The paper explains in what sense the GRW matter density theory is a primitive ontology theory of quantum mechanics and why, thus conceived, the standard objections against the GRW formalism do not apply to GRWm. We consider the different options for conceiving the quantum state in GRWm and argue that dispositionalism is the most attractive one.

The Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide (...) here something that has until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRW world, for example the number of collapses in a system during a chosen time interval. (shrink)

The Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide (...) here something that has until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRWm or GRWf world. (shrink)

The paper seeks to make progress from stating primitive ontology theories of quantum physics – notably Bohmian mechanics, the GRW matter density theory and the GRW flash theory – to assessing these theories. Four criteria are set out: internal coherence; empirical adequacy; relationship to other theories; explanatory value. The paper argues that the stock objections against these theories do not withstand scrutiny. Its focus then is on their explanatory value: they pursue different strategies to ground the (...) textbook formalism of quantum mechanics, and they develop different explanations of quantum non-locality. In conclusion, it is argued that Bohmian mechanics offers a better prospect for making quantum non-locality intelligible than the GRW matter density theory and the GRW flash theory. (shrink)

The wavefunction is the central mathematical entity of quantum mechanics, but it still lacks a universally accepted interpretation. Much effort is spent on attempts to probe its fundamental nature. Here I investigate the consequences of a matter ontology applied to spherical masses of constant bulk density. The governing equation for the center-of-mass wavefunction is derived and solved numerically. The ground state wavefunctions and resulting matter densities are investigated. A lowering of the density from its bulk value (...) is found for low masses due to increased spatial spreading. A discussion of the possibility to experimentally observe these effects is given and the possible consequences for choosing an ontological interpretation for quantum mechanics are commented upon. (shrink)

The paper has two aims: (1) it sets out to show that it is well motivated to seek for an account of quantum non-locality in the framework of ontic structural realism (OSR), which integrates the notions of holism and non-separability that have been employed since the 1980s to achieve such an account. However, recent research shows that OSR on its own cannot provide such an account. Against this background, the paper argues that by applying OSR to the primitive ontology theories (...) of quantum physics, one can accomplish that task. In particular, Bohmian mechanics offers the best prospect for doing so. (2) In general, the paper seeks to bring OSR and the primitive ontology theories of quantum physics together: on the one hand, in order to be applicable to quantum mechanics, OSR has to consider what the quantum ontology of matter distributed in space-time is. On the other hand, as regards the primitive ontology theories, OSR provides the conceptual tools for these theories to answer the question of what the ontological status of the wave-function is. (shrink)

Two views on the direction of time can be distinguished—primitivism and non-primitivism. According to the former, time’s direction is an in-built, fundamental property of the physical world. According to the latter, time’s direction is a derivative property of a fundamentally directionless reality. In the literature, non-primitivism has been widely supported since most our fundamental dynamical laws are time-reversal invariant. In this paper, I offer a way out to the primitivist. I argue that we do have good grounds to support a (...) primitive direction of time in the quantum realm. The rationale depends on exploiting the metaphysical and dynamical underdetermination of quantum theories to make a case in favor of primitivism. In particular, primitivism can be grounded in spontaneous collapse theories. The specific sense in which these theories capture a primitive direction of time is that, when the ontology of the theory is seriously taken into account, it does not remain invariant under time reversal. In taking GRW with a matter-density field, I will argue that primitivism about the direction of time can be defended in the quantum case. (shrink)

GianCarlo Ghirardi passed away on June 1st, 201. He would have turned 83 on October 28, 2018. He was without any doubt one of the most prominent theoretical physicists working on the foundation and the philosophy of quantum mechanics. In this paper I review some of his achievements and underline how his research influenced the philosophy of physics community.

John Bell proposed an ontology for the GRW modification of quantum mechanics in terms of flashes occurring at space- time points. This article spells out the motivation for this ontology, inquires into the status of the wave function in it, critically examines the claim of its being Lorentz invariant, and considers whether it is a parsimonious but nevertheless physically adequate ontology.

