These preprints were automatically compiled into a PDF from the collection of papers deposited in PhilSci-Archive in conjunction with the PSA 2018.

Early work on the frequency theory of probability made extensive use of the notion of randomness, conceived of as a property possessed by disorderly collections of outcomes. Growing out of this work, a rich mathematical literature on algorithmic randomness and Kolmogorov complexity developed through the twentieth century, but largely lost contact with the philosophical literature on physical probability. The present chapter begins with a clarification of the notions of randomness and probability, conceiving of the former as a property of a (...) sequence of outcomes, and the latter as a property of the process generating those outcomes. A discussion follows of the nature and limits of the relationship between the two notions, with largely negative verdicts on the prospects for any reduction of one to the other, although the existence of an apparently random sequence of outcomes is good evidence for the involvement of a genuinely chancy process. (shrink)

Determinism and chance seem to be irreconcilable opposites: either something is chancy or it is deterministic but not both. Yet there are processes which appear to square the circle by being chancy and deterministic at once, and the appearance is backed by well-confirmed scientific theories such as statistical mechanics which also seem to provide us with chances for deterministic processes. Is this possible, and if so how? In this essay I discuss this question for probabilities as they occur in the (...) empirical sciences, setting aside metaphysical questions in connection with free will, divine intervention and determinism in history. (shrink)

'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, and how to overcome (...) pervasive illusions about the direction of time. Roberts explains the significance of time reversal in a way that intertwines physics and philosophy, to establish what the arrow of time means and how we can come to know it. This book is both mathematically and philosophically rigorous yet remains accessible to advanced undergraduates in physics and the philosophy of physics. This title is also available as Open Access on Cambridge Core. (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)

This chapter focuses on the relations between objective probabilities in physical theories at different levels. In general philosophy of probability, it is frequently assumed that a fundamental deterministic theory cannot support probabilistic phenomena at any higher level, or more generally that there cannot be non-trivial probabilities in higher-level theories that are not encoded in probabilities at the lower level. These assumptions face significant challenges from some well-understood physical theories – I focus on statistical mechanics and Bohmian mechanics – where a (...) deterministic description at some lower level gives rise to an effectively probabilistic theory at some higher level; in each case, constraints arising from an objective physical limitation on the acquisition of evidence concerning the lower level plays a crucial role in supporting the higher-level probabilities. (shrink)

An infinite lottery machine is used as a foil for testing the reach of inductive inference, since inferences concerning it require novel extensions of probability. Its use is defensible if there is some sense in which the lottery is physically possible, even if exotic physics is needed. I argue that exotic physics is needed and describe several proposals that fail and at least one that succeeds well enough.

Suppose all of the particles in the universe should happen to come to rest at the same time, in positions so arranged that all of the forces on every particle balance to zero at that time. What would happen next? Or rather, what does Newtonian mechanics say will happen next? Preface Inertia and Stasis 2.1 Stating the Law of Inertia more precisely 2.2 The stasis scenario Indeterministic Examples 3.1 Abstract example 3.2 Second example Non-Lipschitz Forces and Determinism Beyond the Stasis (...) Scenario CiteULike Connotea Del.icio.us What's this? (shrink)

This article surveys the difficulties in establishing determinism for classical physics within the context of several distinct foundational approaches to the discipline. It explains that such problems commonly emerge due to a deeper problem of ‘missing physics'. The Problems of Formalism Norton's Example Three Species of Classical Mechanics 3.1 Mass point physics 3.2 The physics of perfect constraints 3.3 Continuum mechanics Conclusion CiteULike Connotea Del.icio.us What's this?

