We propose a technical reformulation of the measurement problem of quantum mechanics, which is based on the postulate that the final state of a measurement is classical; this accords with experimental practice as well as with Bohr’s views. Unlike the usual formulation (in which the post-measurement state is a unit vector in Hilbert space), our version actually opens the possibility of admitting a purely technical solution within the confines of conventional quantum theory (as opposed to solutions that either modify this (...) theory, or introduce unusual and controversial interpretative rules and/or ontologies). To that effect, we recall a remarkable phenomenon in the theory of Schrödinger operators (discovered in 1981 by Jona-Lasinio, Martinelli, and Scoppola), according to which the ground state of a symmetric double-well Hamiltonian (which is paradigmatically of Schrödinger’s Cat type) becomes exponentially sensitive to tiny perturbations of the potential as ħ→0. We show that this instability emerges also from the textbook wkb approximation, extend it to time-dependent perturbations, and study the dynamical transition from the ground state of the double well to the perturbed ground state (in which the cat is typically either dead or alive, depending on the details of the perturbation). Numerical simulations show that adiabatically arising perturbations may (quite literally) cause the collapse of the wave-function in the classical limit. Thus, at least in the context of a simple mathematical model, we combine the technical and conceptual virtues of decoherence (which fails to solve the measurement problem but launches the key idea that perturbations may come from the environment) with those of dynamical collapse models à la grw (which do solve the measurement problem but are ad hoc), without sharing their drawbacks: single measurement outcomes are obtained (instead of merely diagonal reduced density matrices), and no modification of quantum mechanics is needed. (shrink)

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are (...) covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence. (shrink)

I argue that Bohmian mechanics cannot reasonably be claimed to be a deterministic theory. If one assumes the “quantum equilibrium distribution” provided by the wave function of the universe, Bohmian mechanics requires an external random oracle in order to describe the algorithmic randomness properties of typical outcome sequences of long runs of repeated identical experiments. This oracle lies beyond the scope of Bohmian mechanics, including the impossibility of explaining the randomness property in question from “random” initial conditions. Thus the advantages (...) of Bohmian mechanics over other interpretations of quantum mechanics, if any, must lie at an ontological level, and in its potential to derive the quantum equilibrium distribution and hence the Born rule. (shrink)

Wat is toeval? Bestaat het? Hoe moeten we toeval interpreteren? Is alles logisch te verklaren, of is er meer tussen hemel en aarde? In dit boek kijken we naar een vakantieganger die op Bali onverwacht zijn buurman tegenkomt, de Shakespeare-onderzoeker die per toeval de sleutel tot de ware identiteit van de bard in diens teksten denkt te ontwaren, de man die altijd gezond leefde maar plotseling een ongeneeslijke vorm van kanker krijgt, gelovigen die de hand van God denken te zien (...) in het perfecte samenspel van de natuurconstanten dat leven mogelijk maakt, fysici die de grondslagen van de kwantummechanica of de richting van de tijd onderzoeken, biologen die Darwins evolutietheorie proberen te doorgronden, de filosofie van de vrije wil, en ten slotte Jezus als een toevallig of een noodzakelijk fenomeen. In zijn nieuwste boek geeft mathematisch fysicus Klaas Landsman zowel een inleiding als een visie op al deze onderwerpen, die iedereen met belangstelling voor de combinatie van wetenschap en levensbeschouwing zal raken en op nieuwe gedachten zal brengen. (shrink)

This book presents a multidisciplinary perspective on chance, with contributions from distinguished researchers in the areas of biology, cognitive neuroscience, economics, genetics, general history, law, linguistics, logic, mathematical physics, statistics, theology and philosophy. The individual chapters are bound together by a general introduction followed by an opening chapter that surveys 2500 years of linguistic, philosophical, and scientific reflections on chance, coincidence, fortune, randomness, luck and related concepts. A main conclusion that can be drawn is that, even after all this time, (...) we still cannot be sure whether chance is a truly fundamental and irreducible phenomenon, in that certain events are simply uncaused and could have been otherwise, or whether it is always simply a reflection of our ignorance. Other challenges that emerge from this book include a better understanding of the contextuality and perspectival character of chance (including its scale-dependence), and the curious fact that, throughout history (including contemporary science), chance has been used both as an explanation and as a hallmark of the absence of explanation. As such, this book challenges the reader to think about chance in a new way and to come to grips with this endlessly fascinating phenomenon. (shrink)

