Two of the most difficult problems in the foundations of physics are (1) what gives rise to the arrow of time and (2) what the ontology of quantum mechanics is. They are difficult because the fundamental dynamical laws of physics do not privilege an arrow of time, and the quantum-mechanical wave function describes a high-dimensional reality that is radically different from our ordinary experiences. -/- In this paper, I characterize and elaborate on the ``Wentaculus” theory, a new approach to time’s (...) arrow in a quantum universe that offers a unified solution to both problems. Central to the Wentaculus are (i) Density Matrix Realism, the idea that the quantum state of the universe is objective but can be impure, and (ii) the Initial Projection Hypothesis, a new law of nature that selects a unique initial quantum state. On the Wentaculus, the quantum state of the universe is sufficiently simple to be a law, and the arrow of time can be traced back to an exact boundary condition. It removes the intrinsic vagueness of the Past Hypothesis, eliminates the Statistical Postulate, provides a higher degree of theoretical unity, and contains a natural realization of “strong determinism." I end by responding to four recent objections. In a companion paper, I elaborate on Density Matrix Realism. (shrink)

A century after the discovery of quantum mechanics, the meaning of quantum mechanics still remains elusive. This is largely due to the puzzling nature of the wave function, the central object in quantum mechanics. If we are realists about quantum mechanics, how should we understand the wave function? What does it represent? What is its physical meaning? Answering these questions would improve our understanding of what it means to be a realist about quantum mechanics. In this survey article, I review (...) and compare several realist interpretations of the wave function. They fall into three categories: ontological interpretations, nomological interpretations, and the sui generis interpretation. For simplicity, I will focus on non-relativistic quantum mechanics. (shrink)

A strongly deterministic theory of physics is one that permits exactly one possible history of the universe. In the words of Penrose (1989), "it is not just a matter of the future being determined by the past; the entire history of the universe is fixed, according to some precise mathematical scheme, for all time.” Such an extraordinary feature may appear unattainable in a world like ours. In this paper, I show that it can be achieved in a simple way and (...) discuss its implications for metaphysics and philosophy of science, including natural properties, free will, explanation, and modality. First, I propose a precise definition of strong determinism. Next, I discuss its philosophical ramifications and a toy example. Finally, I provide a realistic example of a strongly deterministic (and simple) physical theory---the Everettian Wentaculus. A surprising consequence is that whether or not our world is strongly deterministic may be empirically underdetermined. (shrink)

The Great Divide in metaphysical debates about laws of nature is between Humeans, who think that laws merely describe the distribution of matter, and non-Humeans, who think that laws govern it. The metaphysics can place demands on the proper formulations of physical theories. It is sometimes assumed that the governing view requires a fundamental / intrinsic direction of time: to govern, laws must be dynamical, producing later states of the world from earlier ones, in accord with the fundamental direction of (...) time in the universe. In this paper, we propose a minimal primitivism about laws of nature (MinP) according to which there is no such requirement. On our view, laws govern by constraining the physical possibilities. Our view captures the essence of the governing view without taking on extraneous commitments about the direction of time or dynamic production. Moreover, as a version of primitivism, our view requires no reduction / analysis of laws in terms of universals, powers, or dispositions. Our view accommodates several potential candidates for fundamental laws, including the principle of least action, the Past Hypothesis, the Einstein equation of general relativity, and even controversial examples found in the Wheeler-Feynman theory of electrodynamics and retrocausal theories of quantum mechanics. By understanding governing as constraining, non-Humeans who accept MinP have the same freedom to contemplate a wide variety of candidate fundamental laws as Humeans do. (shrink)

The mathematical structure of realist quantum theories has given rise to a debate about how our ordinary 3-dimensional space is related to the 3N-dimensional configuration space on which the wave function is defined. Which of the two spaces is our (more) fundamental physical space? I review the debate between 3N-Fundamentalists and 3D-Fundamentalists and evaluate it based on three criteria. I argue that when we consider which view leads to a deeper understanding of the physical world, especially given the deeper topological (...) explanation from the unordered configurations to the Symmetrization Postulate, we have strong reasons in favor of 3D-Fundamentalism. I conclude that our evidence favors the view that our fundamental physical space in a quantum world is 3-dimensional rather than 3N-dimensional. I outline lines of future research where the evidential balance can be restored or reversed. Finally, I draw lessons from this case study to the debate about theoretical equivalence. (shrink)