The philosopher of science faces overwhelming disagreement in the literature on the definition, nature, structure, ontology, and content of scientific theories. These disagreements are at least partly responsible for disagreements in many of the debates in the discipline which put weight on the concept scientific theory. I argue that available theories of theories and conceptual analyses of theory are ineffectual options for addressing this difficulty: they do not move debates forward in a significant way. Directing my attention to debates about (...) the properties of particular, named theories, I introduce ‘theory eliminativism’ as a certain type of debate-reformulation. As a methodological tool it has the potential to be a highly effective way to make progress in the face of the noted problem: post-reformulation disagreements about theory cannot compromise the debate, and the questions that really matter can still be asked and answered. In addition the reformulation process demands that philosophers engage with science and the history of science in a more serious way than is usual in order to answer important questions about the justification for targeting a particular set of propositions (say) in a given context. All things considered, we should expect the benefits of a theory-eliminating debate-reformulation to heavily outweigh the costs for a highly significant number of debates of the relevant type. (shrink)

In this paper I examine the foundations of Laplace's famous statement of determinism in 1814, and argue that rather than derived from his mechanics, this statement is based on general philosophical principles, namely the principle of sufficient reason and the law of continuity. It is usually supposed that Laplace's statement is based on the fact that each system in classical mechanics has an equation of motion which has a unique solution. But Laplace never proved this result, and in fact he (...) could not have proven it, since it depends on a theorem about uniqueness of solutions to differential equations that was only developed later on. I show that the idea that is at the basis of Laplace's determinism was in fact widespread in enlightenment France, and is ultimately based on a re-interpretation of Leibnizian metaphysics, specifically the principle of sufficient reason and the law of continuity. Since the law of continuity also lies at the basis of the application of differential calculus in physics, one can say that Laplace's determinism and the idea that systems in physics can be described by differential equations with unique solutions have a common foundation. (shrink)

The recent discovery of an indeterministic system in classical mechanics, the Norton dome, has shown that answering the question whether classical mechanics is deterministic can be a complicated matter. In this paper I show that indeterministic systems similar to the Norton dome were already known in the nineteenth century: I discuss four nineteenth century authors who wrote about such systems, namely Poisson, Duhamel, Boussinesq and Bertrand. However, I argue that their discussion of such systems was very different from the contemporary (...) discussion about the Norton dome, because physicists in the nineteenth century conceived of determinism in essentially different ways: whereas in the contemporary literature on determinism in classical physics, determinism is usually taken to be a property of the equations of physics, in the nineteenth century determinism was primarily taken to be a presupposition of theories in physics, and as such it was not necessarily affected by the possible existence of systems such as the Norton dome. (shrink)

By appealing to resources found in the scientific understanding literature, I identify in what senses idealisations afford understanding in the context of the (magnetic) Aharonov-Bohm effect. Three types of concepts of understanding are discussed: understanding-what, which has to do with understanding a phenomenon; understanding-with, which has to do with understanding a scientific theory; and understanding-why, which has to do with the reason some phenomenon occurs. Consequently, I outline an account of understanding-with that is suggested by the historical controversy surrounding the (...) Aharonov-Bohm effect. (shrink)

There are two important traditions in the philosophy of induction. According to one tradition, which has dominated for the last couple of centuries, inductive arguments are warranted by rules. Bayesianism is the most popular view within this tradition. Rules of induction provide functional accounts of inductive support, but no rule is universal; hence, no rule is by itself an accurate model of inductive support. According to another tradition, inductive arguments are not warranted by rules but by matters of fact. Norton’s (...) material theory of induction (MTI) is an influential view within this tradition. Norton’s MTI fails to provide an account of inductive support, but it provides a good account of inductive warrant that can help us define the domain of validity of each rule of induction. Despite their limitations, both approaches to induction are illuminating important aspects of how relations of inductive support work. In this article I present a hybrid theory of induction (HTI), in which I acknowledge and articulate the role of both rules and matters of fact in our understanding of inductive support. According to the HTI, rules of induction accurately describe relations of inductive support when they are warranted, and a rule of induction is warranted if the right facts about the matter of the induction obtain. Crucially, the HTI allows us to address the main challenges that each tradition faces while retaining their strengths, thus obtaining a functional and accurate account of inductive support. The HTI also provides a useful general framework to examine and understand induction, to make sense of how different rules of induction can coexist and to tackle some problems in epistemology. Moreover, the HTI allows us to clarify and resolve some current debates on induction, like the apparent divide between Norton and rule-based theorists. (shrink)