The paper explains why an ontology of permanent point particles that are individuated by their relative positions and that move on continuous trajectories as given by a deterministic law of motion constitutes the best solution to the measurement problem in both quantum mechanics and quantum field theory. This case is made by comparing the Bohmian theory to collapse theories such as the GRW matter density and the GRW flash theory. It is argued that the Bohmian (...) theory makes the minimal changes, concerning only the dynamics and neither the ontology nor the account of probabilities, that are necessary to get from classical mechanics to quantum physics. There is no cogent reason to go beyond these minimal changes. (shrink)

The paper retraces the development from the measurement problem to the primitive ontology programme. It assesses the contribution of the GRW theory to this programme and discusses the pros and cons of the GRWm matter density ontology and the GRWf flash ontology in comparison to the Bohmian particle ontology. It thereby pursues the evaluation of the proposals for a primitive ontology of quantum physics.

The Mass Density approach to GRW (GRWm for short) has been widely discussed in the quantum foundations literature. A crucial feature of GRWm is the introduction of a Criterion of Accessibility for mass, which allows to explain the determinacy of experimental outcomes thus also addressing the tails problem of GRW. However, the Criterion of Accessibility leaves the ontological meaning of the non-accessible portion of mass utterly unexplained. In this paper I discuss two viable approaches to non-accessible mass, which I (...) call anti-realist and realist, and will defend the latter. First, I show that the anti-realist approach suffers from various objections. Second, I develop an account of non-accessible mass density states as objectively indeterminate states of affairs. (shrink)

This book offers a theory of how human conceptual life begins, and shows how perceptual information becomes transformed into concepts. Drawing on extensive research, Mandler describes the development of preverbal concept formation, inductive inference, and recall, and explains how these processes form the conceptual basis for language and adult thought.

An equation proposed by Levy, Perdew and Sahni (Phys. Rev. A 30:2745, 1984) is an orbital-free formulation of density functional theory. However, this equation describes a bosonic system. Here, we analyze on a very fundamental level, how this equation could be extended to yield a formulation for a general fermionic distribution of charge and spin. This analysis starts at the level of single electrons and with the question, how spin actually comes into a charge distribution in a non-relativistic (...) model. To this end we present a space-time model of extended electrons, which is formulated in terms of geometric algebra. Wave properties of the electron are referred to mass density oscillations. We provide a comprehensive and non-statistical interpretation of wavefunctions, referring them to mass density components and internal field components. It is shown that these wavefunctions comply with the Schrödinger equation, for the free electron as well as for the electron in electrostatic and vector potentials. Spin-properties of the electron are referred to intrinsic field components and it is established that a measurement of spin in an external field yields exactly two possible results. However, it is also established that the spin of free electrons is isotropic, and that spin-dynamics of single electrons can be described by a modified Landau-Lifshitz equation. The model agrees with the results of standard theory concerning the hydrogen atom. Finally, we analyze many-electron systems and derive a set of coupled equations suitable to characterize the system without any reference to single electron states. The model is expected to have the greatest impact in condensed matter theory, where it allows to describe an N-electron system by a many-electron wavefunction Ψ of four, instead of 3N variables. The many-body aspect of a system is in this case encoded in a bivector potential. (shrink)

The paper argues that a causal explanation of the correlated outcomes of EPR-type experiments is desirable and possible. It shows how Bohmian mechanics and the GRW mass density theory offer such an explanation in terms of a non-local common cause.

The ideas of creatio ex nihilo of the universe and creatio continua of new matter out of nothing entered the arena of natural science with the advent of the Big Bang and the steady-state theories in the mid-twentieth century. Adolf Grünbaum has tried to interpret the steady-state theory in such a way, to show that the continuous formation of new matter out of nothing in this theory can be explained purely physically. In this paper, however, it (...) will be shown that Grünbaum's interpretation encounters at least three problems: not distinguishing between material and efficient causes, inconsistency, and misconceiving the law of density conservation. (shrink)