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

Bell’s Theorem from Physics 36:1–28 (1964) and the (Strong) Free Will Theorem of Conway and Kochen from Notices AMS 56:226–232 (2009) both exclude deterministic hidden variable theories (or, in modern parlance, ‘ontological models’) that are compatible with some small fragment of quantum mechanics, admit ‘free’ settings of the archetypal Alice and Bob experiment, and satisfy a locality condition akin to parameter independence. We clarify the relationship between these theorems by giving reformulations of both that exactly pinpoint their resemblance and their (...) differences. Our reformulation imposes determinism in what we see as the only consistent way, in which the ‘ontological state’ initially determines both the settings and the outcome of the experiment. The usual status of the settings as ‘free’ parameters is subsequently recovered from independence assumptions on the pertinent (random) variables. Our reformulation also clarifies the role of the settings in Bell’s later generalization of his theorem to stochastic hidden variable theories. (shrink)

We tentatively propose two guiding principles for the construction of theories of physics, which should be satisfied by a possible future theory of quantum gravity. These principles are inspired by those that led Einstein to his theory of general relativity, viz. his principle of general covariance and his equivalence principle, as well as by the two mysterious dogmas of Bohr's interpretation of quantum mechanics, i.e. his doctrine of classical concepts and his principle of complementarity. An appropriate mathematical language for combining (...) these ideas is topos theory, a framework earlier proposed for physics by Isham and collaborators. Our "Principle of general tovariance" states that any mathematical structure appearing in the laws of physics must be definable in an arbitrary topos (with natural numbers object) and must be preserved under so-called geometric morphisms. This principle identifies geometric logic as the mathematical language of physics and restricts the constructions and theorems to those valid in intuitionism: neither Aristotle's principle of the excluded third nor Zermelo's Axiom of Choice may be invoked. Subsequently, our "Equivalence principle" states that any algebra of observables (initially defined in the topos Sets) is empirically equivalent to a commutative one in some other topos. (shrink)

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

This is a joint review of Jenann Ismael's 'How physics makes us free' (OUP).

The ambition of this volume is twofold: to provide a comprehensive overview of the field and to serve as an indispensable reference work for anyone who wants to work in it. For example, any philosopher who hopes to make a contribution to the topic of the classical-quantum correspondence will have to begin by consulting Klaas Landsman’s chapter. The organization of this volume, as well as the choice of topics, is based on the conviction that the important problems in (...) the philosophy of physics arise from studying the foundations of the fundamental theories of physics. It follows that there is no sharp line to be drawn between philosophy of physics and physics itself. Some of the best work in the philosophy of physics is being done by physicists, as witnessed by the fact that several of the contributors to the volume are theoretical physicists: viz., Ellis, Emch, Harvey, Landsman, Rovelli, ‘t Hooft, the last of whom is a Nobel laureate. Key features - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences that have grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers. (shrink)

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

God is traditionally taken to be a necessarily existing being who is unsurpassably powerful, knowledgeable, and good. The familiar problem of actual evil claims that the presence of gratuitous suffering in the actual world constitutes evidence against the existence of such a being. In contrast, the problem of possible evil claims that the possibility of bad worlds constitutes evidence against theism. How? It seems plausible to suppose that there are very bad possible worlds. But if God exists in every world, (...) then God exists in those, too. And if God exists in very bad worlds, some say, God is culpable for not ensuring that they are better. In what follows, I consider this argument, survey some responses, and offer a novel solution. Along the way, I argue that theists should maintain that the actual world is a multiverse featuring all and only universes worthy of being created and sustained by God, and – more controversially – I suggest that theists should embrace modal collapse: the claim that this multiverse is the only possible world. (shrink)

Einstein's philosophy of physics was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and "physical laws", to be impossible. Bohr's philosophy, on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic quantum theory that - within an appropriate class of physical theories - suitable mathematical translations of the (...) doctrines of Bohr and Einstein are equivalent. Thus - upon our specific formalization - quantum mechanics accommodates Einstein's Trennungsprinzip if and only if it is interpreted a la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in this constructive way, since their debate was dominated by Einstein's ingenious but ultimately flawed attempts to establish the "incompleteness" of quantum mechanics. This aspect of their debate may still be understood and appreciated, however, as reflecting a much deeper and insurmountable disagreement between Bohr and Einstein about the knowability of Nature. Using the theological controversy on the knowability of God as a analogy, we can say that Einstein was a Spinozist, whereas Bohr could be said to be on the side of Maimonides. Thus Einstein's off-the-cuff characterization of Bohr as a 'Talmudic philosopher' was spot-on. (shrink)