This article suggests a revision of the theory of causal nets. In section 1 we introduce an axiomatization of TCN based on a realistic understanding. It is shown that the causal Markov condition entails three independent principles. In section 2 we analyze indeterministic decay as the major counterexample to one of these principles: screening off by common causes. We call SCC-violating common causes interactive causes. In section 3 we develop a revised version of TCN, called TCN*, which accounts for interactive (...) causes. It is shown that there are interactive causal models that admit of no faithful noninteractive reconstruction. (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)

The paper describes two approaches to determinism: one focuses on the features of global objects, such as possible worlds or models of a theory, whereas the other’s concern is the possible behaviour of individual objects. It then gives an outline of an individuals-based analysis of the determinism of theories. Finally, a general relativistic spacetime with non-isometric extensions is described and used to illustrate a conflict between the two approaches: this spacetime is indeterministic by the first approach but deterministic by the (...) second approach. (shrink)

According to John D. Norton's Material Theory of Induction, all inductive inferences are justified by local facts, rather than their formal features or some grand principles of nature's uniformity. Recently, Richard Dawid (Found Phys 45(9):1101–1109, 2015) has offered a challenge to this theory: in an adaptation of Norton's own celebrated "Dome" thought experiment, it seems that there are certain inductions that are intuitively reasonable, but which do not have any local facts that could serve to justify them in accordance with (...) Norton's requirements. Dawid's suggestion is that “raw induction” might have a limited but important role for such inferences. I argue that the Material Theory can accommodate such inductions, because there are local facts concerning the combinatoric features of the induction’s target populations that can licence the inferences in an analogous way to existing examples of material induction. Since my arguments are largely independent of the details of the Dome, Norton's theory emerges as surprisingly robust against criticisms of excessive narrowness. (shrink)

In a material theory of induction, inductive inferences are warranted by facts that prevail locally. This approach, it is urged, is preferable to formal theories of induction in which the good inductive inferences are delineated as those conforming to some universal schema. An inductive inference problem concerning indeterministic, non-probabilistic systems in physics is posed and it is argued that Bayesians cannot responsibly analyze it, thereby demonstrating that the probability calculus is not the universal logic of induction.

Galileo's refutation of the speed-distance law of fall in his Two New Sciences is routinely dismissed as a moment of confused argumentation. We urge that Galileo's argument correctly identified why the speed-distance law is untenable, failing only in its very last step. Using an ingenious combination of scaling and self-similarity arguments, Galileo found correctly that bodies, falling from rest according to this law, fall all distances in equal times. What he failed to recognize in the last step is that this (...) time is infinite, the result of an exponential dependence of distance on time. Instead, Galileo conflated it with the other motion that satisfies this ‘equal time’ property, instantaneous motion. (shrink)

We often use symmetries to infer outcomes’ probabilities, as when we infer that each side of a fair coin is equally likely to come up on a given toss. Why are these inferences successful? I argue against answering this with an a priori indifference principle. Reasons to reject that principle are familiar, yet instructive. They point to a new, empirical explanation for the success of our probabilistic predictions. This has implications for indifference reasoning in general. I argue that a priori (...) symmetries need never constrain our probability attributions, even when it comes to our initial credences. (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)

According to Popper's rationality principle, agents act in the most adequate way according to the objective situation. I propose a new interpretation of the rationality principle as consisting of an idealization and two abstractions. Based on this new interpretation, I critically discuss the privileged status that Popper ascribes to it as an integral part of all social scientific models. I argue that as an idealization, the rationality principle may play an important role in the social sciences, but it also has (...) inherent limitations that inhibit it from having the privileged status that Popper ascribes to it in all cases. (shrink)