Despite its apparent complexity, our world seems to be governed by simple laws of physics. This volume provides a philosophical introduction to such laws. I explain how they are connected to some of the central issues in philosophy, such as ontology, possibility, explanation, induction, counterfactuals, time, determinism, and fundamentality. I suggest that laws are fundamental facts that govern the world by constraining its physical possibilities. I examine three hallmarks of laws--simplicity, exactness, and objectivity--and discuss whether and how they may be (...) associated with laws of physics. (shrink)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two (...) sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

Two of the most difficult problems in the foundations of physics are (1) what gives rise to the arrow of time and (2) what the ontology of quantum mechanics is. I propose a unified 'Humean' solution to the two problems. Humeanism allows us to incorporate the Past Hypothesis and the Statistical Postulate into the best system, which we then use to simplify the quantum state of the universe. This enables us to confer the nomological status to the quantum state in (...) a way that adds no significant complexity to the best system and solves the ''supervenient-kind problem'' facing the original version of the Past Hypothesis. We call the resultant theory the Humean unification. It provides a unified explanation of time asymmetry and quantum entanglement. On this theory, what gives rise to time's arrow is also responsible for quantum phenomena. The new theory has a separable mosaic, a best system that is simple and non-vague, less tension between quantum mechanics and special relativity, and a higher degree of theoretical and dynamical unity. The Humean unification leads to new insights that can be useful to Humeans and non-Humeans alike. (shrink)

The wave function in quantum mechanics presents an interesting challenge to our understanding of the physical world. In this paper, I show that the wave function can be understood as four intrinsic relations on physical space. My account has three desirable features that the standard account lacks: it does not refer to any abstract mathematical objects, it is free from the usual arbitrary conventions, and it explains why the wave function has its gauge degrees of freedom, something that are usually (...) put into the theory by hand. Hence, this account has implications for debates in philosophy of mathematics and philosophy of science. First, by removing references to mathematical objects, it provides a framework for nominalizing quantum mechanics. Second, by excising superfluous structure such as overall phase, it reveals the intrinsic structure postulated by quantum mechanics. Moreover, it also removes a major obstacle to ``wave function realism.''. (shrink)

What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition that accounts for the time-asymmetry of the universe. The natural choice is given not by a wave function but by a density matrix. I begin by classifying quantum theories into two types: theories with a fundamental wave function and theories with (...) a fundamental density matrix. The Past Hypothesis is compatible with infinitely many initial wave functions, none of which seems to be particularly natural. However, once we turn to density matrices, the Past Hypothesis provides a natural choice---the normalized projection onto the Past Hypothesis subspace in the Hilbert space. Nevertheless, the two types of theories can be empirically equivalent. To provide a concrete understanding of the empirical equivalence, I provide a novel subsystem analysis in the context of Bohmian theories. Given the empirical equivalence, it seems empirically underdetermined whether the universe is in a pure state or a mixed state. Finally, I discuss some theoretical payoffs of the density-matrix theories and present some open problems for future research. (Bibliographic note: the thesis was submitted for the Master of Science in mathematics at Rutgers University.). (shrink)

In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.

In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a unique initial condition in such a world. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix that represents something objective. This stands in sharp contrast to Wave Function (...) Realism, the thesis that the quantum universe is described by a wave function that represents something objective. Second, I suggest that the Past Hypothesis is sufficient to determine a unique and simple density matrix. This is achieved by what I call the Initial Projection Hypothesis: the initial density matrix of the universe is the normalized projection onto the special low-dimensional Hilbert space. Third, because the initial quantum state is unique and simple, we have a strong case for the \emph{Nomological Thesis}: the initial quantum state of the universe is on a par with laws of nature. This new package of ideas has several interesting implications, including on the harmony between statistical mechanics and quantum mechanics, the dynamic unity of the universe and the subsystems, and the alleged conflict between Humean supervenience and quantum entanglement. (shrink)

