An attempt is made to remove singularities arising in general relativity by modifying it so as to take into account the existence of a fundamental rest frame in the universe. This is done by introducing a background metric γμν (in addition to gμν) describing a spacetime of constant curvature with positive spatial curvature. The additional terms in the field equations are negligible for the solar system but important for intense fields. Cosmological models are obtained without singular states but simulating the (...) “big bang.” The field of a particle differs from the Schwarzschild field only very close to, and inside, the Schwarzschild sphere. The interior of this sphere is unphysical and impenetrable. A star undergoing gravitational collapse reaches a state in which it fills the Schwarzschild sphere with uniform density (and pressure) and has the geometry of a closed Einstein universe. Any charge present is on the surface of the sphere. Elementary particles may have similar structures. (shrink)

The Weyl theory of gravitation and electromagnetism, as modified by Dirac, contains a gauge-covariant scalar β which has no geometric significance. This is a flaw if one is looking for a geometric description of gravitation and electromagnetism. A bimetric formalism is therefore introduced which enables one to replace β by a geometric quantity. The formalism can be simplified by the use of a gauge-invariant physical metric. The resulting theory agrees with the general relativity for phenomena in the solar system.

Elementary particles, regarded as the constituents of quarks and leptons, are described classically in the framework of the general relativity theory. There are neutral particles and particles having charges±1/3e. They are taken to be spherically symmetric and to have mass density, pressure, and (if charged) charge density. They are characterized by an equation of state P=−ρ suggested by earlier work on cosmology. The neutral particle has a very simple structure. In the case of the charged particle there is one outstanding (...) model described by a simple analytic solution of the field equations. (shrink)

A spherically symmetric entity with the Weyl-Dirac geometry holding in its interior is investigated. The structure is determined by the presence of the Dirac gauge function, which creates a mass density. Two models are obtained, one that can describe a cosmic body, the other an elementary particle.

It is suggested that the dark matter of the universe is due to the presence of a scalar field described by the gauge function introduced by Dirac in his modification of the Weyl geometry. The behavior of such dark matter is investigated.

It is shown that all spherically symmetric distributions of prematter in the framework of general relativity are static. These results provide a justification for the models of elementary particles proposed previously.

It is proposed to remove the difficulty of nonitegrability of length in the Weyl geometry by modifying the law of parallel displacement and using “standard” vectors. The field equations are derived from a variational principle slightly different from that of Dirac and involving a parameter σ. For σ=0 one has the electromagnetic field. For σ<0 there is a vector meson field. This could be the electromagnetic field with finite-mass photons, or it could be a meson field providing the “missing mass” (...) of the universe. In cosmological models the two natural gauges are the Einstein gauge and the cosmic gauge. With the latter the universe has a fixed size, but the sizes of small systems decrease with time and their masses and energies increase, thus producing the Hubble effect. The field of a particle in this gauge is investigated, and it leads to an interesting solution of the Einstein equations that raises a question about the Schwarzschild solution. (shrink)

An elementary particle is described as a spherically symmetric solution of the Klein-Gordon equation and the Einstein equations of general relativity. It is found that it has a mass of the order of the Planck mass. If one assumes that the motion of its center of mass is determined by the Dirac equations, then it has a spin of 1/2.

Generalizing the work of Einstein and Mayer, it is assumed that at each point of space-time there exists an N-dimensional linear vector space with N≥5. This space is decomposed into a four-dimensional tangent space and an (N - 4)-dimensional internal space. On the basis of geometric considerations, one arrives at a number of fields, the field equations being derived from a variational principle. Among the fields obtained there are the electromagnetic field, Yang-Mills gauge fields, and fields that can be interpreted (...) as describing matter. As a simple example, the case N=6 is considered. (shrink)

In the general relativity theory gravitational energy-momentum density is usually described by a pseudo-tensor with strange transformation properties so that one does not have localization of gravitational energy. It is proposed to set up a gravitational energy-momentum density tensor having a unique form in a given coordinate system by making use of a bimetric formalism. Two versions are considered: (1) a bimetric theory with a flat-space background metric which retains the physics of the general relativity theory and (2) one with (...) a background corresponding to a space of constant curvature which introduces modifications into general relativity under certain conditions. The gravitational energy density in the case of the Schwarzschild solution is obtained. (shrink)

