This paper reviews the hole argument as an argument against spacetime substantivalism. After a careful presentation of the argument itself, I critically review possible responses.

One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question of whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is yes: (...) I state and sketch proofs of two technical results—inspired by simple physical arguments about the generic properties of classical systems—to the effect that, in a precise sense, classical systems evince exactly the geometric structure Lagrangian mechanics provides for the representation of systems, and none provided by Hamiltonian. The argument not only clarifies the conceptual structure of the two systems of mechanics, but also their relations to each other and their respective mechanisms for representing physical systems. It also shows why naïvely structural approaches to the representational content of physical theories cannot work. [Lagrange] grasped that he had gained a method of stating dynamical truths in a way, which is perfectly indifferent to the particular methods of measurement employed in fixing the positions of the various parts of the system. Accordingly, he went on to deduce equations of motion, which are equally applicable whatever quantitative measurements have been made, provided that they are adequate to fix positions. The beauty and almost divine simplicity of these equations is such that these formulae are worthy to rank with those mysterious symbols which in ancient times were held directly to indicate the Supreme Reason at the base of all things. (Whitehead [1948], p. 63)1. Introduction2.Classical Systems3. The Possible Interactions of a Classical System and the Structure of Its Space of States4. Classical Systems Are Lagrangian5. Classical Systems Are Not Hamiltonian6. How Lagrangian and Hamiltonian Mechanics Represent Classical Systems7. The Conceptual Structure of Classical Mechanics. (shrink)

An energy condition, in the context of a wide class of spacetime theories, is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be positive". The remarkable fact I will discuss in this paper is that such simple, general, almost trivial seeming propositions have profound and far-reaching import for our understanding of the structure of relativistic spacetimes. It is therefore especially surprising when one also learns that (...) we have no clear understanding of the nature of these conditions, what theoretical status they have with respect to fundamental physics, what epistemic status they may have, when we should and should not expect them to be satisfied, and even in many cases how they and their consequences should be interpreted physically. Or so I shall argue, by a detailed analysis of the technical and conceptual character of all the standard conditions used in physics today, including examination of their consequences and the circumstances in which they are believed to be violated. (shrink)

In this paper, I put forward a benchmark account of emergence in terms of non-explainability and explicate the relationship that exists between its synchronic and diachronic declinations. I develop an argument whose conclusion is that emergence is essentially a “two-faceted” notion, i.e. it always encapsulates both synchronic and diachronic dimensions. I then compare this account with alternative recent accounts of emergence that define the concept through the notion of unpredictability or topological non-equivalence.

The fact that there exist in nature thoroughly deterministic systems whose future behavior cannot be predicted, no matter how advanced or fined-tune our cognitive and technical abilities turn out to be, has been well established over the last decades or so, essentially in the light of two different theoretical frameworks, namely chaos theory and (some deterministic interpretation of) quantum mechanics. The prime objective of this paper is to show that there actually exists an alternative strategy to ground the divorce between (...) determinism and predictability, a way that is older than—and conceptually independent from—chaos theory and quantum mechanics, and which has not received much attention in the recent philosophical literature about determinism. This forgotten strategy—embedded in the doctrine called “emergent evolutionism”—is nonetheless far from being a mere historical curiosity that should only draw the attention of philosophers out of their concern for comprehensiveness. It has been indeed recently revived in the works of respected scientists. (shrink)

The paper defends an Aristotelian notion of indeterminism, as rigorously formulated in the framework of branching space-times (BST) of Belnap (1992), against the model-theoretic characterization of indeterminism that Montague (1962) introduced into the philosophy of science. It delineates BST branching against the background provided by Earman's (2008) distinction between individual vs. ensemble branching. It describes a construction of physically-motivated BST models, in which histories are isomorphic to Minkowski spacetime. Finally it responds to criticism leveled against BST by addressing some semantical (...) questions, a topological issue, and the past/future asymmetry. (shrink)

Philosophers of biology have worked extensively on how we ought best to interpret the probabilities which arise throughout evolutionary theory. In spite of this substantial work, however, much of the debate has remained persistently intractable. I offer the example of Bayesian models of divergence time estimation as a case study in how we might bring further resources from the biological literature to bear on these debates. These models offer us an example in which a number of different sources of uncertainty (...) are combined to produce an estimate for a complex, unobservable quantity. These models have been carefully analyzed in recent biological work, which has determined the relationship between these sources of uncertainty, both quantitatively and qualitatively. I suggest here that this case shows us the limitations of univocal analyses of probability in evolution, as well as the simple dichotomy between “subjective” and “objective” probabilities, and I conclude by gesturing toward ways in which we might introduce more sophisticated interpretive taxonomies of probability as a path toward advancing debates on probability in the life sciences. (shrink)

This paper gives an overview of logico-philosophical issues of time and determinism. After a brief review of historical roots and 20th century developments, three current research areas are discussed: the definition of determinism, space-time indeterminism, and the temporality of individual things and their possibilities.

