This paper defends the claim that there is a deep tension between the principle of countable additivity and the one-third solution to the Sleeping Beauty problem. The claim that such a tension exists has recently been challenged by Brian Weatherson, who has attempted to provide a countable additivity-friendly argument for the one-third solution. This attempt is shown to be unsuccessful. And it is argued that the failure of this attempt sheds light on the status of the principle of indifference that (...) underlies the tension between countable additivity and the one-third solution. (shrink)

A physical system has a chaotic dynamics, according to the dictionary, if its behavior depends sensitively on its initial conditions, that is, if systems of the same type starting out with very similar sets of initial conditions can end up in states that are, in some relevant sense, very different. But when science calls a system chaotic, it normally implies two additional claims: that the dynamics of the system is relatively simple, in the sense that it can be expressed in (...) the form of a mathematical expression having relatively few variables, and that the the geometry of the system’s possible trajectories has a certain aspect, often characterized by a strange attractor. (shrink)

In the summer of 1980, I was privileged to be on the teaching staff of the Summer Institute on Medieval Philosophy held at Cornell University under the direction of Norman Kretzmann and the auspices of the Council for Philosophical Studies and the National Endowment for the Humanities. While I was giving a series of lectures on supposition theory, I went to my office one morning, and there under the door some anonymous wag from the Institute had slid the pen and (...) ink drawing you see in the graphic. It represents "Supposition" as a dragon, making a rude face at the viewer. The tail of the dragon is divided — not entirely accurately, as it turns out — into the various branches and subbranches of supposition. If the details are not altogether correct, the spirit is certainly understandable. I have absolutely no idea who the inspired artist was, but I have the original framed on the wall in my office. (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?

Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity--including such revolutionary areas as black hole physics, relativistic computers, new cosmology--are presented in this paper. We would like to invite the logician reader to take part in this grand enterprise of the new century. Besides general perspective and motivation, we present initial results in this direction.

We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the refined notion of an event as a "point-coincidence" between scalar fields that completely characterise a spacetime model, we also propose a natural generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a (...) four-dimensional manifold, that is naturally identified with the physical spacetime. (shrink)

While empirical symmetries relate situations, theoretical symmetries relate models of a theory we use to represent them. An empirical symmetry is perfect if and only if any two situations it relates share all intrinsic properties. Sometimes one can use a theory to explain an empirical symmetry by showing how it follows from a corresponding theoretical symmetry. The theory then reveals a perfect symmetry. I say what this involves and why it matters, beginning with a puzzle that is resolved by the (...) subsequent analysis. I conclude by pointing to applications and implications of the ideas developed earlier in the paper. (shrink)

The (recent, Bayesian) cognitive science literature on the Wason Task (WT) has been modeled largely after the (not-so-recent, Bayesian) philosophy of science literature on the Paradox of Confirmation (POC). In this paper, we apply some insights from more recent Bayesian approaches to the (POC) to analogous models of (WT). This involves, first, retracing the history of the (POC), and, then, re-examining the (WT) with these historico-philosophical insights in mind.

An essay review of Richard Johns "A Theory of Physical Probability" (University of Toronto Press, 2002). Forthcoming in Studies in History and Philosophy of Science.

This paper discusses the Bayesian updating rules of ordinary and Jeffrey conditionalisation. Their justification has been a topic of interest for the last quarter century, and several strategies proposed. None has been accepted as conclusive, and it is argued here that this is for a good reason; for by extending the domain of the probability function to include propositions describing the agent's present and future degrees of belief one can systematically generate a class of counterexamples to the rules. Dynamic Dutch (...) Book and other arguments for them are examined critically. A concluding discussion attempts to put these results in perspective within the Bayesian approach. (shrink)