The Weyl-Dirac theory of gravitation and electromagnetism is modified by the introduction of a background metric characterized by a scale constant related to the size of the universe. One is led to a natural gauge giving ${{\dot G} \mathord{\left/ {\vphantom {{\dot G} G}} \right. \kern-0em} G} = - 5.5 \times 10^{ - 12} y^{ - 1} $ . This is smaller by about a factor of ten than the value obtained on the basis of Dirac's large number hypothesis.

The single-particle wave function ψ=ReiS/h has been interpreted classically: At a given point the particle momentum is ▽S, and the relative particle density in an ensemble is R 2 . It is first proposed to modify this interpretation by assuming that physical variables undergo rapid fluctuations, so that ▽S is the average of the momentum over a short time interval. However, it appears that this is not enough. It seems necessary to assume that the density also fluctuates. The fluctuations are (...) taken to be random and to satisfy conditions required for agreement with quantum mechanics. In some cases the fluctuating density may take on instantaneous negative values. One gets agreement with quantum mechanics for the spin correlations of two particles in a singlet state. This comes about because of the correlations between the fluctuations of the variables of the two particles, the effect of which is equivalent to an action at a distance. The relation to Bell's inequality is discussed. (shrink)

The rest-frame of the universe determines a universal, or absolute time, that given by a clock at rest in it. The question is raised whether one can have a satisfactory universal time in general relativity if a gravitational field is present, i.e., whether there are coordinates such that the coordinate time is the time given everywhere by a clock at rest and they provide the correct description of our everyday experience. Several attempts are made to find such coordinates, but the (...) results are unsatisfactory. The question is still open, but it may be that there is no significance to such a universal time in general relativity, because to have a clock at rest in a gravitational field requires nongravitational forces. (shrink)

A classical model of an elementary particle is considered in the framework of the bimetric general relativity theory. The particle is regarded as a spherically symmetric object filling its Schwarzschild sphere and made of matter having mass density, pressure, and charge density. The mass is taken to be the Planck mass, and possible values of the charge are taken as zero, ±1/3e, ±2/3e, and ±e, with e the electron charge.

The relation between wave mechanics and classical mechanics is reviewed, and it is stressed that the latter cannot be regarded as the limit of the former as ℏ →0. The motion of a classical particle (or ensemble of particles) is described by means of a Schrödinger-like equation that was found previously. A system of a quantum particle and a classical particle is investigated (1) for an interaction that leads to stationary states with discrete energies and (2) for an interaction that (...) enables the classical particle to act as a measuring instrument for determining a physical variable of the quantum particle. (shrink)

A number of different forms of the Schwarzschild solution are considered. The static forms all have a singularity at the Schwarzschild radius. This Schwarzschild singularity can be eliminated if one goes over to a stationary or time-dependent form of solution. However, the coordinate transformations needed for this have singularities. It is stressed that coordinate systems connected by singular transformations are not equivalent and the corresponding metrics may describe different physical situations.

Generalizing the work of Einstein and Mayer, it is assumed that at each point of space-time there exists a vector-spinor space with Nv vector dimensions and Ns spinor dimensions, where Nv=2k and Ns=2 k, k⩾3. This space is decomposed into a tangent space with4 vector and4 spinor dimensions and an internal space with Nv−4 vector and Ns−4 spinor dimension. A variational principle leads to field equations for geometric quantities which can be identified with physical fields such as the electromagnetic field, (...) Yang-Mills gauge fields, and wave functions of bosons and fermions. (shrink)

Einstein's approach to unified field theories based on the geometry of distant parallelism is discussed. The simplest theory of this type, describing gravitation and electromagnetism, is investigated. It is found that there is a charge-current density vector associated with the geometry. However, in the static spherically symmetric case no singularity-free solutions for this vector exist.