ArgumentIn 1877, a young mathematician named Joseph Boussinesq presented amémoireto theAcadémiedes sciences which demonstrated that some differential equations may have more than one solution. Boussinesq linked this fact to indeterminism and to a possible solution to the free will versus determinism debate. Boussinesq's main interest was to reconcile his philosophical and religious views with science by showing that matter and motion do not suffice to explain all there is in the world. His argument received mixed criticism that addressed both his (...) philosophical views and the scientific content of his work, pointing to the physical “realisticness” of multiple solutions. While Boussinesq proved to be able to face the philosophical criticism, the scientific objections became a serious problem, thus slowly moving the focus of the debate from the philosophical plane to the scientific one. This change of perspective implied a wide discussion on topics such as instability, the sensitivity to initial conditions, and the conservation of energy. The Boussinesq debate is an example of a philosophically motivated debate that transforms into a scientific one, an example of the influence of philosophy on the development of science. (shrink)

In a world awash in statistical patterns, should we conclude that the universe’s evolution or genesis is somehow subject to chance? I draw attention to alternatives that must be acknowledged if we are to have an adequate assessment of what chance the universe might have had.

Cosmologists often use certain global properties to exclude "physically unreasonable" cosmological models from serious consideration. But, on what grounds should these properties be regarded as "physically unreasonable" if we cannot rule out, even with a robust type of inductive reasoning, the possibility of the properties obtaining in our own universe?

Some have argued that chance and determinism are compatible in order to account for the objectivity of probabilities in theories that are compatible with determinism, like Classical Statistical Mechanics (CSM) and Evolutionary Theory (ET). Contrarily, some have argued that chance and determinism are incompatible, and so such probabilities are subjective. In this paper, I argue that both of these positions are unsatisfactory. I argue that the probabilities of theories like CSM and ET are not chances, but also that they are (...) not subjective probabilities either. Rather, they are a third type of probability, which I call counterfactual probability. The main distinguishing feature of counterfactual-probability is the role it plays in conveying important counterfactual information in explanations. This distinguishes counterfactual probability from chance as a second concept of objective probability. (shrink)

In this paper, it is argued that, contrary to some suggestions in the philosophical literature, dispositions cannot replace laws in the description of the physical world. If for a certain type of physical situation a well-working law-based account is available, then it is not possible to describe that situation equally well in terms of dispositions. Using an example consisting of four laws (Coulomb’s law, Newton’s law of gravitation, the rule for the composition of forces and Newton’s second law), it is (...) shown that when one attempts to replace a law-based account with a disposition-based account, the latter turns out to be either less informative or inferior with respect to theoretical virtues, such as simplicity, unification, non-triviality of predictions and explanatory power. Laws are also better suited to deal with interactions and their screening off. Using inference to the best explanation, one can conclude from this comparison that it is laws rather than dispositions that should be included in our ontological picture of nature. (shrink)

In the recent philosophical literature, several counterexamples to the interpretative principle that symmetry-related models are physically equivalent have been suggested The Oxford handbook of philosophy of physics, Oxford University Press, Oxford, 2013, Noûs 52:946–981, 2018; Fletcher in Found Phys 50:228–249, 2020). Arguments based on these counterexamples can be understood as arguments from scientific practice of roughly the following form: because in scientific practice such-and-such symmetry-related models are treated as representing distinct physical situations, these models indeed represent distinct physical situations. In (...) this paper, a strategy for analysing arguments of this type is presented and applied to the examples that can be found in the literature. I argue that if we are exclusively interested in models understood as representing entire possible worlds, arguments from scientific practice should involve some additional assumptions to guarantee they are relevant for models understood in this way. However, none of the examples presented in the literature satisfy all these additional assumptions, which leads to the conclusion that arguments from scientific practice based on these examples do not undermine the interpretative principle that different symmetry-related models represent the same possible world. (shrink)

I present a simple model of Grünbaum’s staccato run in classical mechanics, the staccato roller coaster. It consists of a bead sliding on a frictionless wire shaped like a roller coaster track with infinitely many hills of diminishing size, each of which is a one-dimensional variant of the so-called Norton dome. The staccato roller coaster proves beyond doubt the dynamical (and hence logical) possibility of supertasks in classical mechanics if the Norton dome is a proper system of classical mechanics with (...) metaphysical import. If not, challenges raised against the metaphysical significance of the Norton dome are shown to be challenges against various arguments for the dynamical possibility of supertasks, and the staccato roller coaster clearly shows the importance of meeting these challenges. And the staccato roller coaster can provide, as well as interesting lessons, illuminating analyses of Burke’s (Mod Schoolman 78:1–8, 2000 ) attempt to refute the dynamical possibility of the staccato run and Pérez Laraudogoitia’s (Synthese 148:433–441, 2006 ) rebuttal of it. (shrink)