I argue that Bayesians need two distinct notions of probability. We need the usual degree-of-belief notion that is central to the Bayesian account of rational decision. But Bayesians also need a separate notion of probability that represents the degree to which evidence supports hypotheses. Although degree-of-belief is well suited to the theory of rational decision, Bayesians have tried to apply it to the realm of hypothesis confirmation as well. This double duty leads to the problem of old evidence, a problem (...) that, we will see, is much more extensive than usually recognized. I will argue that degree-of-support is distinct from degree-of-belief, that it is not just a kind of counterfactual degree-of-belief, and that it supplements degree-of-belief in a way that resolves the problems of old evidence and provides a richer account of the logic of scientific inference and belief. (shrink)

A definition is proposed to give precise meaning to the counterfactual statements that often appear in discussions of the implications of quantum mechanics. Of particular interest are counterfactual statements which involve events occurring at space-like separated points, which do not have an absolute time ordering. Some consequences of this definition are discussed.

This essay touches on a number of topics in philosophy of quantum field theory from the point of view of the LSZ asymptotic approach to scattering theory. First, particle/field duality is seen to be a property of free field theory and not of interacting QFT. Second, it is demonstrated how LSZ side-steps the implications of Haag's theorem. Finally, a recent argument due to Redhead, Malament and Arageorgis against the concept of localized particle states is addressed. Briefly, the argument observes that (...) the Reeh-Schlieder theorem entails that correlations between spacelike separated vacuum expectation values of local field operators are always present, and this, according to the above authors, dictates against the notion of a localized particle state. I claim that this moral is excessive and that a coherent notion of localized particles is given by the LSZ approach. The underlying moral to be drawn from this analysis is that questions concerning the ontology of interacting QFT cannot be appropriately addressed if one restricts oneself to the free theory. (shrink)

Scientific essentialism aims to account for the natural laws' special capacity to support counterfactuals. I argue that scientific essentialism can do so only by resorting to devices that are just as ad hoc as those that essentialists accuse Humean regularity theories of employing. I conclude by offering an account of the laws' distinctive relation to counterfactuals that portrays laws as contingent but nevertheless distinct from accidents by virtue of possessing a genuine variety of necessity.

Many of the "counterintuitive" features of relativistic quantum field theory have their formal root in the Reeh-Schlieder theorem, which in particular entails that local operations applied to the vacuum state can produce any state of the entire field. It is of great interest then that I.E. Segal and, more recently, G. Fleming (in a paper entitled "Reeh-Schlieder meets Newton-Wigner") have proposed an alternative "Newton-Wigner" localization scheme that avoids the Reeh-Schlieder theorem. In this paper, I reconstruct the Newton-Wigner localization scheme and (...) clarify the <em>limited</em> extent to which it avoids the counterintuitive consequences of the Reeh-Schlieder theorem. I also argue that there is no coherent interpretation of the Newton-Wigner localization scheme that renders it free from act-outcome correlations at spacelike separation. (shrink)

I formulate a theory of persistence in the endurantist family and pose a problem for the conjunction of this theory with orthodox versions of special or general relativity. The problem centers around the question: Where are things?

An infinite number of elastically colliding balls is considered in a classical, and then in a relativistic setting. Energy and momentum are not necessarily conserved globally, even though each collision does separately conserve them. This result holds in particular when the total mass of all the balls is finite, and even when the spatial extent and temporal duration of the process are also finite. Further, the process is shown to be indeterministic: there is an arbitrary parameter in the general solution (...) that corresponds to the injection of an arbitrary amount of energy (classically), or energy-momentum (relativistically), into the system at the point of accumulation of the locations of the balls. Specific examples are given that illustrate these counter-intuitive results, including one in which all the balls move with the same velocity after every collision has taken place. (shrink)