Spontaneous localization theory is a quantum theory proposed by GianCarlo Ghirardi, together with Alberto Rimini and Tullio Weber in 1986. However, soon it became clear to Ghirardi that his work was more than just one theory: he actually developed a framework, a family of theories in which the wavefunction jumps, but where the ontology of the theory is underdetermined. After acknowledging that the wavefunction did not provide a satisfactory ontology, he assumed that matter was described (...) by a continuous matter density field in three-dimensional space, whose evolution is governed by a stochastic wavefunction evolution. Alternatively, Bell assumed that the wavefunction would govern a spatiotemporal event ontology, dubbed ‘flashes.’ However, not much work has been done with the perhaps most obvious possibility, namely that physical objects are made of particles. This paper has two aims. First to explain the reason why people require spontaneous localization theory to be more than just a theory about the wavefunction. This is done by showing how the problem everyone in the foundation of quantum mechanics take to be the fundamental problem of quantum mechanics, namely the measurement problem, is a red herring. Then, the paper explores the possibility of spontaneous localization theories of particles. I argue that this discussion is not a mere exercise, as spontaneous localization theories of particles may be amenable to a relativistic extension which does not require a foliation, and because in general the peculiar type of indeterminism of spontaneous localization theories may help shedding new light on the nature of the tension between quantum theory and relativity. (shrink)

It is common to assume that Descartes did not have a conception of an object's matter density independently of its size, but this is a rather incomplete assessment of the early modern natural philosopher's theory. Key to our understanding of Descartes's physics is a consideration of the ratios between the quantities of the different types of matter in which an object consists. As these ratios determine the degree of an object's porosity and elasticity, they also affect (...) in Descartes's theory the phenomena of gravity and weight. (shrink)

I discuss the interpretation of spontaneous collapse theories, with particular reference to Bell's suggestion that the stochastic jumps in the evolution of the wave function should be considered as local beables of the theory. I develop this analogy in some detail for the case of non-relativistic GRW-type theories, using a generalisation of Bell's notion of beables to POV measures. In the context of CSL-type theories, this strategy appears to fail, and I discuss instead Ghirardi and co-workers' mass-density interpretation (...) and its relation to Schrödinger's original charge-density interpretation. This discussion is extended to relativistic CSL-type theories. A few remarks on Everett's interpretation conclude the paper. (shrink)

This book addresses a wide range of topics relating to the properties and behavior of condensed matter under extreme conditions such as intense magnetic and electric fields, high pressures, heat and cold, and mechanical stresses. It is divided into four sections devoted to condensed matter theory, molecular chemistry, theoretical physics, and the philosophy and history of science. The main themes include electronic correlations in material systems under extreme pressure and temperature conditions, surface physics, the transport properties of (...) low-dimensional electronic systems, applications of the density functional theory in molecular systems, and graphene. The book is the outcome of a workshop held at the University of Catania, Italy, in honor of Professor Renato Pucci on the occasion of his 70th birthday. It includes selected invited contributions from collaborators and co-authors of Professor Pucci during his long and successful career, as well as from other distinguished guest authors. (shrink)

1. The philosophical version of the primary-secondary distinction concerns (a) the 'real' properties of matter, (b) the epistemology of sensation, and (c) a contrast challenged by Berkely as illusory. The scientific version of the primary-secondary distinction concerns (a') the physical properties of matter, (b') a contrast essential within the history of atomism, and (c') a contrast challenged by 20th century microphysics as de facto untenable. 2. The primary-secondary distinction within physics can be interpreted in two ways: a. it (...) can refer to content; e.g. 'Matter has the properties of mass, shape, density... etc. -- it only appears to have the properties of warmth, fragrance, etc.' Or, b. it can refer to form; e.g. 'Whatever properties our best theories accord to primary matter, e.g., electrons, these are by definition primary. All other properties of, e.g., macromatter, are derivative.' Concerning 2.a., this interpretation is simply false when 17th, 18th, or 19th century values for the property-variables are introduced. Concerning 2.b., this either uninformative or misleading. It is uninformative when it constitutes no more than a decision to use the word 'primary' as an umbrella-word for all the properties contemporary micro-physics accords to fundamental material particles, whatever these may be. It is misleading when it turns on an implicit contrast between certain properties particles may be said to have when 'harnessed' to a detector, and certain other properties these particles have when free and unharnessed to any detector. This contrast does not exist. Quantum-theoretic information is always about particles-and-their-detectors-in-combination. Dissolve this combination and you destroy any possible knowledge of the particle. Hence the notion of 'completely objectifiable properties of particles' is in principle unsound. (shrink)

Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about 'matter' moving in space, represented by either particle trajectories, fields on space-time, or a discrete (...) set of space-time points. The role of the wave function then is to govern the motion of the matter. (shrink)

In the Metaphysical Foundations of Natural Science (MFNS) Kant develops a conception of matter that is meant to issue in an alternative to what he takes to be the then reigning empiricist account of density. However, in recent years commentator after commentator has argued that Kant’s attempt on this front is faced with insuperable difficulties. Adickes argues that the MFNS theory of density involves Kant in a vicious circle; Tuschling argues that the circle is part of (...) what led Kant to abandon the theory of matter developed in the MFNS; Förster argues that recognition of this circularity played a significant role in Kant’s development of the project now known as the Opus Postumum; and Westphal argues that the circularity problem serves to demonstrate the “untenability of Kant’s metaphysical method” and therefore helps to explain “the radical revision of the relation between mathematics and metaphysics Kant undertakes in his opus postumum.” Indeed, even Kant seems to think that his theory of density is circular: as noted by all of these commentators, in correspondence with one of his former students Kant declares that this theory “seems to lead however to a circle out of which I am not able to come.” Against this growing tide (and even, it seems, against Kant himself) I defend Kant’s theory of density. I argue that the suspicion of a circle results from a confusion of logical relations with causal conditions, and I argue that even Kant seems to have been taken in by this confusion. (shrink)

We derive the first analytical formula for the density of "Dark Matter" (DM) at all length scales, thus also for the rotation curves of stars in galaxies, for the baryonic Tully–Fisher relation and for planetary systems, from Einstein's equations (EE) and classical approximations, in agreement with observations. DM is defined in Part I as the energy of the coherent gravitational field of the universe, represented by the additional equivalent ordinary matter (OM), needed at all length scales, to (...) explain classically, with inclusion of the OM, the _observed coherent_ gravitational field. Our derivation uses both EE and the Newtonian approximation of EE in Part I, to describe semi-classically in Part II the advection of DM, created at the level of the universe, into galaxies and clusters thereof. This advection happens proportional with their own classically generated gravitational field g, due to self-interaction of the gravitational field. It is based on the universal formula ρ D = λgg′ 2 for the density ρ D of DM advected into medium and lower scale structures of the observable universe, where λ is a universal constant fixed by the Tully–Fisher relations. Here g′ is the gravitational field of the universe; g′ is in main part its own source, as implied in Part I from EE. We start from a simple electromagnetic analogy that helps to make the paper generally accessible. This paper allows for the first time the exact calculation of DM in galactic halos and at all levels in the universe, based on EE and Newtonian approximations, in agreement with observations. (shrink)

This article seeks to provide a historically well-informed analysis of an important post-Newtonian area of research in experimental physics between 1798 and 1898, namely the determination of the mean density of the earth and, by the end of the nineteenth century, the gravitational constant. Traditionally, research on these matters is seen as a case of “puzzle solving.” In this article, the author shows that such focus does not do justice to the evidential significance of eighteenth- and nineteenth-century experimental research (...) on the mean density of the earth and the gravitational constant. As Newton’s theory of universal gravitation was mainly based on astronomical observation, it remained to be shown that Newton’s law of universal gravitation did not break down at terrestrial distances. In this context, Cavendish’ experiment and related nineteenth-century experiments played a decisive role, for they provided converging and increasingly stronger evidence for the universality of Newton’s theory of gravitation. More precisely, the author shall argue that, as the accuracy and precision of the experimental apparatuses and the procedures to eliminate external disturbances involved increasingly improved, the empirical support for the universality of Newton’s theory of gravitation improved correspondingly. (shrink)