Two theses figure centrally in work on the epistemology of disagreement: Equal Weight (‘EW’) and Uniqueness (‘U’). According to EW, you should give precisely as much weight to the attitude of a disagreeing epistemic peer as you give to your own attitude. U has it that, for any given proposition and total body of evidence, some doxastic attitude is the one the evidence makes rational (justifies) toward that proposition. Although EW has received considerable discussion, the case for U has not (...) been critically evaluated. Endorsing U, we argue, commits one to the highly controversial thesis that whatever fixes your rational attitudes can do so only by fixing what evidence you have. This commitment imposes a relatively demanding requirement on justified belief in U, one that we argue is not satisfied by what is currently the strongest available case for U, due to Roger White [2005]. Our challenge to U makes more trouble for its proponents than do the worries about U expressed by Gideon Rosen [2001] and Thomas Kelly [2010]. Moreover, if Kelly [2010] is correct in thinking that EW “carries with it a commitment to” U—a claim which we accept for reasons similar to Kelly’s but is beyond this paper’s scope (but see Ballantyne and Coffman [forthcoming])—then our challenge to U bears importantly on EW: to the extent that our challenge to U succeeds, EW also suffers. (shrink)

One of the most common excuses is ignorance. Ignorance does not always excuse, however, for sometimes ignorance is culpable. One of the most natural ways to think of the difference between exculpating and culpable ignorance is in terms of justification; that is, one’s ignorance is exculpating only if it is justified and one’s ignorance is culpable only if it not justified. Rosen :591–610, 2008) explores this idea by first offering a brief account of justification, and then two cases that (...) he claims are counter examples to the justification thesis. The aim of this paper is to defend the justification thesis against Rosen’s two cases. The argument will proceed in the following way. First, I clarify a few things about the nature of culpable ignorance generally and why the justification thesis is so intuitive. I then present Rosen’s purported counterexamples. Once this is done, I argue that Rosen misses an important view of justification in the epistemology literature that I call the pragmatic view. I present a general picture of the pragmatic view, and explain how it fits naturally with our practices of criticizing people’s beliefs, including claims of culpable ignorance. Finally, I address Rosen’s cases arguing that, if the pragmatic view is right, then Rosen’s cases are not counterexamples to the justification thesis. (shrink)

In a 1936 manuscript submitted to the Physical Review, Albert Einstein and Nathan Rosen famously claimed that gravitational waves do not exist. It has generally been assumed that there was a conceptual error underlying this fallacious claim. It will be shown, through a detailed study of the extant referee report, that this claim was probably only the result of a calculational error, the accidental use of a pathological coordinate transformation.

In the May 15, 1935 issue of Physical Review Albert Einstein co-authored a paper with his two postdoctoral research associates at the Institute for Advanced Study, Boris Podolsky and Nathan Rosen. The article was entitled “Can Quantum Mechanical Description of Physical Reality Be Considered Complete?” (Einstein et al. 1935). Generally referred to as “EPR”, this paper quickly became a centerpiece in the debate over the interpretation of the quantum theory, a debate that continues today. The paper features a (...) striking case where two quantum systems interact in such a way as to link both their spatial coordinates in a certain direction and also their linear momenta (in the same direction). As a result of this “entanglement”, determining either position or momentum for one system would fix (respectively) the position or the momentum of the other. EPR use this case to argue that one cannot maintain both an intuitive condition of local action and the completeness of the quantum description by means of the wave function. This entry describes the argument of that 1935 paper, considers several different versions and reactions, and explores the ongoing significance of the issues they raise. (shrink)

In this insightful and controversial book, the eminent philosopher Stanley Rosen takes a new look at the famous 'quarrel' that the moderns have with the ancients, analyzing and comparing ancient philosophers and modern Continental and analytical thinkers from Plato, Descartes, and Kant to Fichte, Nietzsche, and Rorty. He urges that we do not dismiss the classical heritage but appropriate it, for this appropriation is an indispensable step in the process of legitimizing our historical experience.

