We give an account of the appearance and first developments of the statistical model of atoms proposed by Thomas and Fermi, focusing on the main results achieved by Fermi and his group in Rome. Particular attention is addressed to the unknown contribution to this subject by Majorana, anticipating some important results reached later by leading physicists.

The dispute over the viability of various theories of relativistic, dissipative fluids is analyzed. The focus of the dispute is identified as the question of determining what it means for a theory to be applicable to a given type of physical system under given conditions. The idea of a physical theory's regime of propriety is introduced, in an attempt to clarify the issue, along with the construction of a formal model trying to make the idea precise. This construction involves a (...) novel generalization of the idea of a field on spacetime, as well as a novel method of approximating the solutions to partial-differential equations on relativistic spacetimes in a way that tries to account for the peculiar needs of the interface between the exact structures of mathematical physics and the inexact data of experimental physics in a relativistically invariant way. It is argued, on the basis of these constructions, that the idea of a regime of propriety plays a central role in attempts to understand the semantical relations between theoretical and experimental knowledge of the physical world in general, and in particular in attempts to explain what it may mean to claim that a physical theory models or represents a kind of physical system. This discussion necessitates an examination of the initial-value formulation of the partial-differential equations of mathematical physics, which suggests a natural set of conditions---by no means meant to be canonical or exhaustive---one may require a mathematical structure, in conjunction with a set of physical postulates, satisfy in order to count as a physical theory. Based on the novel approximating methods developed for solving partial-differential equations on a relativistic spacetime by finite-difference methods, a technical result concerning a peculiar form of theoretical under-determination is proved, along with a technical result purporting to demonstrate a necessary condition for the self-consistency of a physical theory. (shrink)

On the basis of the exact solutions to the non-stationary spherically symmetric Einstein and Maxwell equations for dust matter and radial electromagnetic field, a model of a wormhole with the pulsating in time inner world and two static throats has been developed. It has been shown that such a wormhole with an arbitrary radius of the Gaussian curvature can connect both two different asymptotically flat space-times and two regions of the selfsame space-time. The problem of the fulfilment of (...) the energy conditions in this wormhole has been investigated, as well as the problem of its traversability investigation has been set. (shrink)

In this analysis, we develop a new approach to investigate the semianalytical solution of the delay differential equations. Mohand transform coupled with the homotopy perturbation method is called Mohand homotopy perturbation transform method and performs the solution results in the form of series. The beauty of this approach is that it does not need to compute the values of the Lagrange multiplier as in the variational iteration method, and also, there is no need to implement the convolution theorem as in (...) the Laplace transform. The main purpose of this scheme is to reduce the less computational work and the error analysis of the problems than others studied in the literature. Some illustrated examples are interpreted to confirm the accuracy of the newly developed scheme. (shrink)

We will consider the relativistic Duffin-Kemmer-Petiau equation in the presence of a pseudoharmonic potential in a magnetic field in the (1+2)-dimensional space-time for spin-one particles. To derive the energy eigenvalues and corresponding eigenfunctions, the analytical Nikiforov-Uvarov Method is used and some explanatory figures are included.

A widely accepted theory holds that emotional experiences occur mainly in a part of the human brain called the amygdala. A different theory asserts that color sensation is located in a small subpart of the visual cortex called V4. If these theories are correct, or even approximately correct, then they are remarkable advances toward a scientific explanation of human conscious experience. Yet even understanding the claims of such theories—much less evaluating them—raises some puzzles. Conscious experience does not present itself as (...) a brain process. Indeed experience seems entirely unlike neural activity. For example, to some people it seems that an exact physical duplicate of you could have different sensations than you do, or could have no sensations at all. If so, then how is it even possible that sensations could turn out to be brain processes? (shrink)

The free energy principle (FEP) portends to provide a unifying principle for the biological and cognitive sciences. It states that for a system to maintain non-equilibrium steady-state with its environment it must minimise its (information-theoretic) free energy. Under the FEP, to minimise free energy is equivalent to engaging in approximate Bayesian inference. According to the FEP, therefore, inference is at the explanatory base of biology and cognition. In this paper, we discuss a specific challenge to this inferential formulation of (...) adaptive self-organisation. We call it the universal ethology challenge: it states that the FEP cannot unify biology and cognition, for life itself (or adaptive self-organisation) does not require inferential routines to select adaptive solutions to environmental pressures (as mandated by the FEP). We show that it is possible to overcome the universal ethology challenge by providing a cautious and exploratory treatment of inference under the FEP. We conclude that there are good reasons for thinking that the FEP can unify biology and cognition under the notion of approximate Bayesian inference, even if further challenges must be addressed to properly draw such a conclusion. (shrink)

The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly by obtaining the period and the solution. The period is given in terms of the complete elliptic integral of the first kind and the solution involves Jacobian elliptic functions. We solve the cubic-quintic Duffing equation under arbitrary initial conditions. Physical applications are provided. The solution to the mixed parity Duffing oscillator is also formally derived. We illustrate the obtained (...) results with concrete examples. We give high accurate trigonometric approximations to the Jacobian function cn. (shrink)