The article puts forward a branching-style framework for the analysis of determinism and indeterminism of scientific theories, starting from the core idea that an indeterministic system is one whose present allows for more than one alternative possible future. We describe how a definition of determinism stated in terms of branching models supplements and improves current treatments of determinism of theories of physics. In these treatments, we identify three main approaches: one based on the study of equations, one based on mappings (...) between temporal realizations, and one based on branching models. We first give an overview of these approaches and show that current orthodoxy advocates a combination of the mapping- and the equations-based approaches. After giving a detailed formal explication of a branching-based definition of determinism, we consider three concrete applications and end with a formal comparison of the branching- and the mapping-based approach. We conclude that the branching-based definition of determinism most usefully combines formal clarity, connection with an underlying philosophical notion of determinism, and relevance for the practical assessment of theories. 1 Introduction2 Determinism in Philosophy of Science: Three Approaches2.1 Determinism: The core idea and how to spell it out2.2 The three approaches in more detail2.3 Representing indeterminism3 Orthodoxy: DMAP, with Invocations of DEQN4 Branching-Style Determinism 4.1 Models and realizations4.2 Faithfulness4.3 Two types of branching topologies 5 Comparing the Approaches5.1 Case studies5.2 Formal comparison of the DMAP and DBRN frameworks6 Conclusions. (shrink)

The metaphor of a branching tree of future possibilities has a number of important philosophical and logical uses. In this paper we trace this metaphor through some of its uses and argue that the metaphor works the same way in physics as in philosophy. We then give an overview of formal systems for branching possibilities, viz., branching time and (briefly) branching space-times. In a next step we describe a number of different notions of possibility, thereby sketching a landscape of possibilities. (...) In the final section of the paper we look at the place of branching-based possibilities in that larger landscape of possibilities. Our main message is that far from being an outlandish metaphysical extravagancy, branching-based possibilities are epistemically as well as metaphysically basic. (shrink)

The logical theory of branching space-times, which provides a relativistic framework for studying objective indeterminism, remains mostly disconnected from discussions of space-time theories in philosophy of physics. Earman has criticized the branching approach and suggested “pruning some branches from branching space-time.” This article identifies the different—order-theoretic versus topological—perspective of both discussions as a reason for certain misunderstandings and tries to remove them. Most important, we give a novel, topological criterion of modal consistency that usefully generalizes an earlier criterion, and we (...) introduce a differential-geometrical version of branching space-times as a non-Hausdorff (generalized) manifold. (shrink)

The term ‘locality’ is used in different contexts with different meanings. There have been claims that relational quantum mechanics is local, but it is not clear then how it accounts for the effects that go under the usual name of quantum non-locality. The present article shows that the failure of ‘locality’ in the sense of Bell, once interpreted in the relational framework, reduces to the existence of a common cause in an indeterministic context. In particular, there is no need to (...) appeal to a mysterious space-like influence to understand it. (shrink)

In the light of his recent (and fully deserved) Nobel Prize, this pedagogical paper draws attention to a fundamental tension that drove Penrose’s work on general relativity. His 1965 singularity theorem (for which he got the prize) does not in fact imply the existence of black holes (even if its assumptions are met). Similarly, his versatile definition of a singular space–time does not match the generally accepted definition of a black hole (derived from his concept of null infinity). To overcome (...) this, Penrose launched his cosmic censorship conjecture(s), whose evolution we discuss. In particular, we review both his own (mature) formulation and its later, inequivalent reformulation in the pde literature. As a compromise, one might say that in “generic” or “physically reasonable” space–times, weak cosmic censorship postulates the appearance and stability of event horizons, whereas strong cosmic censorship asks for the instability and ensuing disappearance of Cauchy horizons. As an encore, an “Appendix” by Erik Curiel reviews the early history of the definition of a black hole. (shrink)