The Hole Argument was originally formulated by Einstein and it haunted him as he struggled to understand the meaning of spacetime coordinates in the context of the diffeomorphism invariance of general relativity. This argument has since been put to philosophical use by Earman and Norton to argue against a substantival conception of spacetime. In the present work I demonstrate how Earman and Norton’s Hole Argument can be extended to exclude everything and not merely substantival manifolds. These casualties of the hole (...) demonstrate that the Hole Argument hinges essentially on our notion of determinism and not on the diffeomorphic freedom of general relativity. Just as Earman and Norton argue that we should not let our metaphysics run roughshod over the structure of our physical theories, so I will argue that, in particular, we should not uncritically allow our metaphysics to dictate what our physical theories must determine. The central conviction which drives the arguments of this paper is that deterministic theories are not required to determine for future moments what they cannot determine for any present or past moments. I provide two arguments to the effect that a physically informed notion of determinism does not require general relativity to determine substantival facts. Consequently the Hole Argument cannot be used against substantival spacetime. The position that I advocate is an instance of “sophisticated determinism.”. (shrink)

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. This paper presents a case study of a new type of intertheoretic relation that is inspired by Montague’s analysis of the linguistic syntax-semantics relation. The paper develops a simple model of this relation. To motivate the adoption of our new model, we show that this model (...) extends the scope of application of the Nagelian models and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework. (shrink)

Deception has long been an important topic in philosophy. However, the traditional analysis of the concept, which requires that a deceiver intentionally cause her victim to have a false belief, rules out the possibility of much deception in the animal kingdom. Cognitively unsophisticated species, such as fireflies and butterflies, have simply evolved to mislead potential predators and/or prey. To capture such cases of “functional deception,” several researchers Machiavellian intelligence II, Cambridge University Press, Cambridge, pp 112–143, 1997; Searcy and Nowicki, The (...) evolution of animal communication, Princeton University Press, Princeton, 2005; Skyrms, Signals, Oxford University Press, Oxford 2010) have endorsed the broader view that deception only requires that a deceiver benefit from sending a misleading signal. Moreover, in order to facilitate game-theoretic study of deception in the context of Lewisian sender-receiver games, Brian Skyrms has proposed an influential formal analysis of this view. Such formal analyses have the potential to enhance our philosophical understanding of deception in humans as well as animals. However, as we argue in this paper, Skyrms’s analysis, as well as two recently proposed alternative analyses, are seriously flawed and can lead us to draw unwarranted conclusions about deception. (shrink)

Essay review of Gauging What’s Real: The Conceptual Foundations of Contemporary Gauge Theories R. Healey. Oxford University Press (2007). To be published in the Studies in History and Philosophy of Modern Physics, 39(3):687-693, 2008.

If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using a generalized eigenvector formalism based on the Segré classification of symmetric rank 2 tensors with respect to a Lorentzian metric. Securing the correct relationship between the two null cones dynamically plausibly is achieved using the naive gauge freedom. New variables tied to the generalized eigenvector (...) formalism reduce the configuration space to the causality-respecting part. In this smaller space, gauge transformations do not form a group, but only a groupoid. The flat metric removes the difficulty of defining equal-time commutation relations in quantum gravity and guarantees global hyperbolicity. (shrink)

An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite number of elements. With this restriction indeterminism, energy nonconservation and creatio ex nihilo no longer occur. A numerical analysis of finite systems of colliding balls is given, and the asymptotic behaviour that corresponds to the potentially infinite system is (...) inferred. (shrink)

In the static field configuration, a spatially-Variable Speed of Light (VSL) scalar gravity model with Lorentz-Poincaré interpretation was shown to reproduce the phenomenology implied by the Schwarzschild metric. In the present development, we effectively cover configurations with source kinematics due to an induced sweep velocity field w. The scalar-vector model now provides a Hamiltonian description for particles and photons in full accordance with the first Post-Newtonian (1-PN) approximation of General Relativity Theory (GRT). This result requires the validity of Poincaré’s Principle (...) of Relativity, i.e. the unobservability of ‘preferred’ frame movement. Poincaré’s principle fixes the amplitude of the sweep velocity field of the moving source, or equivalently the ‘vector potential’ ξ of GRT (e.g.; S. Weinberg, Gravitation and cosmology, [1972]), and provides the correct 1-PN limit of GRT. The implementation of this principle requires acceleration transformations derived from gravitationally modified Lorentz transformations. A comparison with the acceleration transformation in GRT is done. The present scope of the model is limited to weak-field gravitation without retardation and with gravitating test particles. In conclusion the model’s merits in terms of a simpler space, time and gravitation ontology—in terms of a Lorentz-Poincaré-type interpretation—are explained (e.g. for ‘frame dragging’, ‘harmonic coordinate condition’). (shrink)