Changing our minds isn't easy. Even when we recognize our views are disputed by intelligent and informed people, we rarely doubt our rightness. Why is this so? How can we become more open-minded, putting ourselves in a better position to tolerate conflict, advance collective inquiry, and learn from differing perspectives in a complex world? -/- Nathan Ballantyne defends the indispensable role of epistemology in tackling these issues. For early modern philosophers, the point of reflecting on inquiry was to understand (...) how our beliefs are often distorted by prejudice and self-interest, and to improve the foundations of human knowledge. Ballantyne seeks to recover and modernize this classical tradition by vigorously defending an interdisciplinary approach to epistemology, blending philosophical theorizing with insights from the social and cognitive sciences. -/- Many of us need tools to help us think more circumspectly about our controversial views. Ballantyne develops a method for distinguishing between our reasonable and unreasonable opinions, in light of evidence about bias, information overload, and rival experts. This method guides us to greater intellectual openness--in the spirit of skeptics from Socrates to Montaigne to Bertrand Russell--making us more inclined to admit that sometimes we don't have the right answers. With vibrant prose and fascinating examples from science and history, Ballantyne shows how epistemology can help us know our limits. (shrink)

When we dream, we feel emotions in response to objects and events that exist only in the dream. What should we say about these emotions? One key question is whether these emotions can be said to be ‘fitting’, that is, appropriate to the evoking scenario. However, how we evaluate these emotions for fittingness may depend on the nature of dreams. According to the imagination model, dreamers do not believe that dream objects are real or that dream events are really happening. (...) In contrast, the hallucination model suggests that we falsely believe dream events are real and many of these beliefs are irrational. Under these conditions, an interesting possibility arises: dream emotions may be “essentially unfitting”, or in other words, feeling emotions in response to dream events is always unfitting. If fittingness requires a match between emotion and evaluative properties of objects or events, it is prima facie plausible that dream emotions could fail to fit under the imagination model because it is unfitting to have an emotion towards an object we do not believe to be real. Further, under the hallucination model, dream emotions could be unfitting because their objects do not exist even if we believe them to be real, or alternatively, because of the irrational nature of dream beliefs. More nuance, however, is required. By comparing dream emotions to the emotions we experience while imagining, engaging with fiction, and hallucinating, we evaluate the possibility of essential unfittingness of dream emotions. We conclude that although there are compelling arguments in support of the claim that dream emotions are essentially unfitting, these arguments are not entirely convincing, and it is more plausible that particular dream emotions can be assessed for fittingness under either model of dreaming. (shrink)

Epistemic trespassers judge matters outside their field of expertise. Trespassing is ubiquitous in this age of interdisciplinary research and recognizing this will require us to be more intellectually modest.

Region R Question: How many objects — entities, things — are contained in R? Ignore the empty space. Our question might better be put, 'How many material objects does R contain?' Let's stipulate that A, B and C are metaphysical atoms: absolutely simple entities with no parts whatsoever besides themselves. So you don't have to worry about counting a particle's top half and bottom half as different objects. Perhaps they are 'point-particles', with no length, width or breadth. Perhaps they are (...) extended in space without possessing spatial parts (if that is possible). Never mind. We stipulate that A, B and C are perfectly simple. We also stipulate that they are connected as follows. A and B are stuck together in such a way that when a force is applied to one of them, they move together 'as a unit'. Moreover, the two of them together exhibit behavior that neither would exhibit on its own — Perhaps they emit a certain sound, or glow in the dark — whereas C is.. (shrink)