Kant's special metaphysics is intended to provide the a priori foundation for Newtonian science, which is to be achieved by exhibiting the a priori content of Newtonian concepts and laws. Kant envisions a two-step mathematical construction of the dynamical concept of matter involving a geometrical construction of matter’s bulk and a symbolic construction of matter’s density. Since Newton himself defines quantity of matter in terms of bulk and density, there is no reason why we (...) shouldn’t interpret Kant’s Dynamics as a defence of a Newtonian concept of matter. When Kant’s reasoning is understood in relation to his criteria for mathematical construction, it is possible to maintain that matter theory is central to the Metaphysical Foundations, but that this does not undermine Kant’s stated aim of giving an a priori foundation for Newtonian science. (shrink)

The gravitational equations were derived in general relativity using the assumption of their covariance relative to arbitrary transformations of coordinates. It has been repeatedly expressed an opinion over the past century that such equality of all coordinate systems may not correspond to reality. Nevertheless, no actual verification of the necessity of this assumption has been made to date. The paper proposes a theory of gravity with a constraint, the degenerate variants of which are general relativity and the unimodular (...) class='Hi'>theory of gravity. This constraint is interpreted from a physical point of view as a sufficient condition for the adiabaticity of the process of the evolution of the space–time metric. The original equations of the theory of gravity with the constraint are formulated. On this basis, a unified model of the evolution of the modern, early, and very early Universe is constructed that is consistent with the observational astronomical data but does not require the hypotheses of the existence of dark energy, dark matter or inflatons. It is claimed that: physical time is anisotropic, the gravitational field is the main source of energy of the Universe, the maximum global energy density in the Universe was 64 orders of magnitude smaller the Planckian one, and the entropy density is 18 orders of magnitude higher the value predicted by GR. The value of the relative density of neutrinos at the present time and the maximum temperature of matter in the early Universe are calculated. The wave equation of the gravitational field is formulated, its solution is found, and the nonstationary wave function of the very early Universe is constructed. It is shown that the birth of the Universe was random. (shrink)

I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie-Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms (...) to a general view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified and often ambiguous picture that treats reduction simply as a matter of taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest's Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest's Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity. (shrink)

Differences That Matter challenges existing ways of theorising the relationship between feminism and postmodernism which ask 'is or should feminism be modern or postmodern?' Sara Ahmed suggests that postmodernism has been allowed to dictate feminist debates and calls instead for feminist theorists to speak (back) to postmodernism, rather than simply speak on (their relationship to) it. Such a 'speaking back' involves a refusal to position postmodernism as a generalisable condition of the world and requires closer readings of what postmodernism (...) is actually 'doing' in a variety of disciplinary contexts. Sara Ahmed hence examines constructions of postmodernism in relation to rights, ethics, subjectivity, authorship, meta-fiction and film. (shrink)

Lewis 313) has recently presented an argument claiming that, under the Ghirardi–Rimini–Weber theory of quantum mechanics, arithmetic does not apply to ordinary macroscopic objects such as marbles . In this paper, I disentangle two different lines of Lewis's argument, one devoted to what I call the standard GRW interpretation and the other to the mass density interpretation . I present both strains of Lewis's argument, and move on to criticise Lewis's position, focusing on his argument with respect to (...) MDI. I analyse the structure of his argument, and follow this with a novel refutation of Lewis's argument, drawing on the original presentation of MDI as developed by Ghirardi et al. 5). I briefly consider the debate that ensued between Bassi and Ghirardi and Clifton and Monton and interpret it within the context of my analysis. I conclude that Lewis's Counting Anomaly fails to generate a genuine problem. (shrink)

Conscience is an idea that has significant currency in liberal democratic societies. Yet contemporary moral philosophical scholarship on conscience is surprisingly sparse. This paper seeks to offer a rigorous philosophical account of the role of conscience in moral life with a view to informing debates about the ethics of conscientious objection in medicine. I argue that conscience is concerned with a commitment to moral integrity and that restrictions on freedom of conscience prevent agents from living a moral life. In section (...) one I argue that conscience is a principle of moral awareness in rational agents, and that it yields an awareness of the personal nature of moral obligation. Conscience also monitors the coherence between an agent’s identity-conferring beliefs and intentions and their practical actions. In section two I consider how human beings are harmed when they are forced to violate their conscience. Restrictions on the exercise of conscience prevent people from living in accord with their own considered understanding of the requirements of morality and undermine one’s capacity for moral agency. This article concludes with a consideration of how a robust theory of conscience can inform our understanding of conscientious objection in medicine. I argue that it is in the interest of individual practitioners and the medical profession generally to foster moral agency among doctors. This provides a prima facie justification for permitting at least some kinds of conscientious objection. (shrink)