The Free Will Theorem of Conway \& Kochen on the one hand follows from uncontroversial parts of modern physics and elementary mathematical and logical reasoning, but on the other hand seems predicated on an undefined notion of free will. Although Conway and Kochen informally claim that their theorem supports indeterminism and, in its wake, a libertarian agenda for free will, inferring the former from the Free Will Theorem is a \emph{petitio principii}. Of course, this also considerably weakens the case for (...) the latter. A recent reformulation of the Free Will Theorem due to Cator and the author uses a mathematically precise formulation of the idea that experimentalists freely choose their settings even in a deterministic world, and thence construes the theorem as providing constraints on determinism. In the present paper we argue that the concept of free will used in this version of the theorem is essentially the one proposed by Lewis, also known as `local miracle compatibilism'. To do so, we give a mathematical reformulation of this idea, which we believe to be well within its spirit and which may be of independent interest. On this double reformulation the Free Will Theorem shows that local miracle compatibilism contradicts the parts of modern physics used in its assumptions. Therefore, although the intention of Conway and Kochen was to support free will through their theorem, what they actually achieved is the opposite: a well-known, philosophically viable version of free will now turns out to be incompatible with physics! (shrink)

In 1927, the Scottish philosopher John Anderson arrived in Australia to take up the chair of Philosophy at the University of Sydney. By the late 1930s, the ‘macrostructure’ of his realist system was in place. It includes a theory of process and a substantial metaphysics, one that opposes positivism, linguistic philosophy and all forms of idealism. However, beyond Australia it remains largely unknown, despite its bearing on a number of current issues in psychology and the social sciences generally. This article (...) outlines Anderson’s transition from Hegelian idealism to realism, describes aspects of his ontology and epistemology, compares some of Anderson’s ideas with Dewey’s pragmatism and explains their relevance to present-day psychology. (shrink)

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.

In this paper, we put forward a new account of emergence called “transformational emergence”. Such an account captures a variety of emergence that can be considered as being diachronic and weakly ontological. The fact that transformational emergence actually constitutes a genuine form of emergence is motivated. Besides, the account is free of traditional problems surrounding more usual, synchronic versions of emergence, and it can find a strong empirical support in a specific physical phenomenon, the fractional quantum Hall effect, which has (...) long been touted as a paradigmatic case of emergence. (shrink)

If the force on a particle fails to satisfy a Lipschitz condition at a point, it relaxes one of the conditions necessary for a locally unique solution to the particle’s equation of motion. I examine the most discussed example of this failure of determinism in classical mechanics—that of Norton’s dome—and the range of current objections against it. Finding there are many different conceptions of classical mechanics appropriate and useful for different purposes, I argue that no single conception is preferred. Instead (...) of arguing for or against determinism, I stress the wide variety of pragmatic considerations that, in a specific context, may lead one usefully and legitimately to adopt one conception over another in which determinism may or may not hold. (shrink)

Although C. D. Broad's notion of Becoming has received a fair amount of attention in the philosophy-of-time literature, there are no serious attempts to show how to replace the standard 'block' spacetime models by models that are more congenial to Broad's idea that the sum total of existence is continuously increased by Becoming or the coming into existence of events. In the Newtonian setting Broad-type models can be constructed in a cheating fashion by starting with a Newtonian block model, carving (...) chips off the block, and assembling the chips in an appropriately structured way. However, attempts to construct Broad-type models in a non-cheating fashion reveal a number of problematic aspects of Becoming that have not received adequate attention in the literature. The paper then turns to an assessment of the problem and prospects of adapting Becoming models to relativistic spacetimes. The results of the assessment differ in both minor and major ways from the ones in the extant literature. Finally, the paper describes how the causal set approach to quantum gravity promises to provide a mechanism for realizing Becoming, though the form of Becoming that emerges may not conform to any of the versions discussed in the philosophical literature. (shrink)

It is argued that seemingly “merely technical” issues about the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have interesting implications for foundations problems in classical and quantum physics. For example, pursuing these technical issues reveals a sense in which quantum mechanics can cure some of the forms of indeterminism that crop up in classical mechanics; and at the same time it reveals the possibility of a form of indeterminism in quantum mechanics that is quite distinct (...) from the indeterminism of state vector collapse. More generally, the examples considered indicate that the classical–quantum correspondence is more intricate and delicate than is generally appreciated. The aim of the article is to give a series of examples that reveal why the technical issues about self-adjointness are relevant to the philosophy of science and that help to make the issues accessible to philosophers of science. (shrink)

I discuss candidates for definitions of determinism in the context of general relativistic spacetimes, and argue that a definition which does not make recourse to any particular region of spacetime should be preferred over alternatives; one such notion is discussed in detail in the light of various physical examples. The emerging picture of determinism is a pluralist one: sometimes there is no unique way of making our intuitive concept of determinism precise. Instead, what is crucial for assessment of determinism of (...) the theory are auxiliary conditions under which it counts as deterministic or indeterministic, and justification for using them in a given situation. (shrink)