This book is a contribution to the flourishing field of formal and philosophical work on truth and the semantic paradoxes. Our aim is to present several theories of truth, to investigate some of their model-theoretic, recursion-theoretic and proof-theoretic aspects, and to evaluate their philosophical significance. In Part I we first outline some motivations for studying formal theories of truth, fix some terminology, provide some background on Tarski’s and Kripke’s theories of truth, and then discuss the prospects of classical type-free truth. (...) In Chapter 4 we discuss some minimal adequacy conditions on a satisfactory theory of truth based on the function that the truth predicate is intended to fulfil on the deflationist account. We cast doubt on the adequacy of some non-classical theories of truth and argue in favor of classical theories of truth. Part II is devoted to grounded truth. In chapter 5 we introduce a game-theoretic semantics for Kripke’s theory of truth. Strategies in these games can be interpreted as reference-graphs of the sentences in question. Using that framework, we give a graph-theoretic analysis of the Kripke-paradoxical sentences. In chapter 6 we provide simultaneous axiomatizations of groundedness and truth, and analyze the proof-theoretic strength of the resulting theories. These range from conservative extensions of Peano arithmetic to theories that have the full strength of the impredicative system ID1. Part III investigates the relationship between truth and set-theoretic comprehen- sion. In chapter 7 we canonically associate extensions of the truth predicate with Henkin-models of second-order arithmetic. This relationship will be employed to determine the recursion-theoretic complexity of several theories of grounded truth and to show the consistency of the latter with principles of generalized induction. In chapter 8 it is shown that the sets definable over the standard model of the Tarskian hierarchy are exactly the hyperarithmetical sets. Finally, we try to apply a certain solution to the set-theoretic paradoxes to the case of truth, namely Quine’s idea of stratification. This will yield classical disquotational theories that interpret full second-order arithmetic without set parameters, Z2- . We also indicate a method to recover the parameters. An appendix provides some background on ordinal notations, recursion theory and graph theory. (shrink)

We study the computational complexity of deciding whether a given set of term equalities and inequalities has a solution in an ω-categorical algebra ????. There are ω-categorical groups where this pro...

We study the computational complexity of deciding whether a given set of term equalities and inequalities has a solution in an ω-categorical algebra ????. There are ω-categorical groups where this pro...

Einstein and Hilbert both struggled to reconcile general covariance and causality in their early work on general relativity. In Einstein’s case, this first led to his infamous “hole argument”, a stumbling block that persuaded him early on that generally covariant field equations for gravitation could never be found. After his breakthrough to general covariance in the fall of 1915, the resolution came in form of the “point-coincidence argument.” Hilbert from the beginning took a different view of the “causality problem,” though (...) he shifted his position somewhat in the light of Einstein’s breakthrough in November 1915. Nevertheless, his aim was to establish initial conditions that would lead to a well-defined Cauchy problem in general relativity. Hilbert consistently advocated the use of coordinate conditions in order to obtain solutions of the field equations that would maintain the causal ordering of events. Einstein’s “causality problem” thus differs from that of Hilbert, and the latter was never a victim of Einstein’s “hole argument.”. (shrink)

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

In this paper, a generalized -dimensional Calogero–Bogoyavlenskii–Schiff equation is considered. Based on the Hirota bilinear method, three kinds of exact solutions, soliton solution, breather solutions, and lump solutions, are obtained. Breathers can be obtained by choosing suitable parameters on the 2-soliton solution, and lump solutions are constructed via the long wave limit method. Figures are given out to reveal the dynamic characteristics on the presented solutions. Results obtained in this work may be conducive (...) to understanding the propagation of localized waves. (shrink)

This essay is an informal examination of the efforts made by mathematical logicians from Russell on, to evade the paradoxes revealed by uncritical methods of definition and predication. Where systems are described it is with a minimum of formal apparatus, so that the climate is one of rather vague statement and imprecise question. Russell’s drastic banning of type–offending formulas gives the starting–point for queries about the connection of sense and formalism, and the conclusion may be summed up as the detection (...) of a contrast between mechanisation and sensefulness which is seen as constituting a line of tension, as it were a geological weakness in formal structures, which permits the insertion of a philosophic wedge. Interesting as such an idea is, it is not clear between what regions this line has been drawn. On the one hand the undecidability results of Gödel show that formal methods can be extended indefinitely beyond the scope of what is mechanisable; on the other the author methodically refrains from defining what he means by ‘sense’. In so far as he explicitly leaves his meaning on this point to be gathered form his treatment of non–sense, and the paradoxes are here taken as representative of the latter, we might suppose that he is equating sense with consistency. For expressions leading to paradox were only ruled senseless by Russell because they lead to inconsistency. But it is fairly clear that something more epistemologically interesting is intended, since the author dismisses from consideration ‘la déductivité structurale, sens immédiat d’une vaste architecture symbolique d’abord vide, et intégralement traduisible en syntaxe’. Such translatability has, incidentally, its limits, as Gödel’s results again show, and it is our belief that the discussion might have been put in a more exact and workmanlike frame if the list of works consulted had contained more than one, and that a relatively minor, publication of Gödel. (shrink)