Here Julie Landsman chronicles one year as a teacher in a program for students in such serious trouble they are asked to leave their middle schools and attend a special program for disruptive students. She allows her readers to get to know the students, their home and street situations, and how their stories develop over the year, and in doing so, shows the complexity of young people, their beauty, and their individuality.

In recent decades, there has been astonishing growth in scientific theorizing about multiverses. Once considered outré or absurd, multiple universe theories appear to be gaining considerable scientific respectability. There are, of course, many such theories, including (i) Everett’s (1957) many worlds interpretation of quantum mechanics, defended by Deutsch (1997) and others; (ii) Linde’s (1986) eternal inflation view, which suggests that universes form like bubbles in a chaotically inflating sea; (iii) Smolin’s (1997) fecund universe theory, which proposes that universes are generated (...) through black holes; (iv) the cyclic model, recently defended using string/M theory by Steinhardt and Turok (2007), which holds that distinct universes are formed in a never-ending sequence of Big Bangs and Big Crunches; and (v) Tegmark’s (2007) “Level IV” multiverse, which contains many universes governed by distinct mathematical and scientific laws. While not all of these preclude each other, the details and implications of each one are hotly contested. In one area within the philosophy of religion (the debate concerning the “fine-tuning” argument), scientific multiverse theories are widely held to be hostile to theism. This is because such theories appear to account for the relevant data – the biophilic parameters of the universe we inhabit – without appeal to an intelligent designer. Yet, in recent years, several philosophers and one physicist have offered reasons for thinking that if theism is true, the actual world comprises (or probably comprises) many universes. I first set out some requirements – both scientific and otherwise – for such a theory. I then survey some problems such theories are held to face, and some prospects they are thought to have. Finally, I examine arguments both for and against the claim that multiverse theories can help theists respond to the problem of evil. I conclude that such theories advantage neither the theist or the atheist in the debate about evil: they merely require reframing arguments from evil. (shrink)

Aumann and Serrano :810–836, 2008) introduce the axiom of duality, which ensures that risk measures respect comparative risk aversion. This paper characterizes all dual risk measures by a simple equivalent condition. This equivalence provides a decomposition result and a construction method, which is used to analyze concrete dual measures. Moreover, this paper aims to extend this characterization to the most general setting. Compared with Aumann and Serrano, it, therefore, relaxes the axiom of positive homogeneity, and allows for risk-neutral and risk-seeking (...) agents, as well as for all integrable gambles. (shrink)

In contemporary analytic philosophy, the problem of evil refers to a family of arguments that attempt to show, by appeal to evil, that God does not exist. Some very important arguments in this family focus on gratuitous evil. Most participants in the relevant discussions, including theists and atheists, agree that God is able to prevent all gratuitous evil and that God would do so. On this view, of course, the occurrence of even a single instance of gratuitous evil falsifies theism. (...) The most common response to such arguments attempts to cast doubt on the claim that gratuitous evil really occurs. The focus of these two survey papers will be a different response—one that has received less attention in the literature. This response attempts to show that God and gratuitous evil are compatible. If it succeeds, then the occurrence of gratuitous evil does not, after all, count against theism. After introducing some key terms, I survey the literature surrounding the attempts by Michael Peterson and John Hick to execute this strategy. In a follow-up paper, I discuss the attempts of William Hasker, Peter van Inwagen, and Michael Almeida, respectively. (shrink)

God is traditionally understood to be a perfect being who is the creator and sustainer of all that is. God's creative and sustaining activity is often thought to involve choosing a possible world for actualization. It is generally said that either there is (a) exactly one best of all possible worlds, or there are (b) infinitely many increasingly better worlds, or else there are (c) infinitely many unsurpassable worlds within God's power to actualize. On each view, critics have offered arguments (...) for atheism that turn on God's choice of a world. In what follows, I first discuss some background issues, and I then survey the contemporary literature on these arguments. (shrink)