This paper develops a model of individual decision-making under bounded rationality in which discretionary cognitive adjustment creates a durable stock that complements choice of action. While it increases utility, adjustment also entails a cost, because focusing attention optimally is effortful and mental resources are scarce. Associated behavioral phenomena are categorized based on whether the operative motivation in adjusting is forward-looking utility maximization or justification of prior action. The theory is in line with prior conceptions of cognitive dissonance, but also (...) offers a more empirically consistent explanation of the endowment effect, persuasive advertising, and sunk-cost effects than existing accounts. (shrink)

In this paper it is argued that Habermas' critique of German Idealism is misguided and that his rejection of the philosophy of the subject is unjustified. Critical Theory needs to recognise the importance of subjectivity for all social philosophy if its theoretical aims are to be achieved. In order to demonstrate the relevance of subjectivity to Critical Theory the essay draws on analytic philosophy of mind and on the work of Manfred Frank and Dieter Henrich.

An Aristotelian philosophy of nature rejects the modern prejudice in favor of the microscopic, a rejection that is crucial if we are to penetrate the mysteries of the quantum world. I defend an Aristotelian model by drawing on both quantum chemistry and recent work on the measurement problem. By building on the work of Hans Primas, using the distinction between quantum and classical properties that emerges in quantum chemistry at the thermodynamic or continuum limit, I develop a new version of (...) the Copenhagen interpretation, a version that is realist, holistic, and hylomorphic in character, allowing for the attribution of fundamental causal powers to human observers and their instruments. I conclude with a critique of non-hylomorphic theories of primitive ontology, including Bohmian mechanics, Everettianism, and GRW mass-density. (shrink)

GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as (...) either single case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds because single case propensities suffer from various well know problems such as unlimited frequency tolerance and lack of a rationalisation of the principal principle. (shrink)

We study the Vapnik–Chervonenkis density of definable families in certain stable first-order theories. In particular, we obtain uniform bounds on the VC density of definable families in finite $\mathrm {U}$-rank theories without the finite cover property, and we characterize those abelian groups for which there exist uniform bounds on the VC density of definable families.

We review the early works which were precursors of the Conceptual Density Functional Theory. Starting from Thomas–Fermi approximation and from the exact formulation of Density Functional Theory by Hohenberg and Kohn’s theorem, we will introduce electronegativity and the theory of hard and soft acids and bases. We will also present a general introduction to the Fukui functions, and their relation with nucleophilicity and electrophilicity, with an emphasis towards the importance of these concepts for chemical reactivity.

A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a picture of an external reality. The new formalism, developed first for the single-particle case, has the advantage of generalizing immediately to quantum field theory and to the description of relativistic phenomena such as particle creation and annihilation.

The core structures of d 111 ¢ screw dislocations in bcc metals are studied using density functional theory in the local-density approximation. For Mo and Fe, direct calculations of the core structures show the cores to be symmetric with respect to 180° rotations around an axis perpendicular to the dislocation line. The magnetic moment in the Fe core is shown to be reduced relative to the bulk value. Calculations of n surfaces and the elastic constants B , (...) C ' and c 44 are reported for Fe and all group VB and VIB metals. Using a criterion suggested by Vitek and Duesbery the calculations point to symmetric core structures for all the studied metals. (shrink)

Ψ and out corresponding to the marble being inside or outside the box. These states are eigenvectors of the operator Bˆ , measuring whether the marble is inside or outside the box. The formalism of quantum mechanics..