The prospect of using genome technologies to modify the human germline has raised profound moral disagreement but also emphasizes the need for wide-ranging discussion and a well-informed policy response. The Hinxton Group brought together scientists, ethicists, policymakers, and journal editors for an international, interdisciplinary meeting on this subject. This consensus statement formulated by the group calls for support of genome editing research and the development of a scientific roadmap for safety and efficacy; recognizes the ethical challenges involved in clinical reproductive (...) applications of genome editing but, importantly, rejects the idea that human reproductive germline modification is necessarily morally unacceptable; and highlights the importance of meaningful engagement in discussions of genome editing and the development of regulation and oversight mechanisms to govern future uses of such technologies. (shrink)

Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, a special type of Alexandroff spaces was (...) used by Ian Rumfitt to elucidate the logic of vague concepts in a new way. According to his approach, conceptual spaces such as the color spectrum give rise to classical systems of concepts that have the structure of atomic Boolean algebras. More precisely, concepts are represented as regular open regions of an underlying conceptual space endowed with a topological structure. Something is subsumed under a concept iff it is represented by an element of the conceptual space that is maximally close to the prototypical element p that defines that concept. This topological representation of concepts comes along with a representation of the familiar logical connectives of Aristotelian syllogistics in terms of natural settheoretical operations that characterize regular open interpretations of classical Boolean propositional logic. In the last 20 years, conceptual spaces have become a popular tool of dealing with a variety of problems in the fields of cognitive psychology, artificial intelligence, linguistics and philosophy, mainly due to the work of Peter Gärdenfors and his collaborators. By using prototypes and metrics of similarity spaces, one obtains geometrical discretizations of conceptual spaces by so-called Voronoi tessellations. These tessellations are extensionally equivalent to topological tessellations that can be constructed for Alexandroff spaces. Thereby, Rumfitt’s and Gärdenfors’s constructions turn out to be special cases of an approach that works for a more general class of spaces, namely, for weakly scattered Alexandroff spaces. This class of spaces provides a convenient framework for conceptual spaces as used in epistemology and related disciplines in general. Alexandroff spaces are useful for elucidating problems related to the logic of vague concepts, in particular they offer a solution of the Sorites paradox (Rumfitt). Further, they provide a semantics for the logic of clearness (Bobzien) that overcomes certain problems of the concept of higher2 order vagueness. Moreover, these spaces help find a natural place for classical syllogistics in the framework of conceptual spaces. The crucial role of order theory for Alexandroff spaces can be used to refine the all-or-nothing distinction between prototypical and nonprototypical stimuli in favor of a more fine-grained gradual distinction between more-orless prototypical elements of conceptual spaces. The greater conceptual flexibility of the topological approach helps avoid some inherent inadequacies of the geometrical approach, for instance, the so-called “thickness problem” (Douven et al.) and problems of selecting a unique metric for similarity spaces. Finally, it is shown that only the Alexandroff account can deal with an issue that is gaining more and more importance for the theory of conceptual spaces, namely, the role that digital conceptual spaces play in the area of artificial intelligence, computer science and related disciplines. Keywords: Conceptual Spaces, Polar Spaces, Alexandroff Spaces, Prototypes, Topological Tessellations, Voronoi Tessellations, Digital Topology. (shrink)

A simple proof of a weak version of Eliezer's theorem on unphysical solutions of the Lorentz-Dirac equation is given. This version concerns a free particle scattered by a spatially localized electric field in one space dimension. (The solutions are also solutions in three space dimensions.) It establishes that for certain physically reasonable localized fields, all solutions which are free (i.e., unaccelerated) before they enter the field have unbounded proper acceleration and velocity asymptotic to that of (...) light in the future. For any given initial velocity, the fields yielding this unphysical behavior can be arbitrarily weak. The result is then extended to a class of static fields which need not be spatially localized, including Coulomb fields. For this case the same conclusion is obtained omitting the assumption that the particle be free in the past.The rest of the paper discusses solutions to the localized field problem which are assumed free in the future rather than the past. Some strange features of these solutions are noted. The possibility of experimentally detecting deviations from the Coulomb law for a particle obeying the Lorentz-Dirac equation is discussed. (shrink)