It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying Newton’s methods in Principia is neo-Newtonian or Galilean space-time. I argue to the contrary that inertial frames are not needed in Newton’s theory of motion, and that the right space-time structure for Newton’s Principia requires the notion of parallelism of spatial directions at different times and nothing more. Only relative motions are definable in this framework, never absolute (...) ones. (shrink)

As it is well known, classical special relativity allows the existence of three different kinds of particles: bradyons, luxons and tachyons. Bradyons have non-zero mass and hence always travel slower than light. Luxons are particles with zero mass, like the photon, and they always travel with invariant velocity. Tachyons are hypothetical superluminal particles that always move faster than light. The existence of bradyons and luxons is firmly established, while the tachyons were never reliably observed. In quantum field theory, the appearance (...) of tachyonic degrees of freedom indicates vacuum instability rather than a real existence of the faster-than-light particles. However, recent controversial claims of the OPERA experiment about superluminal neutrinos triggered a renewed interest in superluminal particles. Driven by a striking analogy of the old Frenkel-Kontorova model of a dislocation dynamics to the theory of relativity, we conjecture in this note a remarkable possibility of existence of the forth type of particles, elvisebrions, which can be superluminal. The characteristic feature of elvisebrions, distinguishing them from tachyons, is that they are outside the realm of special relativity and their energy remains finite when the elvisebrion velocity approaches the light velocity. (shrink)

It is customary to distinguish experimental from purely observational sciences. The former include physics and molecular biology, the latter astronomy and palaeontology. Experiments involve actively intervening in the course of nature, as opposed to observing events that would have happened anyway. When a molecular biologist inserts viral DNA into a bacterium in his laboratory, this is an experiment; but when an astronomer points his telescope at the heavens, this is an observation. Without the biologist’s handiwork the bacterium would never have (...) contained foreign DNA; but the planets would have continued orbiting the sun whether or not the astronomer had directed his telescope skyward. The observational/experimental distinction would probably be difficult to make precise 1, as the notion of an ‘intervention’ is not easily defined, but it is intuitively fairly clear, and is frequently invoked by scientists and historians of science. Experimentation, or ‘putting questions to nature’, is often cited as a hallmark of the modern scientific method, something that permitted the enormous advances of the last 350 years. And it is sometimes said that the social sciences lag behind the natural because controlled experiments cannot be done so readily in the former. Moreover in certain sciences, e.g. epidemiology, students are explicitly taught that experimental data is preferable to observational data, particularly for doing causal inference. So the distinction between observational and experimental science has quite wide currency, and is often regarded as methodologically significant. Surprisingly, mainstream philosophy of science has had rather little to say about the observational/experimental distinction. 2 For example, discussions of confirmation usually invoke a notion of ‘evidence’, to be contrasted with ‘theory’ or ‘hypothesis’; the aim is to understand how the evidence bears on the hypothesis. But whether this ‘evidence’ comes from observation or experiment generally plays no role in the discussion; this is true …. (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)

among philosophers and therefore a short reminder will do. Pierre was a normal speaker of French, before he moved to London and learnt English without ever using any dictionary or similar devices. During his time in France he had heard about London, and because of what he..