I demonstrate that a "speech act" theory of meaning for imperatives is—contra a dominant position in philosophy and linguistics—theoretically desirable. A speech act-theoretic account of the meaning of an imperative !φ is characterized, broadly, by the following claims. -/- LINGUISTIC MEANING AS USE !φ’s meaning is a matter of the speech act an utterance of it conventionally functions to express—what a speaker conventionally uses it to do (its conventional discourse function, CDF). -/- IMPERATIVE USE AS PRACTICAL !φ's CDF is to (...) express a practical (non-representational) state of mind—one concerning an agent's preferences and plans, rather than her beliefs. -/- Opposed to speech act accounts is a preponderance of views which deny that a sentence's linguistic meaning is a matter of what speech act it is used to perform, or its CDF. On such accounts, meaning is, instead, a matter of "static" properties of the sentence—e.g., how it depicts the world as being (or, more neutrally, the properties of a model-theoretic object with which the semantic value of the sentence co-varies). On one version of a static account, an imperative 'shut the window!' might, for instance, depict the world as being such that the window must be shut. -/- Static accounts are traditionally motivated against speech act-theoretic accounts by appeal to supposedly irremediable explanatory deficiencies in the latter. Whatever a static account loses in saying (prima facie counterintuitively) that an imperative conventionally represents, or expresses a picture of the world, is said to be offset by its ability to explain a variety of phenomena for which speech act-theoretic accounts are said to lack good explanations (even, in many cases, the bare ability to offer something that might meet basic criteria on what a good explanation should be like). -/- I aim to turn the tables on static accounts. I do this by showing that speech act accounts are capable of giving explanations of phenomena which fans of static accounts have alleged them unable to give. Indeed, for a variety of absolutely fundamental phenomena having to do with the conventional meaning of imperatives (and other types of practical language), speech act accounts provide natural and theoretically satisfying explanations, where a representational account provides none. (shrink)

Two theses are central to recent work on the epistemology of disagreement: Conciliationism:?In a revealed peer disagreement over P, each thinker should give at least some weight to her peer's attitude. Uniqueness:?For any given proposition and total body of evidence, the evidence fully justifies exactly one level of confidence in the proposition. 1This paper is the product of full and equal collaboration between its authors. Does Conciliationism commit one to Uniqueness? Thomas Kelly 2010 has argued that it does. After some (...) scene-setting (?1), in ?2 we explain and criticize Kelly's argument, thereby defeating his larger argument that Conciliationism deserves no dialectical special treatment. But we argue further that Conciliationists are committed to a disjunction, one of whose disjuncts is Uniqueness, that amounts to an ?extremely strong and unobvious position? (??3?4). If we are correct, theorists should not treat Conciliationism as a default position in debates about the epistemic significance of disagreement. (shrink)

This article evaluates an emerging element in popular debate and inquiry: DYOR. (Haven’t heard of the acronym? Then Do Your Own Research.) The slogan is flexible and versatile. It is used frequently on social media platforms about topics from medical science to financial investing to conspiracy theories. Using conceptual and empirical resources drawn from philosophy and psychology, we examine key questions about the slogan’s operation in human cognition and epistemic culture.

ABSTRACT: Most of what we believe comes to us from the word of others, but we do not always believe what we are told. We often reject thinkers' reports by attributing biases to them. We may call this debunking. In this essay, I consider how debunking might work and then examine whether, and how often, it can help to preserve rational belief in the face of disagreement.

Walter Sinnott-Armstrong has developed and progressively refined an argument against moral intuitionism—the view on which some moral beliefs enjoy non-inferential justification. He has stated his argument in a few different forms, but the basic idea is straightforward. To start with, Sinnott-Armstrong highlights facts relevant to the truth of moral beliefs: such beliefs are sometimes biased, influenced by various irrelevant factors, and often subject to disagreement. Given these facts, Sinnott-Armstrong infers that many moral beliefs are false. What then shall we think (...) of our own moral beliefs? Either we have reason to think some of our moral beliefs are reliably formed or we have no such reason. If the latter, our moral beliefs are unjustified. If we have reason to think some moral beliefs are reliably formed, then those beliefs are not non-inferentially justified, because then we’ll have reason to accept something—namely, that they are reliably formed—that entails or supports those beliefs. But then, either way, our moral beliefs are not non-inferentially justified, and so moral intuitionism is false. This paper takes issue with Sinnott-Armstrong’s interesting and widely discussed argument, which we here call the Empirical Defeat Argument (EDA). According to us, the EDA does not defeat moral intuitionism. In section 1, we will set out the argument, briefly reviewing the rationale Sinnott-Armstrong offers for the premises. Then, in section 2, we identify a critical but dubious epistemological assumption concerning the nature of defeat that undergirds the argument. Finally, in section 3, we will defend our challenge to the EDA by answering two objections. (shrink)

Intellectual humility is commonly thought to be a mindset, disposition, or personality trait that guides our reactions to evidence as we seek to pursue the truth and avoid error. Over the last decade, psychologists, philosophers, and other researchers have begun to explore intellectual humility, using analytical and empirical tools to understand its nature, implications, and value. This review describes central questions explored by researchers and highlights opportunities for multidisciplinary investigation.