Socrates is one of the most important yet enigmatic philosophers of all time; his fame has endured for centuries despite the fact that he never actually wrote anything. In 399 B.C.E., he was tried on the charge of impiety by the citizens of Athens, convicted by a jury, and sentenced to death (ordered to drink poison derived from hemlock). About these facts there is no disagreement. However, as the sources collected in this book and the scholarly essays that follow them (...) show, several of even the most basic facts about these events were controversial in antiquity, and the questions persist today: How and why was Socrates brought to trial? Why did the jurors, members of the world's first democracy, find him guilty? When he was given an opportunity to escape execution, why did he refuse to do so and instead accept the punishment that he and his friends agreed was unjustly assigned to him? How exactly did Socrates die? Differences of opinion on these and other issues continue to arouse our curiosity and to challenge new generations of students and scholars. The Trial and Execution of Socrates: Sources and Controversies is the first work to collect in one place all of the major ancient sources on Socrates' death--those of both his critics and his defenders--as well as recent scholarly views. Part I includes new translations of Plato's Euthyphro, Apology, Crito, and the death scene from Phaedo, as well as other ancient sources that shed light on Socrates' trial and execution. Part II features some of the most influential recent scholarship on this historically momentous event with work by M. F. Burnyeat, Robert Parker, Mark L. McPherran, Thomas C. Brickhouse and Nicholas D. Smith, Richard Kraut, Christopher Gill, and Enid Bloch (whose essay is published here for the first time). Ideal for undergraduate surveys of ancient Greek philosophy and upper-level courses on Socrates and Socratic philosophy, this unique collection provides an unprecedented look into the many perplexing questions surrounding the trial and execution of this remarkable man. (shrink)

Artificial intelligence research and regulation seek to balance the benefits of innovation against any potential harms and disruption. However, one unintended consequence of the recent surge in AI research is the potential re-orientation of AI technologies to facilitate criminal acts, term in this article AI-Crime. AIC is theoretically feasible thanks to published experiments in automating fraud targeted at social media users, as well as demonstrations of AI-driven manipulation of simulated markets. However, because AIC is still a relatively young and inherently (...) interdisciplinary area—spanning socio-legal studies to formal science—there is little certainty of what an AIC future might look like. This article offers the first systematic, interdisciplinary literature analysis of the foreseeable threats of AIC, providing ethicists, policy-makers, and law enforcement organisations with a synthesis of the current problems, and a possible solution space. (shrink)

This article has not been written for specialists of exact solutions of Einstein's field equations but for physicists who are interested in nontrivial information on this topic. We recall the history and some basic properties of exact solutions of Einstein's vacuum equations. We show that the field equations for stationary axisymmetric vacuum gravitational fields can be expressed by only one nonlinear differential equation for a complex function. This compact form of the field equations allows the (...) generation of almost all stationary axisymmetric vacuum gravitational fields. We present a new stationary two-body solution of Einstein's equations as an application of this generation technique. This new solution proves the existence of a macroscopic, repulsive spin-spin interaction in general relativity. Some estimates that are related to this new two-body solution are given. (shrink)

Like American politics, the academic debate over justice is polarized, with almost all theories of justice falling within one of two traditions: egalitarianism and libertarianism. This book provides an alternative to the partisan standoff by focusing not on equality or liberty, but on the idea that we should give people the things that they deserve. Mulligan argues that a just society is a meritocracy, in which equal opportunity prevails and social goods are distributed strictly on the basis of merit. That (...) gives citizens their just deserts. In addition to its novel conceptual approach, meritocracy is distinctive from existing work in two ways. First, it is grounded in research on how people actually think about justice. Empirical research reveals that people don't think that social goods should be distributed equally. Nor do they dismiss the idea of social justice. Across ideological and cultural lines, people want rewards to reflect merit. Second, the book discusses hot-button political issues and makes concrete policy recommendations. These issues include anti-meritocratic bias against women and racial minorities and the United States’ widening economic inequality. Justice and the Meritocratic State offers a new theory of justice and provides solutions to our most vexing social and economic problems. It will be of keen interest to philosophers, economists, and political theorists. (shrink)

Online educational technologies offer opportunities for providing individualized feedback and detailed profiles of students' skills. Yet many technologies for mathematics education assess students based only on the correctness of either their final answers or responses to individual steps. In contrast, examining the choices students make for how to solve the equation and the ways in which they might answer incorrectly offers the opportunity to obtain a more nuanced perspective of their algebra skills. To automatically make sense of step‐by‐step (...) class='Hi'>solutions, we propose a Bayesian inverse planning model for equation solving that computes an assessment of a learner's skills based on her pattern of errors in individual steps and her choices about what sequence of problem‐solving steps to take. Bayesian inverse planning builds on existing machine learning tools to create a generative model relating (mis)‐understandings to equation solving choices. Two behavioral experiments demonstrate that the model can interpret people's equation solving and that its assessments are consistent with those of experienced teachers. A third experiment uses this model to tailor guidance for learners based on individual differences in misunderstandings, closing the loop between assessing understanding, and using that assessment within an educational technology. Finally, because the bottleneck in applying inverse planning to a new domain is in creating the model of possible student misunderstandings, we show how to combine inverse planning with an existing production rule model to make inferences about student misunderstandings of fraction arithmetic. (shrink)