Theism is the view that God exists; naturalism is the view that there are no supernatural beings, processes, mechanisms, or forces. This Element explores whether things are better, worse, or neither on theism relative to naturalism. It introduces readers to the central philosophical issues that bear on this question, and it distinguishes a wide range of ways it can be answered. It critically examines four views, three of which hold that things are better on theism than on naturalism, and one (...) of which holds just the opposite. (shrink)

The question of whether God exists has long preoccupied philosophers. Many accounts of God have been proposed, and many arguments for and against God’s existence have been offered and discussed. But while philosophers have been busy trying to determine whether or not God exists, they have generally neglected to ask this question: "Does it _matter _whether God exists?" _Does God Matter?_ features ten original essays written by prominent philosophers of religion that address this very important, yet surprisingly neglected, question. One (...) natural way to approach this question is to seek to understand what difference God’s existence would—or does—make to the value of the world and the well-being of its inhabitants. The three essays in Section I defend versions of _pro-theism_: the view that God’s existence would, or does, make things better than they would otherwise be. The three subsequent essays in Section II defend _anti-theism_: the view that God’s existence would, or does, make things worse than they would otherwise be. The final four essays in Section III consider the interplay between the existential and axiological debates concerning the existence of God. This book presents important research on a growing topic in philosophy of religion that will also be of keen interest to scholars working in other areas of philosophy, and in other disciplines. (shrink)

In recent decades, scientific theories have postulated the existence of many universes beyond our own. The details and implications of these theories are hotly contested. Some philosophers argue that these scientific models count against the existence of God. Others, however, argue that if God exists, a multiverse is precisely what we should expect to find. Moreover, these philosophers claim that the idea of a divinely created multiverse can help believers in God respond to certain arguments for atheism. These proposals are, (...) of course, also extremely controversial. This volume collects together twelve newly published essays – two by physicists, and ten by philosophers – that discuss various aspects of this issue. Some of the essays support the idea of a divinely created multiverse; others oppose it. Scientific, philosophical, and theological issues are considered. (shrink)

Beginning with Anderson, spontaneous symmetry breaking in infinite quantum systems is often put forward as an example of emergence in physics, since in theory no finite system should display it. Even the correspondence between theory and reality is at stake here, since numerous real materials show ssb in their ground states, although they are finite. Thus against what is sometimes called ‘Earman's Principle’, a genuine physical effect seems theoretically recovered only in some idealisation, disappearing as soon as the idealisation is (...) removed.We review the well-known arguments that no finite system can exhibit ssb, using the formalism of algebraic quantum theory in order to control the thermodynamic limit and unify the description of finite- and infinite-volume systems. Using the striking mathematical analogy between the thermodynamic limit and the classical limit, we show that a similar situation obtains in quantum mechanics versus classical mechanics.This discrepancy between formalism and reality is quite similar to the measurement problem, and hence we address it in the same way, adapting an argument of the Landsman and Reuvers that was originally intended to explain the collapse of the wave-function within conventional quantum mechanics. Namely, exponential sensitivity to perturbations of the dynamics as the system size increases causes symmetry breaking already in finite but very large quantum systems. This provides continuity between finite- and infinite-volume descriptions of quantum systems featuring ssb and hence restores Earman's Principle. (shrink)

In recent years, epistemologists have devoted enormous attention to this question: what should happen when two epistemic peers disagree about the truth-value of some proposition? Some have argued that that in all such cases, both parties are rationally required to revise their position in some way. Others have maintained that, in at least some cases, neither party is rationally required to revise her position. In this paper, I examine a provocative and under-appreciated argument for the latter view due to Elgin (...) Disagreement, Oxford University Press, Oxford, pp 53–68, 2010; The Philosopher’s Magazine, fourth quarter, pp 77–82, 2012; True enough, MIT Press, Cambridge, 2017; in: Johnson Voicing dissent: the ethics and epistemology of making disagreement public, Routledge, New York, pp 10–21, 2018). I defend it against a series of objections, and I then identify some fruitful ways in which her view could be developed further. (shrink)