If there are fundamental laws of nature, can they fail to be exact? In this paper, I consider the possibility that some fundamental laws are vague. I call this phenomenon 'fundamental nomic vagueness.' I characterize fundamental nomic vagueness as the existence of borderline lawful worlds and the presence of several other accompanying features. Under certain assumptions, such vagueness prevents the fundamental physical theory from being completely expressible in the mathematical language. Moreover, I suggest that such vagueness can be regarded as (...) 'vagueness in the world.' For a case study, we turn to the Past Hypothesis, a postulate that (partially) explains the direction of time in our world. We have reasons to take it seriously as a candidate fundamental law of nature. Yet it is vague: it admits borderline (nomologically) possible worlds. An exact version would lead to an untraceable arbitrariness absent in any other fundamental laws. However, the dilemma between fundamental nomic vagueness and untraceable arbitrariness is dissolved in a new quantum theory of time's arrow. (shrink)

How does one arrive at a life in politics and policy? What happens to one's ideals when confronted with the reality that the only way to get things done in Washington is compromise? Who are the men and women who help shape our national agenda, and what drives their work? Dispatches From the Eastern Front provides fascinating, intensely personal, yet universal answers to these central questions. Recounting four decades inside Washington politics, Gerald Felix Warburg brings remarkable candor to a (...) most unusual memoir. An idealistic California baby boomer transported to the intimidating world of Capitol Hill policymaking at a young age, Warburg finds himself working to reform nuclear energy, strategic arms control, and foreign policy. As his access and power grow, greater challenges loom: how to maintain principles while cutting deals, and how to balance public purpose with private interests. An eclectic career reveals the slow and often painful development of emotional intelligence for work at the highest reaches of the public arena. (shrink)

In this paper, I introduce an intrinsic account of the quantum state. This account contains three desirable features that the standard platonistic account lacks: (1) it does not refer to any abstract mathematical objects such as complex numbers, (2) it is independent of the usual arbitrary conventions in the wave function representation, and (3) it explains why the quantum state has its amplitude and phase degrees of freedom. -/- Consequently, this account extends Hartry Field’s program outlined in Science Without Numbers (...) (1980), responds to David Malament’s long-standing impossibility conjecture (1982), and establishes an important first step towards a genuinely intrinsic and nominalistic account of quantum mechanics. I will also compare the present account to Mark Balaguer’s (1996) nominalization of quantum mechanics and discuss how it might bear on the debate about “wave function realism.” In closing, I will suggest some possible ways to extend this account to accommodate spinorial degrees of freedom and a variable number of particles (e.g. for particle creation and annihilation). -/- Along the way, I axiomatize the quantum phase structure as what I shall call a “periodic difference structure” and prove a representation theorem as well as a uniqueness theorem. These formal results could prove fruitful for further investigation into the metaphysics of phase and theoretical structure. -/- (For a more recent version of this paper, please see "The Intrinsic Structure of Quantum Mechanics" available on PhilPapers.). (shrink)

If the Past Hypothesis underlies the arrows of time, what is the status of the Past Hypothesis? In this paper, I examine the role of the Past Hypothesis in the Boltzmannian account and defend the view that the Past Hypothesis is a candidate fundamental law of nature. Such a view is known to be compatible with Humeanism about laws, but as I argue it is also supported by a minimal non-Humean "governing'' view. Some worries arise from the non-dynamical and time-dependent (...) character of the Past Hypothesis as a boundary condition, the intrinsic vagueness in its specification, and the nature of the initial probability distribution. I show that these worries do not have much force, and in any case they become less relevant in a new quantum framework for analyzing time's arrows---the Wentaculus. Hence, the view that the Past Hypothesis is a candidate fundamental law should be more widely accepted than it is now. (shrink)

Shaʻar rishon. Hagut hilkhatit u-midrashit be-sifrut Ḥazal -- Shaʻar sheni. Haguto ha-hilkhatit shel ha-Rambam -- Shaʻar shelishi. Hagut ṿa-halakhah bi-yeme ha-benayim -- Shaʻar reviʻi. Hagut rabanit ba-ʻet ha-ḥadashah.