A growing number of decision theorists have, in recent years, defended the view that rationality is permissive under risk: Different rational agents may be more or less risk-averse or risk-inclined. This can result in them making different choices under risk even if they value outcomes in exactly the same way. One pressing question that arises once we grant such permissiveness is what attitude to risk we should implement when choosing on behalf of other people. Are we permitted to implement any (...) of the rationally permissible risk attitudes, is there some specific risk attitude that is required when choosing for others, or are we required to defer to the risk attitudes of the people on whose behalf we are choosing? This article elaborates on this question, explains its wider practical and theoretical significance, provides an overview of existing answers, and explores how to go about providing a more systematic account of how to choose on behalf of others in risky contexts. (shrink)

Transmissible cancers are elusive and understudied parasitic life forms caused by malignant clonal cells (nine lineages are known so far). They emerge by completing sequential steps that include breaking cell cooperation, evade anti‐cancer defences and shedding cells to infect new hosts. Transmissible cancers impair host fitness, and their importance as selective force is likely largely underestimated. It is, therefore, crucial to determine how common they might be in the wild. Here, we draw a parallel between the steps required for a (...) transmissible cancer to emerge and the steps required for an intelligent civilisation to emerge in the Milky Way using a modified Drake equation. Using numerical analyses, we estimate the potential number of extant marine and bivalve species in which transmissible cancers might exist. Our results suggest that transmissible cancers are more common than expected, and that new lineages can be found by screening a large number of species. (shrink)

Abstract: We propose a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this semantic view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show that this (...) theory provides a general framework within which we can understand the relation between vague terms and concepts and the corresponding crisp portions of reality. We also sketch how it might be possible to formulate within this framework a theory of vagueness which dispenses with the notion of truth-value gaps and other artifacts of more familiar approaches. Central to our approach is the idea that judgments about reality involve in every case (1) a separation of reality into foreground and background of attention and (2) the feature of granularity. On this basis we attempt to show that even vague judgments made in naturally occurring contexts are not marked by truth-value indeterminacy. We distinguish, in addition to crisp granular partitions, also vague partitions, and reference partitions, and we explain the role of the latter in the context of judgments that involve vagueness. We conclude by showing how reference partitions provide an effective means by which judging subjects are able to temper the vagueness of their judgments by means of approximations. (shrink)

We propose a new account of vagueness and approximation in terms of the theory of granular partitions. We distinguish different kinds of crisp and non-crisp granular partitions and we describe the relations between them, concentrating especially on spatial examples. We describe the practice whereby subjects use regular grid-like reference partitions as a means for tempering the vagueness of their judgments, and we demonstrate how the theory of reference partitions can yield a natural account of this practice, which is referred to (...) in the literature as ‘approximation’. (shrink)

The continued advance of global value chains as the mode of production for an increasing number of goods and services has impacted considerably on the economies and societies both of the developed world and the emerging economies. Although there have been many efforts at reform there is evidence of unresolved dilemmas of human rights, environmental issues and ethical dilemmas in the operation of the global value chain. This paper focuses on the role and performance of Apple Inc in the global (...) value chain in Asia. Apple is the most successful corporation on earth measured in financial terms and yet has failed to find a solution to recurrent employment and environmental problems occurring in plants manufacturing Apple components. This analysis informs the current theoretical debate on the development of the global value chain and the continuing institutional failure that leaves employees vulnerable and the environment neglected. (shrink)

C. I. Lewis’s conception of the given element in perceptual experience was one of the targets of Sellars’ famous charge that many such conceptions fall victim to the Myth of the Given. Yet exactly what makes a conception of the given mythical has remained unclear. Here I aim to clarify this issue by discussing Eric Watkins’ recent claim that a conception exactly like the one Lewis articulated in Mind and the World Order in fact avoids the Myth. Watkins motivates this (...) claim in part by raising objections for John McDowell’s account of the Myth and argues that a better account can be extracted from Kant. I defend McDowell’s position (and reject Watkins’ Kantian account) by arguing that these objections are based on a failure to appreciate an implication of the claim (which Watkins accepts) that rational thought operates in “the logical space of reasons.” Specifically, I focus on the implication that a thinker must be in a position to understand the rational significance of her perceptual experience. Along the way I explain in what ways Watkins’ conception of the given in experience mirrors the view of Lewis. (shrink)

In this paper we argue that the problem of the one and the many, as first proposed in the West by Parmenides, can be resolved without recourse to either monism or nominalism by an appeal to distinct though mutually ordered principles of distinction in the realm of material substances, namely that of material individuation, distinction according to form, and supposital distinction. This solution, rooted in St. Thomas Aquinas and St. Albert the Great, maintains that what distinguishes one material substance from (...) any other substance absolutely is the agency of the Divine Intellect. This agency elicits in the created material substance the actuality of the relation of creation, which is the cause or principle that, in inhering in the ens creatum as a property subsisting in it, sustains the material substance in its mode of being as suppositum by formally perfecting its distinction with reference to God the Creator. (shrink)