It is common knowledge that the Aristotelian idea of an unmoved mover was abandoned definitively with the advent of modern science and, in particular, Newton’s precise formulation of mechanics. Here I show that the essential attribute of an unmoved mover is not incompatible with such mechanics; quite the contrary, it makes this possible. The unmoved mover model proposed does not involve supertasks, and leads both to an outrageous form of indeterminism and a new, accountable form of interaction. The process presents (...) a more precise characterization of the crucial going-to-the-limit operation. It has long been acknowledged in the existing literature that, theoretically, in infinite Newtonian systems, masses can move from rest to motion through supertasks. Numerous minor variations on the original schemes have already been published. Against this backdrop, this paper introduces three significant additions: 1) It formulates for the first time a limit postulate for systematically addressing infinite systems; 2) It shows that an Aristotelian unmoved mover is possible in systems of infinitely many particles that interact with each other solely by contact collision; 3) It shows how interaction at a distance can emerge in systems of infinitely many particles that interact with each other solely by contact. (shrink)

This paper shows that, in Newtonian mechanics, unstable three-dimensional rigid bodies must exist. Laraudogoitia recently provided examples of one- and two-dimensional homogeneous unstable rigid bodies, conjecturing the instability would persist for three-dimensional bodies in four-dimensional space. My result proves that, if one admits non homogeneous balls or hollow spheres, then the conjecture is true without having to resort to tetra-dimensionality. Furthermore, I show that instability also holds for at least certain simple classes of elastic bodies. Altogether, the laws of classical (...) dynamics actually lead to the existence of unstable material bodies belonging to the three types of entities accepted therein: point particles, rigid bodies and continuous deformable bodies. A whole range of forms of indeterminism which, until now, has not been considered in the literature. I end with a new conjecture on the connection existing between all these forms of instability and the dimensionality of space. (shrink)

Norton’s very simple case of indeterminism in classical mechanics has given rise to a literature critical of his result. I am interested here in posing a new objection different from the ones made to date. The first section of the paper expounds the essence of Norton’s model and my criticism of it. I then propose a specific modification in the absence of gravitational interaction. The final section takes into consideration a surprising consequence for classical mechanics from the new model introduced (...) here. (shrink)

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)

In this paper, I compare Pierre-Simon Laplace's celebrated formulation of the principle of determinism in his 1814 Essai philosophique sur les probabilités with the formulation of the same principle offered by Roger Joseph Boscovich in his Theoria philosophiae naturalis, published 56 years earlier. This comparison discloses a striking general similarity between the two formulations of determinism as well as certain important differences. Regarding their similarities, both Boscovich's and Laplace's conceptions of determinism involve two mutually interdependent components—ontological and epistemic—and they are (...) both intimately linked with the principles of causality and continuity. Regarding their differences, however, Boscovich's formulation of the principle of determinism turns out not only to be temporally prior to Laplace's but also—being founded on fewer metaphysical principles and more rooted in and elaborated by physical assumptions—to be more precise, complete and comprehensive than Laplace's somewhat parenthetical statement of the doctrine. A detailed analysis of these similarities and differences, so far missing in the literature on the history and philosophy of the concept of determinism, is the main goal of the present paper. (shrink)

Virtually all philosophers of science have construed fundamental theories as descriptions of entities, properties, and/or structures. Call this the “descriptive-ontological” view. I argue that this view is incorrect, at least insofar as physical theories are concerned. I propose a novel construal of theories that I call the “prescriptive-dynamical” view. The central tenet of this view, roughly put, is that the _essential_ content of fundamental physical theories is a _prescription for interfacing with natural systems and translating local data into compact theoretical (...) language_. The descriptive-ontological aspects of theories, if any, are taken as _inessential_ content on this view: they do not contribute to the predictive success of the theory. Rather than describing _what is there_, the essence of a physical theory is to tell us _what to do_ when interfacing with a physical system. (shrink)

We describe a case of indeterminacy in general relativity for homogeneous and isotropic cosmologies for a class of dark energy fluids. The cosmologies are parametrized by an equation of state variable, with one instance giving the same solution as Norton’s mechanical dome. Our example goes beyond previously studied cases in that indeterminacy lies in the evolution of spacetime itself: the onset of the Big Bang is indeterminate. We show further that the indeterminacy is resolved if the dynamics is viewed relationally.