One of the recurrent problems in the foundations of physics is to explain why we rarely observe certain phenomena that are allowed by our theories and laws. In thermodynamics, for example, the spontaneous approach towards equilibrium is ubiquitous yet the time-reversal-invariant laws that presumably govern thermal behaviour in the microscopic level equally allow spontaneous departure from equilibrium to occur. Why are the former processes frequently observed while the latter are almost never reported? Another example comes from quantum mechanics where the (...) formalism, if considered complete and universally applicable, predicts the existence of macroscopic superpositions—monstrous Schr¨odinger cats—and these are never observed: while electrons and atoms enjoy the cloudiness of waves, macroscopic objects are always localized to definite positions. (shrink)

The line of argument pursued in this paper is to proceed from Einstein’s fundamental problem situation to a consideration of scientific representation with respect to the Special theory of relativity (STR). Einstein’s fundamental problem situation, which is Kantian in spirit, is how the conceptual freedom of the scientist is compatible with the need for an objective representation of an independently given material world. To solve this philosophical issue Einstein employs a number of constraints, which are central to the STR. The (...) issue of scientific representation leads to a consideration of the notion of reality and to the realistic commitments implied in the STR. From this point of view, the paper concludes that Einstein was committed to a kind of ‘structural’ realism. (shrink)

We consider to what extent the fundamental question of spacetime singularities is relevant for the philosophical debate about the nature of spacetime. After reviewing some basic aspects of the spacetime singularities within general relativity, we argue that the well known difficulty to localize them in a meaningful way may challenge the received metaphysical view of spacetime as a set of points possessing some intrinsic properties together with some spatiotemporal relations. Considering the algebraic formulation of general relativity, we argue that the (...) spacetime singularities highlight the philosophically misleading dependence on the standard geometric representation of spacetime. †To contact the author, please write to: Department of Philosophy, University of Lausanne, CH-1015 Lausanne, Switzerland; e-mail: [email protected]. (shrink)

The representation theorems of expected utility theory show that having certain types of preferences is both necessary and sufficient for being representable as having subjective probabilities. However, unless the expected utility framework is simply assumed, such preferences are also consistent with being representable as having degrees of belief that do not obey the laws of probability. This fact shows that being representable as having subjective probabilities is not necessarily the same as having subjective probabilities. Probabilism can be defended on the (...) basis of the representation theorems only if attributions of degrees of belief are understood either antirealistically or purely qualitatively, or if the representation theorems are supplemented by arguments based on other considerations (simplicity, consilience, and so on) that single out the representation of a person as having subjective probabilities as the only true representation of the mental state of any person whose preferences conform to the axioms of expected utility theory. (shrink)

Does the Bayesian theory of confirmation put real constraints on our inductive behavior? Or is it just a framework for systematizing whatever kind of inductive behavior we prefer? Colin Howson (Hume's Problem) has recently championed the second view. I argue that he is wrong, in that the Bayesian apparatus as it is usually deployed does constrain our judgments of inductive import, but also that he is right, in that the source of Bayesianism's inductive prescriptions is not the Bayesian machinery itself, (...) but rather what David Lewis calls the ``Principal Principle''. (shrink)

The demand for 'criteria of correctness' to identify recurring particulars in Wittgenstein's private language argument favors an idealist interpretation of quantum phenomena.The indeterminacy principle in quantum physics and the logic of the private language argument share a common concern with the limitations by which microphysical or sensation particulars can be reidentified. Wittgenstein's criteria for reidentifying particular recurrent private sensations are so general as to apply with equal force to quantum particulars, and to support the idealist thesis that quantum phenomena are (...) themselves essentially mental or dependent on mental occurrences. (shrink)

Although black holes are objects of central importance across many fields of physics, there is no agreed upon definition for them, a fact that does not seem to be widely recognized. Physicists in different fields conceive of and reason about them in radi- cally different, and often conflicting, ways. All those ways, however, seem sound in the relevant contexts. After examining and comparing many of the definitions used in practice, I consider the problems that the lack of a universally accepted (...) definition leads to, and discuss whether one is in fact needed for progress in the physics of black holes. I conclude that, within reasonable bounds, the profusion of different definitions is in fact a virtue, making the investigation of black holes possible and fruitful in all the many different kinds of problems about them that physicists consider, although one must take care in trying to translate results between fields. (shrink)