In this paper we argue that the problem of the one and the many, as first proposed in the West by Parmenides, can be resolved without recourse to either monism or nominalism by an appeal to distinct though mutually ordered principles of distinction in the realm of material substances, namely that of material individuation, distinction according to form, and supposital distinction. This solution, rooted in St. Thomas Aquinas and St. Albert the Great, maintains that what distinguishes one material substance from (...) any other substance absolutely is the agency of the Divine Intellect. This agency elicits in the created material substance the actuality of the relation of creation, which is the cause or principle that, in inhering in the ens creatum as a property subsisting in it, sustains the material substance in its mode of being as suppositum by formally perfecting its distinction with reference to God the Creator. (shrink)

In the centennial of Ettore Majorana’s birth (1906–1938?), we re-examine some aspects of his fundamental scientific production in atomic and molecular physics, including a not well known short communication. There, Majorana critically discusses Fermi’s solution of the celebrated Thomas–Fermi equation for electron screening in atoms and positive ions. We argue that some of Majorana’s seminal contributions in molecular physics already prelude to the idea of exchange interactions (or Heisenberg–Majorana forces) in his later works on theoretical nuclear physics. In (...) all his papers, he tended to emphasize the symmetries at the basis of a physical problem, as well as the limitations, rather than the advantages, of the approximations of the method employed. (shrink)

The philosophy of biology is witnessing an increasing enthusiasm for what can be called “individuals thinking”. Individuals thinking is a perspective on the metaphysics of biological entities according to which conceiving of them as individuals rather than kinds enables us to expose ongoing metaphysical debates as focusing on the wrong question, and to achieve better accounts of the metaphysics of biological entities. In this paper, I examine two cases of individuals thinking, the claim that species are individuals and the claim (...) that life on Earth is an individual. I argue that these claims fail to do the metaphysical work that one would want them to do. I highlight problems with the specific claims as well as with the general notion of ‘individual’, and argue that naturalistic metaphysicians of biology should think of the metaphysical status of theoretical entities, such as species and life, as fundamentally theory-dependent. This implies a metaphysical pluralism, that allows that in some theories species, life, and other such entities may feature as individuals, whereas in others they may feature as kinds. (shrink)

This paper deals with Natorp’s version of the Marburg mathematical philosophy of science characterized by the following three features: The core of Natorp’s mathematical philosophy of science is contained in his “knowledge equation” that may be considered as a mathematical model of the “transcendental method” conceived by Natorp as the essence of the Marburg Neo-Kantianism. For Natorp, the object of knowledge was an infinite task. This can be elucidated in two different ways: Carnap, in the Aufbau, contended that this (...) endeavor can be divided into two distinct parts, namely, a finite “constitution” of the object of knowledge and an infinite incompletable empirical description. In contrast, and more in the original spirit of Cohen and Natorp, the physicist and philosopher Margenau in The Nature of Physical Reality (Margenau. 1950) conceived the infinity of this “Aufgabe” as an infinite dialectical process, in which relative “data” and “conceptual constructs” determine each other. This dialectical process eliminates the dichotomy between Anschauung and Begriff that distinguished the Marburg Neo-Kantianism from Kantian orthodoxy, namely, the abandonment of the difference between intuition and concept. Finally, the paper deals with the non-Archimedean geometrical systems that played a central role in Natorp’s defence of Cohen’s “infinitesimal” metaphysics. (shrink)

'The Greate Invention of Algebra' casts new light on the work of Thomas Harriot, an innovative thinker and practitioner in several branches of the mathematical sciences, including navigation, astronomy, optics, geometry, and algebra. Although on his death Harriot left behind over four thousand manuscript sheets, much of his work remains unpublished. This book focuses on one hundred and forty of Harriot's manuscript pages, those concerned with the structure and solution of equations. The original material has been carefully ordered, translated, and (...) annotated to provide the first complete edition of his work on this subject, and an extended introduction provides the reader with a lucid background to the work and explains its contents. Illustrations from the manuscripts provide fascinating reference material. The appendix discusses correlations between Harriot's manuscripts and the texts of his contemporaries Viète, Warner, and Torporley. The clear and concise exposition makes this an excellent reference volume for historians of mathematics and those interested in the history of science. This is an important new resource for understanding the development of algebra in seventeenth-century England. (shrink)

In this article we provide an in-depth description of a new model of informed consent called ‘meta consent’ and consider its practical implementation. We explore justifications for preferring meta consent over alternative models of consent as a solution to the problem of secondary use of health data for research. We finally argue that meta consent strikes an appropriate balance between enabling valuable research and protecting the individual.