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory (...) to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives. (shrink)

In this innovative and important work, Gerald Gaus advances a revised and more realistic account of public reason liberalism, showing how, in the midst of fundamental disagreement about values and moral beliefs, we can achieve a moral and political order that treats all as free and equal moral persons. The first part of this work analyzes social morality as a system of authoritative moral rules. Drawing on an earlier generation of moral philosophers such as Kurt Baier and Peter Strawson (...) as well as current work in the social sciences, Gaus argues that our social morality is an evolved social fact, which is the necessary foundation of a mutually beneficial social order. The second part considers how this system of social moral authority can be justified to all moral persons. Drawing on the tools of game theory, social choice theory, experimental psychology and evolutionary theory, Gaus shows how a free society can secure a moral equilibrium that is endorsed by all, and how a just state respects, and develops, such an equilibrium. (shrink)

Despite its apparent complexity, our world seems to be governed by simple laws of physics. This volume provides a philosophical introduction to such laws. I explain how they are connected to some of the central issues in philosophy, such as ontology, possibility, explanation, induction, counterfactuals, time, determinism, and fundamentality. I suggest that laws are fundamental facts that govern the world by constraining its physical possibilities. I examine three hallmarks of laws-simplicity, exactness, and objectivity-and discuss whether and how they may be (...) associated with laws of physics. (shrink)

Searching through semantic memory may involve the use of several retrieval cues. In a verbal fluency task, the set of available cues is limited and every candidate word is a target. Individuals exhibit clustering behavior as predicted by optimal foraging theory. In another semantic search task, the remote associates task, three cues are presented and a single target word has to be found. Whereas the task has been widely studied as a task of creativity or insight problem solving, in this (...) article, the RAT is treated as a semantic retrieval task and assessed from the perspective of information foraging theory. Experiments are presented that address the superadditive combination of cues and the anti-clustering behavior in the recall sequence. A new type of search behavior in the RAT is put forward that involves maximizing the difference in activation between target and distractors. This type of search is advantageous when the target is weak and cue patches are contaminated with strong competitors. (shrink)

Physical laws are strikingly simple, although there is no a priori reason they must be so. I propose that nomic realists of all types (Humeans and non-Humeans) should accept that simplicity is a fundamental epistemic guide for discovering and evaluating candidate physical laws. This principle of simplicity clarifies and addresses several problems of nomic realism and simplicity. A consequence is that the oft-cited epistemic advantage of Humeanism over non-Humeanism disappears, undercutting an influential epistemological argument for Humeanism. Moreover, simplicity is shown (...) to be more tightly connected to lawhood than to mere truth. (shrink)

While philosophers and scientists sometimes suggest (or take for granted) that consciousness is an essential condition for free will and moral responsibility, there is surprisingly little discussion of why consciousness (and what sorts of conscious experience) is important. We discuss some of the proposals that have been offered. We then discuss our studies using descriptions of humanoid robots to explore people’s attributions of free will and responsibility, of various kinds of conscious sensations and emotions, and of reasoning capacities, and examine (...) the relationships between these attributions. Our initial results suggest that people’s attributions of free will are strongly influenced by their attributions of conscious emotions, such as happiness and disappointment, including Strawsonian emotions, such as pride and regret. These results provide some support for an intriguing proposal: Free will requires the capacity to make decisions that really matter to the agent, and for anything to really matter to the agent, she must be able to consciously experience the good and bad effects of the decisions she makes—to suffer and regret, or to enjoy and feel proud of, their outcomes. (shrink)

What is the proper metaphysics of quantum mechanics? In this dissertation, I approach the question from three different but related angles. First, I suggest that the quantum state can be understood intrinsically as relations holding among regions in ordinary space-time, from which we can recover the wave function uniquely up to an equivalence class (by representation and uniqueness theorems). The intrinsic account eliminates certain conventional elements (e.g. overall phase) in the representation of the quantum state. It also dispenses with first-order (...) quantification over mathematical objects, which goes some way towards making the quantum world safe for a nominalistic metaphysics suggested in Field (1980, 2016). Second, I argue that the fundamental space of the quantum world is the low-dimensional physical space and not the high-dimensional space isomorphic to the ``configuration space.'' My arguments are based on considerations about dynamics, empirical adequacy, and symmetries of the quantum mechanics. Third, I show that, when we consider quantum mechanics in a time-asymmetric universe (with a large entropy gradient), we obtain new theoretical and conceptual possibilities. In such a model, we can use the low-entropy boundary condition known as the Past Hypothesis (Albert, 2000) to pin down a natural initial quantum state of the universe. However, the universal quantum state is not a pure state but a mixed state, represented by a density matrix that is the normalized projection onto the Past Hypothesis subspace. This particular choice has interesting consequences for Humean supervenience, statistical mechanical probabilities, and theoretical unity. (shrink)