Although black holes are objects of central importance across many fields of physics, there is no agreed upon definition for them, a fact that does not seem to be widely recognized. Physicists in different fields conceive of and reason about them in radically different, and often conflicting, ways. All those ways, however, seem sound in the relevant contexts. After examining and comparing many of the definitions used in practice, I consider the problems that the lack of a universally accepted definition (...) leads to, and discuss whether one is in fact needed for progress in the physics of black holes. I conclude that, within reasonable bounds, the profusion of different definitions is in fact a virtue, making the investigation of black holes possible and fruitful in all the many different kinds of problems about them that physicists consider, although one must take care in trying to translate results between fields. (shrink)

This paper introduces and examines the prospects of the recent research in a holographic relation between entanglement and spacetime pioneered by Mark van Raamsdonk and collaborators. Their thesis is that entanglement in a holographic quantum state is crucial for connectivity in its spacetime dual. Utilizing this relation, the paper develops a thought experiment that promises to probe the nature of spacetime by monitoring the behavior of a spacetime when all entanglement is removed between local degrees of freedom in its dual (...) quantum state. The thought experiment suggests a picture of spacetime as consisting of robust nodes that are connected by non-robust bulk spacetime that is sensitive to changes in entanglement in the dual quantum state. However, rather than pursuing the thought experiment in further detail, the credibility of the relation between spacetime and entanglement in this zero entanglement limit is questioned. The energy of a quantum system generally increases when all entanglement is removed between subsystems, and so does the energy of its spacetime dual. If a system is subdivided into an infinite number of subsystems and all entanglement between them is removed, then the energy of the quantum system and the energy of its spacetime dual are at risk of diverging. While this is a prima facie worry for the thought experiment, it does not constitute a conclusive refutation. (shrink)

Michel Janssen and Harvey Brown have driven a prominent recent debate concerning the direction of an alleged arrow of explanation between Minkowski spacetime and Lorentz invariance of dynamical laws in special relativity. In this article, I critically assess this controversy with the aim of clarifying the explanatory foundations of the theory. First, I show that two assumptions shared by the parties—that the dispute is independent of issues concerning spacetime ontology, and that there is an urgent need for a constructive interpretation (...) of special relativity—are problematic and negatively affect the debate. Second, I argue that the whole discussion relies on a misleading conception of the link between Minkowski spacetime structure and Lorentz invari-ance, a misconception that in turn sheds more shadows than light on our understand-ing of the explanatory nature and power of Einstein’s theory. I state that the arrow connecting Lorentz invariance and Minkowski spacetime is not explanatory and uni-directional, but analytic and bidirectional, and that this analytic arrow grounds the chronogeometric explanations of physical phenomena that special relativity offers. (shrink)

I argue that a common philosophical approach to the interpretation of physical theories—particularly quantum field theories—has led philosophers astray. It has driven many to declare the quantum field theories employed by practicing physicists, so-called ‘effective field theories’, to be unfit for philosophical interpretation. In particular, such theories have been deemed unable to support a realist interpretation. I argue that these claims are mistaken: attending to the manner in which these theories are employed in physical practice, I show that interpreting effective (...) field theories yields a robust foundation for a more refined approach to scientific realism in the context of quantum field theory. The paper concludes by briefly sketching some general morals for interpretive practice in the philosophy of physics. (shrink)

This paper explores the link between the case for indeterminism in an epistemological fashion and methodological individualism in the thought of two defenders of both stances: Karl Popper and Friedrich Hayek. The relation between these issues has not received much attention before and even less so with regard to these two thinkers. First, Popper’s defence of indeterminism from an epistemic viewpoint and Hayek’s views about the indeterminism of action are studied. Second, their positions about methodological individualism are considered. Finally, several (...) comparative questions are aired. (shrink)