When making decisions, humans can observe many kinds of information about others' activities, but their effects on performance are not well understood. We investigated social learning strategies using a simple problem-solving task in which participants search a complex space, and each can view and imitate others' solutions. Results showed that participants combined multiple sources of information to guide learning, including payoffs of peers' solutions, popularity of solution elements among peers, similarity of peers' solutions to their own, and (...) relative payoffs from individual exploration. Furthermore, performance was positively associated with imitation rates at both the individual and group levels. When peers' payoffs were hidden, popularity and similarity biases reversed, participants searched more broadly and randomly, and both quality and equity of exploration suffered. We conclude that when peers' solutions can be effectively compared, imitation does not simply permit scrounging, but it can also facilitate propagation of good solutions for further cumulative exploration. (shrink)

In this article, I revisit Karl Marx’s claim in his Economic and Phil-osophic Manuscripts of 1844, that the subject in its “individual existence is at the same time a social being.” I redefine what has been translated as “social being” as “common being” in order to extrapolate an understanding of subjectivity that is a socio-ontological and collectively structured collectivity. In doing so, I demonstrate (1) that this common being is a collection of different socio-ontological traits; (2) that in order for (...) this common being to be approximated we must take into account all modes of subjectivity production that intersect in what will appear as the subject; and (3) that the Other is the constitutive parameter of the common being on which the subject depends. Finally, I revisit three exemplary modes of practice - namely critique, solidarity, and utopia - and show that conceiving of the subject as a common being renders critique constellational, solidarity overdetermined, and utopia a koinotopia. (shrink)

Natural kinds are often contrasted with other kinds of scientific kinds, especially functional kinds, because of a presumed categorical difference in explanatory value: supposedly, natural kinds can ground explanations, while other kinds of kinds cannot. I argue against this view of natural kinds by examining a particular type of explanation—mechanistic explanation—and showing that functional kinds do the same work there as traditionally recognized natural kinds are supposed to do in “standard” scientific explanations. Breaking down this categorical distinction between traditional natural (...) kinds and other kinds of kinds, I argue, delivers two goods: It provides us with a view of natural kindhood that does justice to the epistemic roles of kinds in scientific explanations. And it allows us to solve a problem that HPC theory, currently one of the more popular accounts of natural kindhood, confronts. (shrink)

In this paper I defend the compossibility of presentism and time travel from two objections. One objection is that the presentist’s model of time leaves nowhere to travel to; the second objection attempts to equate presentist time travel with suicide. After targeting some misplaced scrutiny of the first objection, I show that presentists have the resources to account for the facts that make for time travel on the traditional Lewisian view. In light of this ability, I argue that both of (...) the objections fail. (shrink)

Human beings have the unique ability to view the world in a detached way: We can think about the world in terms that transcend our own experience or interest, and consider the world from a vantage point that is, in Nagel's words, "nowhere in particular". At the same time, each of us is a particular person in a particular place, each with his own "personal" view of the world, a view that we can recognize as just one aspect of the (...) whole. How do we reconcile these two standpoints--intellectually, morally, and practically? To what extent are they irreconcilable and to what extent can they be integrated? Thomas Nagel's ambitious and lively book tackles this fundamental issue, arguing that our divided nature is the root of a whole range of philosophical problems, touching, as it does, every aspect of human life. He deals with its manifestations in such fields of philosophy as: the mind-body problem, personal identity, knowledge and skepticism, thought and reality, free will, ethics, the relation between moral and other values, the meaning of life, and death. Excessive objectification has been a malady of recent analytic philosophy, claims Nagel, it has led to implausible forms of reductionism in the philosophy of mind and elsewhere. The solution is not to inhibit the objectifying impulse, but to insist that it learn to live alongside the internal perspectives that cannot be either discarded or objectified. Reconciliation between the two standpoints, in the end, is not always possible. (shrink)

Natural kinds are often contrasted with other kinds of scientific kinds, especially functional kinds, because of a presumed categorical difference in explanatory value: supposedly, natural kinds can ground explanations, while other kinds of kinds cannot. I argue against this view of natural kinds by examining a particular type of explanation—mechanistic explanation—and showing that functional kinds do the same work there as traditionally recognized natural kinds are supposed to do in “standard” scientific explanations. Breaking down this categorical distinction between traditional natural (...) kinds and other kinds of kinds, I argue, delivers two goods: It provides us with a view of natural kindhood that does justice to the epistemic roles of kinds in scientific explanations. And it allows us to solve a problem that HPC theory, currently one of the more popular accounts of natural kindhood, confronts. (shrink)

Many significant problems in metaphysics are tied to ontological questions, but ontology and its relation to larger questions in metaphysics give rise to a series of puzzles that suggest that we don't fully understand what ontology is supposed to do, nor what ambitions metaphysics can have for finding out about what the world is like. Thomas Hofweber aims to solve these puzzles about ontology and consequently to make progress on four metaphysical debates tied to ontology: the philosophy of arithmetic, the (...) metaphysics of ordinary objects, the problem of universals, and the question of whether the fact-like aspect of reality is independent of us. Crucial parts of the proposed solution involve considerations about quantification and its relationship to ontology, the place of reference in natural languages, the relationship between syntactic form and focus, whether there could be any ineffable facts, and others. (shrink)

