature are as the Humean believes, it is an unexplained cosmic coincidence that the actual Humean mosaic is as extremely regular as it is. This is a strong and well-known objection to the Humean account of laws. Yet, as reasonable as this objection may seem, it is nowadays sometimes dismissed. The reason: its unjustified implicit assignment of equiprobability to each possible Humean mosaic; that is, its assumption of the principle of indifference, which has been attacked on (...) many grounds ever since it was first proposed. In place of equiprobability, recent formal models represent the doxastic state of total ignorance as suspension of judgment. In this paper I revisit the cosmic coincidence objection to Humean laws by assessing which doxastic state we should endorse. By focusing on specific features of our scenario I conclude that suspending judgment results in an unnecessarily weak doxastic state. First, I point out that recent literature in epistemology has provided independent justifications of the principle of indifference. Second, given that the argument is framed within a Humean metaphysics, it turns out that we are warranted to appeal to these justifications and assign a uniform and additive credence distribution among Humean mosaics. This leads us to conclude that, contrary to widespread opinion, we should not dismiss the cosmic coincidence objection to the Humean account of laws. (shrink)

Fundamental physics makes no clear use of causal notions; it uses laws that operate in relevant respects in both temporal directions and that relate whole systems across times. But by relating causation to evidence, we can explain how causation fits in to a physical picture of the world and explain its temporal asymmetry. This paper takes up a deliberative approach to causation, according to which causal relations correspond to the evidential relations we need when we decide on one thing in (...) order to achieve another. Tamsin's taking her umbrella is a cause of her staying dry, for example, if and only if her deciding to take her umbrella for the sake of staying dry is adequate grounds for believing she'll stay dry. This correspondence explains why causation matters: knowledge of causal structure helps us make decisions that are evidence of outcomes we seek. The account also explains why we can control the future and not the past, and why causes come before their effects. When agents properly deliberate, their decisions can never count as evidence for any outcomes they may seek in the past. From this it follows that causal relations don't run backwards. This deliberative asymmetry is itself traced back to asymmetries of evidence and entropy, providing a new way of deriving causal asymmetry from temporally symmetric laws. (shrink)

This paper assesses branching spacetime theories in light of metaphysical considerations concerning time. I present the A, B, and C series in terms of the temporal structure they impose on sets of events, and raise problems for two elements of extant branching spacetime theories—McCall’s ‘branch attrition’, and the ‘no backward branching’ feature of Belnap’s ‘branching space-time’—in terms of their respective A- and B-theoretic nature. I argue that McCall’s presentation of branch attrition can only be coherently formulated on a model with (...) at least two temporal dimensions, and that this results in severing the link between branch attrition and the flow of time. I argue that ‘no backward branching’ prohibits Belnap’s theory from capturing the modal content of indeterministic physical theories, and results in it ascribing to the world a time-asymmetric modal structure that lacks physical justification. (shrink)

Bertrand Russell famously argued that causation is not part of the fundamental physical description of the world, describing the notion of cause as “a relic of a bygone age”. This paper assesses one of Russell’s arguments for this conclusion: the ‘Directionality Argument’, which holds that the time symmetry of fundamental physics is inconsistent with the time asymmetry of causation. We claim that the coherence and success of the Directionality Argument crucially depends on the proper interpretation of the ‘ time symmetry’ (...) of fundamental physics as it appears in the argument, and offer two alternative interpretations. We argue that: if ‘ time symmetry’ is understood as the time -reversal invariance of physical theories, then the crucial premise of the Directionality Argument should be rejected; and if ‘ time symmetry’ is understood as the temporally bidirectional nomic dependence relations of physical laws, then the crucial premise of the Directionality Argument is far more plausible. We defend the second reading as continuous with Russell’s writings, and consider the consequences of the bidirectionality of nomic dependence relations in physics for the metaphysics of causation. (shrink)