This dissertation examines the dynamical dark matter problem in twentieth century astrophysics from the point of view of History and Philosophy of Science. The dynamical dark matter problem describes the situation astronomers find themselves in with regard to the dynamics of large scale astrophysical systems such as galaxies and galaxy clusters: The observed motions are incompatible with the visible distribution matter given the accepted law of gravitation. This discrepancy has two classes of possible solutions: either there exists (...) copious amounts of some kind of matter that neither emits nor absorbs radiation , or the law of gravitation must be revised. ;Chapter 2 describes the physical and philosophical foundations of dynamical inferences---inferences from discrepancies between well-founded theoretical expectations and reliable observations to the characteristics of candidate solutions. Chapter 3 discusses the history of dark matter . Chapter 4 reviews the present evidence bearing on the dark matter problem. Chapter 5 evaluates the important candidate matter solutions in light of the available evidence. Chapter 6 evaluates two candidate gravitational solutions on evidential and methodological grounds, and addresses the problem of theory choice. I do not try to solve the dark matter problem, but to uncover and evaluate patterns of inference involved in evidential arguments for and against candidate solutions. ;I show that Newton's "Reasoning from Phenomena" is a good framework from which to understand what is going on in this field. I argue that "higher order" and especially non-dynamical evidence is the best hope for solving this problem in dynamics. This is so in part because of "the dark matter double bind": the very existence of the dark matter problem means that we cannot be sure of the overall matter distribution in astrophysical systems, and this in turn means that the observed motions by themselves cannot provide relative confirmation of any theory of gravitational interactions taking place at these scales. I use Newton's Rules of Reasoning to argue that we should retain General Relativity as our theory of gravity at galactic and greater scales, despite the lack of positive evidence to confirm it over its rivals at these scales. (shrink)

We present a new “reason-based” approach to the formal representation of moral theories, drawing on recent decision-theoretic work. We show that any moral theory within a very large class can be represented in terms of two parameters: a specification of which properties of the objects of moral choice matter in any given context, and a specification of how these properties matter. Reason-based representations provide a very general taxonomy of moral theories, as differences among theories can be attributed (...) to differences in their two key parameters. We can thus formalize several distinctions, such as between consequentialist and non-consequentialist theories, between universalist and relativist theories, between agent-neutral and agent-relative theories, between monistic and pluralistic theories, between atomistic and holistic theories, and between theories with a teleological structure and those without. Reason-based representations also shed light on an important but under-appreciated phenomenon: the “underdetermination of moral theory by deontic content”. (shrink)

The quantum theory of atoms in molecules (QTAIM) uses physics to define an atom and its contribution to observable properties in a given system. It does so using the electron density and its flow in a magnetic field, the current density. These are the two fields that Schrödinger said should be used to explain and understand the properties of matter. It is the purpose of this paper to show how QTAIM bridges the conceptual gulf that separates (...) the observations of chemistry from the realm of physics and do so in a manner that is both rigorous and conceptually simple. Since QTAIM employs real measurable fields, it enables one to present the findings of complex quantum mechanical calculations in a pictorial manner that isolates the essential physics. The time has arrived for a sea change in our attempts to predict and classify the observations of chemistry, time to replace the use of simplified and arbitrary models with the full predictive power of physics, as applied to an atom in a molecule. (shrink)

Spontaneous collapse theories of quantum mechanics turn the usual Schrödinger equation into a stochastic dynamical law. In particular, in this paper, I will focus on the GRW theory. Two philosophical issues that can be raised about GRW concern (i) the ontology of the theory, in particular the nature of the wave function and its role within the theory, and (ii) the interpretation of the objective probabilities involved in the dynamics of the theory. During the last years, (...) it has been claimed that we can take advantage of dispositional properties in order to develop an ontology for GRW theory, and also in order to ground the objective probabilities which are postulated by it. However, in this paper, I will argue that the dispositional interpretations which have been discussed in the literature so far are either flawed or – at best – incomplete. If we want to endorse a dispositional interpretation of GRW theory we thus need an extended account that specifies the precise nature of those properties and which makes also clear how they can correctly ground all the probabilities postulated by the theory. Thus, after having introduced several different kinds of probabilistic dispositions, I will try to fill the gap in the literature by proposing a novel and complete dispositional account of GRW, based on what I call spontaneous weighted multi-track propensities. I claim that such an account can satisfy both of our desiderata. (shrink)