This chapter contains sections titled: The Concept of Neutrality Liberal Moral Neutrality Liberal Political Neutrality The Implications of Liberal Political Neutrality Notes.

In this paper, I characterize and elaborate on the “Wentaculus” theory, a new approach to time’s arrow in a quantum universe that offers a unified solution to the problems of what gives rise to the arrow of time and what the ontology of quantum mechanics is.

Whether one's interests lie in psychological practice, counseling, research, or the classroom, psychologists today must deal with a broad range of ethical issues--from charging fees to maintaining a client's confidentiality, and from conducting research to respecting clients, colleagues, and students. Now in a new edition, Ethics in Psychology, the most widely read and cited ethics textbook in psychology, considers many of the ethical questions and dilemmas that psychologists encounter in their everyday practice, research, and teaching. The book has been completely (...) updated in response to evolving trends in psychological research and practice, as well as extensive changes in the American Psychological Association's ethics code. Taking a practical, common sense approach to ethics in modern-day psychological practice, this useful book offers constructive means for both preventing problems and resolving ethical predicaments. This new edition retains the key features which have contributed to its popularity, including extensive case studies that provide illustrative guidance on a wide variety of topics, such as fee setting, advertising for clients, research ethics, sexual attraction, classroom ethics, managed care issues, confidentiality, and much more. Highly readable, the book unites an accessible style with humorous anecdotes that highlight the human side of ethics and make the book a pleasure to read. Ethics in Psychology will be an indispensable guide to ethical decision-making for all psychologists and students in psychology. (shrink)

Using firsthand accounts gleaned from notebooks, interviews, and correspondence of such twentieth-century scientists as Einstein, Fermi, and Millikan, Holton shows how the idea of the scientific imagination has practical implications for the history and philosophy of science and the larger understanding of the place of science in our culture.

A Nobel Prize-winning scientist and a leading brain researcher show how the brain creates conscious experience.

Philosophers working in the nascent field of ‘experimental philosophy’ have begun using methods borrowed from psychology to collect data about folk intuitions concerning debates ranging from action theory to ethics to epistemology. In this paper we present the results of our attempts to apply this approach to the free will debate, in which philosophers on opposing sides claim that their view best accounts for and accords with folk intuitions. After discussing the motivation for such research, we describe our methodology of (...) surveying people’s prephilosophical judgments about the freedom and responsibility of agents in deterministic scenarios. In two studies, we found that a majority of participants judged that such agents act of their own free will and are morally responsible for their actions. We then discuss the philosophical implications of our results as well as various difficulties inherent in such research. (shrink)

What exists at the fundamental level of reality? On the standard picture, the fundamental reality contains (among other things) fundamental matter, such as particles, fields, or even the quantum state. Non-fundamental facts are explained by facts about fundamental matter, at least in part. In this paper, I introduce a non-standard picture called the "cosmic void” in which the universe is devoid of any fundamental material ontology. Facts about tables and chairs are recovered from a special kind of laws that satisfy (...) strong determinism. All non-fundamental facts are completely explained by nomic facts. I discuss a concrete example of this picture in a strongly deterministic version of the many-worlds theory of quantum mechanics. I discuss some philosophical and scientific challenges to this view, as well as some connections to ontological nihilism. (shrink)