Currently, the most popular views about how to update de se or self-locating beliefs entail the one-third solution to the Sleeping Beauty problem.2 Another widely held view is that an agent‘s credences should be countably additive.3 In what follows, I will argue that there is a deep tension between these two positions. For the assumptions that underlie the one-third solution to the Sleeping Beauty problem entail a more general principle, which I call the Generalized Thirder Principle, and there are situations (...) in which the latter principle and the principle of Countable Additivity cannot be jointly satisfied. The most plausible response to this tension, I argue, is to accept both of these principles, and to maintain that when an agent cannot satisfy them both, she is faced with a rational dilemma. (shrink)

Econophysics is a new and exciting cross-disciplinary research field that applies models and modelling techniques from statistical physics to economic systems. It is not, however, without its critics: prominent figures in more mainstream economic theory have criticized some elements of the methodology of econophysics. One of the main lines of criticism concerns the nature of the modelling assumptions and idealizations involved, and a particular target are ‘kinetic exchange’ approaches used to model the emergence of inequality within the distribution of individual (...) monetary income. This article will consider such models in detail, and assess the warrant of the criticisms drawing upon the philosophical literature on modelling and idealization. Our aim is to provide the first steps towards informed mediation of this important and interesting interdisciplinary debate, and our hope is to offer guidance with regard to both the practice of modelling inequality, and the inequality of modelling practice. _1_ Introduction _1.1_ Econophysics and its discontents _1.2_ Against burglar economics _2_ Modelling Inequality _2.1_ Mainstream economic models for income distribution _2.2_ Econophysics models for income distribution _3_ Idealizations in Kinetic Exchange Models _3.1_ Binary interactions _3.2_ Conservation principles _3.3_ Exchange dynamics _ 4 _ Fat Tails and Savings _ 5 _ Evaluation. (shrink)

Jim Weatherall has suggested that Einstein's hole argument, as presented by Earman and Norton, is based on a misleading use of mathematics. I argue on the contrary that Weatherall demands an implausible restriction on how mathematics is used. The hole argument, on the other hand, is in no new danger at all.

This paper states and proves a precise sense in which, if all the measurable properties of an ordinary quantum mechanical system are ultimately derivable from position, then time in quantum mechanics can have no preferred direction. In particular, I show that when the position observable forms a complete set of commuting observables, Galilei invariant quantum mechanics is guaranteed to be time reversal invariant.

Economists reason causally. Like many other scientists, they aim at formulating justified causal claims about their object of study. This thesis contributes to our understanding of how causal reasoning proceeds in economics. By using the research on the causes of unemployment as a case study, three questions are adressed. What are the meanings of causal claims? How can a causal claim be adequately supported by evidence? How are causal beliefs affected by incoming facts? In the process of answering these semantic, (...) epistemic and dynamical questions, the richness of causal reasoning in economics is brought to the foreground. In the part on semantics, it is argued that the meaning of causal generalizations in policy-oriented economics is best captured by using the concept of ‘inferential relation’ rather than the one of ‘referential relation’. This part contributes to develop an inferentialist semantics by distinguishing among types of inferential relations. In the part on epistemology, it is argued that justification in sciences like economics often relies, and ought to rely, on evidential variety―i.e. the combination of evidence from multiple sources. An interpretation of independence among evidential sources is offered: two evidential sources are fully independent if and only if the reasons why they would be unreliable do not overlap. It is then shown that the variety-of-evidence thesis does not hold under extreme circumstances. The part on dynamics focuses on deviant-case study. A storyline is provided for what deviant-case study aims at and how it proceeds in what is characterized as an ‘eclectic science’. (shrink)

Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned. Each argument concludes that rationality requires your credences to be probabilities. I contend that each argument is invalid as formulated. In each case there is a mirror-image theorem and (...) a corresponding argument of exactly equal strength that concludes that rationality requires your credences not to be probabilities. Some further consideration is needed to break this symmetry in favour of probabilism. (shrink)