Determinism fails easily if spacetimes with points removed from the spacetime manifold are taken to be physically reasonable representations of a way the world could be according to classical general relativity. I discuss a recently proposed condition for determining which spacetimes have holes—epistemic hole freeness—and show that epistemic hole freeness gives the correct verdict in some non-globally hyperbolic spacetimes with a closed subset removed, certain spacetimes with genuinely indeterministic features count as having an epistemic hole, which implies that the requirement (...) of epistemic hole freeness enforces a form of determinism, and there is a large class of spacetimes that intuitively are radically indeterministic and unphysical due to containing a hole, but are free from epistemic holes. I show that a few natural ways of remedying are not satisfactory. (shrink)

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

The Abrahamic traditions regard God as the world’s author. But what kind of author? A novelist? A playwright? Perhaps a composer of classical music? I will argue that it is best to regard God as like an improvisational play director or the leader of a jazz ensemble. Each determines the broad melodic contours or coarse-grained plot beforehand, while allowing their musicians or actors, and chance, to fill in the more fine-grained details. This analogy allows us to regard God as the (...) ultimate author of this world, while allowing us to be, while less than co-authors, more than mere enactors of a pre-written piece. These metaphors are particularly well-suited to illustrate and flesh out an Open Theistic view of things. (shrink)

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

In this thesis I will examine the philosophy of the physicist Max Born. As well as his scientific work, Born wrote on a number of philosophical topics: causation, realism, determinism, and probability. They appear as an interest throughout his career, but he particularly concentrates on them from the 1940s onwards. Born is a significant figure in the development of quantum mechanics whose philosophical work has been left largely unexamined. It is the aim of this thesis to elucidate and to critically (...) examine that work. I will give a defence of presentist historiography in the history and philosophy of science and a brief biography of Born. With regards to causation, the thesis will argue that he holds that there exist principles regarding causal relations that have guided the development of physics and have, in the modern formulation of the subject, been confirmed as having an empirical status. I will argue that he is a selective realist, initially with regards to invariant properties and, later on, a structural realist. With regards to determinism, I will argue that Born has produced an argument, compatible with modern philosophical definitions of determinism, that we were never entitled to conclude from the success of classical mechanics that the world was deterministic. Finally, I will argue that Born holds an objective interpretation of probabilities in quantum mechanics which, due to his strong belief in the physical reality of quantum-mechanical probabilities and his apparent disbelief in the superposition of the wave-function, is most likely a long-run propensity theory. (shrink)

The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is (...) Heisenberg's `quantum-theoretical Umdeutung (reinterpretation) of classical observables', which lies at the basis of quantization theory. Similarly, Bohr's correspondence principle (in somewhat revised form) and Schroedinger's wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit N goes to infinity of a large system with $N$ degrees of freedom (at fixed h), and through decoherence and consistent histories. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain ``classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are ``einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories. This combination of ideas and techniques does not quite resolve the measurement problem, but it does make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it. (shrink)

A thoroughly physical view on reality and our common sense view on agency and free will seem to be in a direct conflict with each other: if everything that happens is determined by prior physical events, so too are all our actions and conscious decisions; you have no choice but to do what you are destined to do. Although this way of thinking has intuitive appeal, and a long history, it has recently began to gain critical attention. A number of (...) arguments have been raised in defense of the idea that our will could be genuinely free even if the universe is governed by deterministic laws of physics. Determinism and free will have been argued to be compatible before, of course, but these recent arguments seem to take a new step in that they are relying on a more profound and concrete view on the central elements of the issue, the fundamental laws of physics and the nature of causal explanation in particular. The basic idea of this approach is reviewed in here, and it is shown how a careful analysis of physics and causal explanation can indeed enhance our understanding of the issue. Although it cannot be concluded that the problem of free will would now be completely solved (or dissolved), it is clear that these recent developments can bring significant advancement to the debate. (shrink)

This essay considers and evaluates recent results and arguments from classical chaotic systems theory and non-relativistic quantum mechanics that pertain to the question of whether our world is deterministic or indeterministic. While the classical results are inconclusive, quantum mechanics is often assumed to establish indeterminism insofar as the measurement process involves an ineliminable stochastic element, even though the dynamics between two measurements is considered fully deterministic. While this latter claim concerning the Schrödinger evolution must be qualified, the former fully depends (...) on a resolution of the measurement problem. Two alleged proofs that nature is indeterministic, relying, in turn, on Gleason's theorem and Conway and Kochen's recent 'free will theorem', are shown to be wanting qua proofs of indeterminism. We are thus left with the conclusion that the determinism question remains open. (shrink)