We attempt to clarify the main conceptual issues in approaches to ‘objectification’ or ‘measurement’ in quantum mechanics which are based on superselection rules. Such approaches venture to derive the emergence of classical ‘reality’ relative to a class of observers; those believing that the classical world exists intrinsically and absolutely are advised against reading this paper. The prototype approach (K. Hepp, Helv. Phys. Acta45 (1972), 237–248) where superselection sectors are assumed in the state space of the apparatus is shown to be (...) untenable. Instead, one should couple system and apparatus to an environment, and postulate superselection rules for the latter. These are motivated by the locality of any observer or other (actual or virtual) monitoring system. In this way ‘environmental’ solutions to the measurement problem (H.D. Zeh, Found. Phys.1 (1970), 69–76; W. H. Zurek, Phys. Rev.D26 (1982), 1862–1880 and Progr. Theor. Phys.89 (1993), 281–312) become consistent and acceptable, too. Points of contact with the modal interpretation are briefly discussed. We propose a minimal value attribution to observables in theories with superselection rules, in which only central observables have properties. In particular, the eigenvector-eigenvalue link is dropped. This is mainly motivated by Ockham's razor. (shrink)

In contemporary analytic philosophy, the problem of evil refers to a family of arguments that attempt to show, by appeal to evil, that God does not exist. Some very important arguments in this family focus on gratuitous evil. Most participants in the relevant discussions, including theists and atheists, agree that God is able to prevent all gratuitous evil, and that God would do so. On this view, of course, the occurrence of even a single instance of gratuitous evil falsifies theism. (...) The most common response to such arguments attempts to cast doubt on the claim that gratuitous evil really occurs. The focus of these two survey papers will be a different response – one that has received less attention in the literature. This response attempts to show that God and gratuitous evil are compatible. If it succeeds, then the occurrence of gratuitous evil does not, after all, count against theism. In the prequel to this paper, I surveyed the literature surrounding the attempts by Michael Peterson and John Hick to execute this strategy. Here, I survey the attempts due to William Hasker, Peter van Inwagen, and Michael Almeida, respectively. (shrink)

What the Emperor Built: Architecture and Empire in the Early Ming. By Aurelia Campbell. Seattle: University of Washington Press, 2020. Pp. xiv + 217. $65.

If one formulates Helmholtz’s ideas about perception in terms of modern-day theories one arrives at a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts. Using constructs from statistical physics it can be shown that the problems of inferring what cause our sensory inputs and learning causal regularities in the sensorium can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on (...) Empirical Bayes and hierarchical models of how sensory information is generated. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of the brain’s organisation and responses. In this paper, we suggest that these perceptual processes are just one emergent property of systems that conform to a free-energy principle. The free-energy considered here represents a bound on the surprise inherent in any exchange with the environment, under expectations encoded by its state or configuration. A system can minimise free-energy by changing its configuration to change the way it samples the environment, or to change its expectations. These changes correspond to action and perception, respectively, and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment implies that the system’s state and structure encode an implicit and probabilistic model of the environment. We will look at models entailed by the brain and how minimisation of free-energy can explain its dynamics and structure. (shrink)

Growing Up White is for everyone who wants to know more about our schools, our community, our country, and ourselves. Julie Landsman takes the reader on an inventory of her life, pulling from events and scenes, a set of lessons learned. She discloses honestly and unflinchingly the privileges she has experienced as a white person and connects those to her presence in city classrooms where she taught for over 25 years. As a teacher Julie made mistakes, learned from them, (...) made more and concludes that understanding race in America is an ongoing process. Her book is rich with suggestions for working in our schools today, where we find a primarily white teaching force and an expanding population of students of color. She believes that these students make our schools rich and exciting places in which to work. Landsman also believes that white teachers can reach their students in deep and positive ways. Because she invites you to go along with her in revealing the basis of her upbringing and her choices, the story itself is engaging. Readers arrive at the final chapters with an appreciation not only for the complexity of our history as individuals around race, gender and class but with real hope in education as a way to create a place where all children get a fair chance at success. (shrink)

We clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical statement: a quantum system described by a noncommutative C*-algebra of observables is empirically accessible only through associated commutative C*-algebras. The Born probabilities emerge as the relative frequencies of outcomes in long runs of measurements on a quantum system; it is not necessary to adopt the frequency interpretation of single-case probabilities (which will (...) be the subject of a sequel paper). Our derivation of the Born rule uses ideas from a program begun by Finkelstein (1965) and Hartle (1968), intending to remove the Born rule as a separate postulate of quantum mechanics. Mathematically speaking, our approach refines previous elaborations of this program - notably the one due to Farhi, Goldstone, and Gutmann (1989) as completed by Van Wesep (2006) - in replacing infinite tensor products of Hilbert spaces by continuous fields of C*-algebras. In combination with our interpretational context, this technical improvement circumvents valid criticisms that earlier derivations of the Born rule have provoked, especially to the effect that such derivations were mathematically flawed as well as circular. Furthermore, instead of relying on the controversial eigenvector-eigenvalue link in quantum theory, our derivation just assumes that pure states in classical physics have the usual interpretation as truthmakers that assign sharp values to observables. (shrink)

On what basis does God choose a possible world to make actual? Theists typically claim that God freely selects exactly one world on the basis of its axiological characteristics. But suppose that there are infinitely many unsurpassable worlds from which to choose; or else that there are no unsurpassable worlds, but instead an infinite hierarchy of increasingly better worlds. On each of these scenarios, philosophers have alleged that God is unable rationally to choose a world for actualization. In the former (...) case, God lacks sufficient reason to select any particular world, since there are infinitely many other equally good candidates. In the latter case, God lacks sufficient reason to select any particular world, since for any world there are infinitely many better candidates. These considerations generate arguments for atheism, as follows. On theism, God is supposed to be the explanation for this world ’s being actual, and God requires sufficient reasons for action. So on either scenario or, since there is an actual world, and since God could not have had a sufficient reason for selecting it, this world was not actualized by God. In response, defenders of theism have urged that God need not have sufficient reason for choosing a world on or : God may defensibly choose a world at random. In what follows, I evaluate this reply. I conclude that it succeeds only on the enormously implausible assumption that there is exactly one randomizer available to God. (shrink)

God is traditionally taken to be a perfect being, and the creator and sustainer of all that is. So, if theism is true, what sort of world should we expect? To answer this question, we need an account of the array of possible worlds from which God is said to choose. It seems that either there is (a) exactly one best possible world; or (b) more than one unsurpassable world; or (c) an infinite hierarchy of increasingly better worlds. Influential arguments (...) for atheism have been advanced on each hierarchy, and these jointly comprise a daunting trilemma for theism. In this paper, I argue that if theism is true, we should expect the actual world to be a multiverse comprised of all and only those universes which are worthy of creation and sustenance. I further argue that this multiverse is the unique best of all possible worlds. Finally, I explain how his unconventional view bears on the trilemma for theism. (shrink)

English summary: German linguistics, formerly internationally inspiring, fell into a deep crisis at the beginning of the twentieth century. Since the First World War, those in the field have been looking for ways to regain its lost scientific and social recognition. This desire for relevance was particularly clear when practitioners of the different approaches to linguistic innovation competed for the scarce resources of public research funding. The remaining funding documents of the German Research Foundation demonstrate which specific linguistic approaches were (...) proclaimed as critical by researchers, and which were honored by outside funders during changing political contexts. Thus, the history of German philology and the development of its dynamics is here - for the first time - traced from the perspective of public support for research, from the time of the Weimar Republic until the first decades of the Federal Republic. German text. German description: Die ehemals international impulsgebende deutsche Sprachwissenschaft geriet am Anfang des zwanzigsten Jahrhunderts in eine tiefe Krise. Seit dem Ersten Weltkrieg suchte das Fach nach Wegen, die verlorene wissenschaftliche und gesellschaftliche Anerkennung wieder zu erlangen.Dieser Wille zur Relevanz zeigte sich besonders deutlich, wo die verschiedenen Neuerungsansatze der Sprachforschung um die knappen Mittel der staatlichen Forschungsforderung konkurrierten. An den erhaltenen Forderakten der Deutschen Forschungsgemeinschaft ist abzulesen, welche spezifischen Aufgabenstellungen die Sprachwissenschaft in wechselnden politischen Kontexten jeweils 'nach aussen' proklamierte und 'von aussen' honoriert bekam.So wird hier aus der Perspektive der staatlichen Forschungsforderung die Geschichte der deutschen Sprachforschung in ihrer Entwicklungsdynamik erstmals von der Weimarer Republik bis in die ersten Jahrzehnte der Bundesrepublik nachgezeichnet. (shrink)