Recent work on the nature of luck widely endorses the thesis that an event is good or bad luck for an individual only if it is significant for that individual. In this paper, I explore this thesis, showing that it raises questions about interests, well-being, and the philosophical uses of luck. In Sect. 1, I examine several accounts of significance, due to Pritchard (2005), Coffman (2007), and Rescher (1995). Then in Sect. 2 I consider what some theorists want to ‘do’ (...) with luck, taking important examples from epistemology (explaining Gettier-style examples) and political philosophy (offering a rationale for the just distribution of resources in society), while suggesting implications for significance. Drawing together lessons from Sects. 1 and 2, I develop a new account of significance in Sect. 3 before concluding with reflections on the debate in Sect. 4. (shrink)

Nathan Carlin revisits the role of religion in bioethics, an increasingly secular enterprise, and argues that pastoral theologians can enrich moral imagination in bioethics by cultivating an aesthetic sensibility that is theologically-informed, psychologically-sophisticated, therapeutically-oriented, and experientially-grounded. To achieve these ends, Carlin employs Paul Tillich's method of correlation by positioning four principles of bioethics with four images of pastoral care.

David Lewis and Peter van Inwagen have claimed that there are no “knockdown” arguments in philosophy. Their claim appears to be at odds with common philosophical practice: philosophers often write as though their conclusions are established or proven and that the considerations offered for these conclusions are decisive. In this paper, I examine some questions raised by Lewis’s and van Inwagen’s contention. What are knockdown arguments? Are there any in philosophy? If not, why not? These questions concern the nature of (...) the philosophical enterprise and our answers have implications for the limits on the attitudes of informed, rational thinkers. (shrink)

Abstract Both parties in the active philosophical debate concerning the conceptual character of perception trace their roots back to Kant's account of sensible intuition in the Critique of Pure Reason. This striking fact can be attributed to Kant's tendency both to assert and to deny the involvement of our conceptual capacities in sensible intuition. He appears to waver between these two positions in different passages, and can thus seem thoroughly confused on this issue. But this is not, in fact, the (...) case, for, as I will argue, the appearance of contradiction in his account stems from the failure of some commentators to pay sufficient attention to Kant's developmental approach to philosophy. Although he begins by asserting the independence of intuition, Kant proceeds from this nonconceptualist starting point to reveal a deeper connection between intuitions and concepts. On this reading, Kant's seemingly conflicting claims are actually the result of a careful and deliberate strategy for gradually convincing his readers of the conceptual nature of perception. (shrink)

Shadow Philosophy: Plato’s Cave and Cinema is an accessible and exciting new contribution to film-philosophy, which shows that to take film seriously is also to engage with the fundamental questions of philosophy. Nathan Andersen brings Stanley Kubrick’s film A Clockwork Orange into philosophical conversation with Plato’s Republic , comparing their contributions to themes such as the nature of experience and meaning, the character of justice, the contrast between appearance and reality, the importance of art, and the impact of images. (...) At the heart of the book is a novel account of the analogy between Plato’s allegory of the cave and cinema, developed in conjunction with a provocative interpretation of the most powerful image from A Clockwork Orange , in which the lead character is strapped to a chair and forced to watch violent films. Key features of the book include: a comprehensive bibliography of suggested readings on Plato, on film, on philosophy, and on the philosophy of film a list of suggested films that can be explored following the approach in this book, including brief descriptions of each film, and suggestions regarding its philosophical implications a summary of Plato’s Republic , book by book, highlighting both dramatic context and subject matter. Offering a close reading of the controversial classic film A Clockwork Orange , and an introductory account of the central themes of the philosophical classic The Republic , this book will be of interest to both scholars and students of philosophy and film, as well as to readers of Plato and fans of Stanley Kubrick. (shrink)