In this book G. A. Cohen examines the libertarian principle of self-ownership, which says that each person belongs to himself and therefore owes no service or product to anyone else. This principle is used to defend capitalist inequality, which is said to reflect each person's freedom to do as as he wishes with himself. The author argues that self-ownership cannot deliver the freedom it promises to secure, thereby undermining the idea that lovers of freedom should embrace capitalism and the inequality (...) that comes with it. He goes on to show that the standard Marxist condemnation of exploitation implies an endorsement of self-ownership, since, in the Marxist conception, the employer steals from the worker what should belong to her, because she produced it. Thereby a deeply inegalitarian notion has penetrated what is in aspiration an egalitarian theory. Purging that notion from socialist thought, he argues, enables construction of a more consistent egalitarianism. (shrink)

Philosophers often suggest that their theories of free will are supported by our phenomenology. Just as their theories conflict, their descriptions of the phenomenology of free will often conflict as well. We suggest that this should motivate an effort to study the phenomenology of free will in a more systematic way that goes beyond merely the introspective reports of the philosophers themselves. After presenting three disputes about the phenomenology of free will, we survey the (limited) psychological research on the experiences (...) relevant to the philosophical debates and then describe some pilot studies of our own with the aim of encouraging further research. The data seem to support compatibilist descriptions of the phenomenology more than libertarian descriptions. We conclude that the burden is on libertarians to find empirical support for their more demanding metaphysical theories with their more controversial phenomenological claims. (shrink)

This paper talks about Heidegger’s concept of authentic existence. One has to accept or “own” his very self in order to attain authenticity. No matter how incomplete one’s existence intrinsically is, he must own such an existence in that only in doing so can one fully realize the magnitude and necessity for himself to exist authentically. Needless to say, however, the call for the human person to exist authentically requires him to come to terms with fear, dread, and concern. Fear, (...) because the person is a being who is “hurled over” into the world; dread, because one has to face squarely his own facticity; and concern, because one has to relate himself to the world without losing grip of one’s own existence. (shrink)

Let ℋ be a finite-dimensional complex Hilbert space and D the set of density matrices on ℋ, i.e., the positive operators with trace 1. Our goal in this note is to identify a probability measure u on D that can be regarded as the uniform distribution over D. We propose a measure on D, argue that it can be so regarded, discuss its properties, and compute the joint distribution of the eigenvalues of a random density matrix distributed according to this (...) measure. (shrink)

In the present study it has been examined how children?s creative writing tasks may contribute to teachers? understanding of children?s values. Writings of 300 elementary school children about what they would do if they were the boss of The Netherlands were obtained and seemed to reflect different types of values. Most children were concerned with charity. Also, writings concerned materialist values and socio?political topics, such as human rights, power and tolerance. Analyses of group?specific differences showed girls to write more about (...) charity and health when compared to boys. Children from low socio?economic backgrounds wrote less about environmental issues compared to children from middle and high socio?economic backgrounds. Children from ethnic minority backgrounds who wrote more about obtaining goods for themselves and less about environmental issues than Dutch?origin children. In addition, age differences were found in line with an increase in social and moral development. These differences are discussed in light of differential socialisation practices. (shrink)

We expect the laws of nature that describe the universe to be exact, but what if that isn't true? In this popular science article, I discuss the possibility that some candidate fundamental laws of nature, such as the Past Hypothesis, may be vague. This possibility is in conflict with the idea that the fundamental laws of nature can always and faithfully be described by classical mathematics. -/- [Bibliographic note: this article is featured on the magazine website under a different title (...) as "The fuzzy law that could break the idea of a mathematical universe" and on the magazine cover as "The Flaw at the Heart of Reality: Why precise mathematical laws can never fully explain the universe." It is a popular version of the article "Nomic Vagueness" that can be found on arXiv: 2006.05298.]. (shrink)

This paper investigates Western professional bankers’ perceptions of Islamic finance. Exploiting data from an original survey, we carry out a principal component analysis to characterize the main dimensions on which financial agents diverge. The PCA extracts five dimensions—accounting for 61 % of the variance in the agents’ answers—that we interpret with the help of a pilot field survey. In addition to confirm the increased association of Islamic financial values with ethical practices in the West, our results allow us to understand (...) how the observed growth of the industry has been conceptualized by conventional agents. The five dimensions identified shed light on the multitude of constructs that have informed the diffusion of Islamic financial ideas to international markets. This supports the fact that Islamic finance cannot be seen as a single movement but is characterized by opposing and concurrent logics in global markets. (shrink)