We argue that Hamiltonian mechanics is more fundamental than Lagrangian mechanics. Our argument provides a non-metaphysical strategy for privileging one formulation of a theory over another: ceteris paribus, a more general formulation is more fundamental. We illustrate this criterion through a novel interpretation of classical mechanics, based on three physical conditions. Two of these conditions suffice for recovering Hamiltonian mechanics. A third condition is necessary for Lagrangian mechanics. Hence, Lagrangian systems are a proper subset of Hamiltonian systems. Finally, we provide (...) a geometric interpretation of the principle of stationary action and rebut arguments for privileging Lagrangian mechanics. (shrink)

In a deterministically evolving world, the usefulness of nontrivial probabilities can seem mysterious. I use the ‘Mentaculus’ machinery developed by David Albert and Barry Loewer to show how all probabilities in such a world can be derived from a single, initial chance event. I go on to argue that this is the only genuine chance event. Perhaps surprisingly, we have good evidence of its existence and nature. I argue that the existence of this chance event justifies our epistemic reliance on (...) nontrivial probabilities. (shrink)

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

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)

Stephen Hawking, among others, has proposed that the topological stability of a property of space-time is a necessary condition for it to be physically significant. What counts as stable, however, depends crucially on the choice of topology. Some physicists have thus suggested that one should find a canonical topology, a single ‘right’ topology for every inquiry. While certain such choices might be initially motivated, some little-discussed examples of Robert Geroch and some propositions of my own show that the main candidates—and (...) each possible choice, to some extent—faces the horns of a no-go result. I suggest that instead of trying to decide what the ‘right’ topology is for all problems, one should let the details of particular types of problems guide the choice of an appropriate topology. (shrink)

In this note, I apply Norton’s (Philos Sci 79(2):207–232, 2012) distinction between idealizations and approximations to argue that the epistemic and inferential advantages often taken to accrue to minimal models (Batterman in Br J Philos Sci 53:21–38, 2002) could apply equally to approximations, including “infinite” ones for which there is no consistent model. This shows that the strategy of capturing essential features through minimality extends beyond models, even though the techniques for justifying this extended strategy remain similar. As an application (...) I consider the justification and advantages of the approximation of a inertial reference frame in Norton’s dome scenario (Philos Sci 75(5):786–798, 2008), thereby answering a question raised by Laraudogoitia (Synthese 190(14):2925–2941, 2013). (shrink)

We offer a framework for organizing the literature regarding the debates revolving around infinite idealizations in science, and a short summary of the contributions to this special issue.

Various fault modes of determinism in classical physics are outlined. It is shown how quantum mechanics can cure some forms of classical indeterminism. †To contact the author, please write to: Department of HPS, University of Pittsburgh, 1017 Cathedral of Learning, Pittsburgh, PA 15260; e‐mail: [email protected].

The laws of nature are central to our understanding of the world. And while there is often broad agreement about the technical formulations of the laws, there can be sharp disagreement about the metaphysical nature of the laws. For instance, the Newtonian laws of nature can be stated and analyzed by appealing to a set of possible worlds. Yet, some philosophers argue the worlds are mere notational devices, while others take them to be robust, concrete entities in their own right. (...) In this paper, I use a recent view of laws called the Mentaculus as a case study to illustrate the wide variety of metaphysical pictures that can accompany such a view. I conclude that the technical features of the laws -- typically (though not always) given to us by practicing scientists -- are compatible with many different metaphysical foundations. (shrink)