According to the permissibility solution to the lottery paradox, the paradox can be solved if we conceive of epistemic justification as a species of permissibility. Clayton Littlejohn has objected that the permissibility solution draws on a sufficient condition for permissible belief that has implausible consequences and that the solution conflicts with our lack of knowledge that a given lottery ticket will lose. The paper defends the permissibility solution against Littlejohn's objections.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Ministers of the Law: A Natural Law Theory of Legal AuthorityThomas J. BushlackMinisters of the Law: A Natural Law Theory of Legal Authority Jean Porter Grand Rapids, Mich.: Eerdmans, 2010. 368 pp. $30.00Jean Porter’s most recent book is the fruit of her participation with the Emory Center for the Study of Law and Religion since 2005. In this project she undertakes two interrelated tasks. First, she provides compelling (...) reasons for Christian ethicists to engage in questions internal to the discipline of jurisprudence. Second, she demonstrates how a natural law theory grounded in the work of the medieval scholastics can address some of the questions of contemporary jurisprudence. Readers familiar with her previous work will be delighted that she has extended her constructive account of natural law into the realms of jurisprudence and in the process also engages cultural psychology, rhetoric, political philosophy, and international law.Porter begins her engagement with jurisprudence in chapter 1 by noting a paradox recognized by many legal philosophers in the Anglophone world. Legal systems, as they have developed in the West, are characterized by a high degree of autonomy and independence vis-à-vis other social dynamics such as politics or morality. At the same time, however, no legal system can function in complete isolation from considerations of politics and morality. How can we account for the paradoxical autonomy of legal authority? Porter suggests that a scholastic account of natural law can provide a rationally defensible solution to this paradox by developing an account of natural authority (in chapter 2).The force of Porter’s argument rests on the capacity of her account to justify political and legal authority as a natural expression of the authority that any community exercises vis-à-vis its individual members. A community’s authority over its members is justified on the grounds that in prescribing or prohibiting particular acts, it must appeal to claims that could potentially be recognized as justifiable by any rational member of that community. The concept that creates this important hinge between an individual’s good and the good of the community is, of course, the common good. Scholars interested in the concept of the common good will find that her reflection upon it is both rooted deeply in the Christian tradition and applied with fresh insight to the realm of politics (chapter 3) and law (chapter 4). [End Page 210]One potential objection to Porter’s account of natural law could arise in response to her insistence that natural inclinations “underdetermine” the normative content of a natural law morality, leaving her account open to charges of cultural relativism or of being merely descriptive as opposed to normative. However, in this work she is able to turn these criticisms into assets for her account of natural law. She shows (successfully, I believe) how her theory of natural law is able to account for the plurality of moral, political, and legal systems that exist in our world today while still providing normative grounds for critiquing existing social systems. And in chapter 5 she demonstrates how nonderogable, jus cogens principles can be developed from her account of natural law and applied to the field of international law and human rights. In fact, the final section left me hungry for further development of her insights regarding the relationship between natural and international law.This book is written with the same rigorous logic and careful research that has made Porter one of the leading scholars of natural law theory in the field today. As such, this book would be suitable for academics in a wide variety of fields, such as law, political theory, and of course Christian ethics, or for advanced graduate students. It is most certainly a groundbreaking work for demonstrating how a theological account of natural law can engage in constructive dialogue with legal theory and politics at both a theoretical and a practical level.Thomas J. BushlackUniversity of St. ThomasCopyright © 2012 The Society of Christian Ethics... (shrink)

This study presents a modified simplest equation method to investigate some real and exact solutions of conformable time fractional Benjamin-Bona-Mahony equation and Chan-Hilliard equation. We use traveling wave transformation to obtain the results in the form of series solution. Some calculations are performed through Mathematica software to analyze the accuracy of this approach. Graphical representations are reported for more significant results at different fractional-order which demonstrates that this approach is very simple, adequate, and legitimate.

Experimental philosophy is the name for a recent movement whose participants use the methods of experimental psychology to probe the way people think about philosophical issues and then examine how the results of such studies bear on traditional philosophical debates. Given both the breadth of the research being carried out by experimental philosophers and the controversial nature of some of their central methodological assumptions, it is of no surprise that their work has recently come under attack. In this paper we (...) respond to some criticisms of experimental philosophy that have recently been put forward by Antti Kauppinen. Unlike the critics of experimental philosophy, we do not think the fledgling movement either will or should fall before it has even had a chance to rise up to explain what it is, what it seeks to do (and not to do), and exactly how it plans to do it. Filling in some of the salient details is the main goal of the present paper. (shrink)