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)

Dignity plays a central role in current thinking about law and human rights, but there is sharp disagreement about its meaning. Combining conceptual precision with a broad historical background, Michael Rosen puts these controversies in context and offers a novel, constructive proposal. “Penetrating and sprightly...Rosen rightly emphasizes the centrality of Catholicism in the modern history of human dignity. His command of the history is impressive...Rosen is a wonderful guide to the recent German constitutional thinking about human dignity...[ (...) class='Hi'>Rosen] is in general an urbane and witty companion, achieving his aim of accessibly written philosophy.” —Samuel Moyn, The Nation “[An] elegant, interesting and lucid exploration of the concept of dignity...Drawing on classical, liberal and Catholic traditions, Rosen hopes to rehabilitate dignity to its rightful place near the centre of moral thought...Rosen's admirable book deserves wide attention from political theorists, jurisprudes and political philosophers.” —Simon Blackburn, Times Higher Education “Dignity deserves to be widely read, not only for its intrinsic interest, but also as a corrective to the habit of discussing such topics in abstraction from their social context. Whether or not one agrees with Rosen's arguments, there can be no doubt he has widened our horizons.” —Rae Langton, Times Literary Supplement. (shrink)

It is widely supposed that every entity falls into one of twocategories: Some are concrete; the rest abstract. The distinction issupposed to be of fundamental significance for metaphysics andepistemology. This article surveys a number of recent attempts to sayhow it should be drawn.

Recently, Michael Huemer has defended the Principle of Phenomenal Conservatism: If it seems to S that p, then, in the absence of defeaters, S thereby has at least some degree of justification for believing that p. This principle has potentially far-reaching implications. Huemer uses it to argue against skepticism and to defend a version of ethical intuitionism. I employ a reductio to show that PC is false. If PC is true, beliefs can yield justification for believing their contents in cases (...) where, intuitively, they should not be able to do so. I argue that there are cases where a belief that p can behave like an appearance that p and thereby make it seem to one that p. (shrink)

A correct observation to the effect that a does not exist, where ‘a’ is a singular term, could be true on any of a variety of grounds. Typically, a true, singular negative existential is true on the unproblematic ground that the subject term ‘a’ designates something that does not presently exist. More interesting philosophically is a singular, negative existential statement in which the subject term ‘a’ designates nothing at all. Both of these contrast sharply with a singular, negative existential in (...) which the subject term is a name from fiction. I argue that such singular, negative existential statements are false. My account of fictional characters differs significantly from Kripke’s. It is shown that an objection to my account rests on a serious misunderstanding. Finally, a crucial aspect of the account is emphasized. (shrink)

To counter the imbalance in vaccine distribution during the COVID-19 pandemic, Albertsen and more recently Germani _et al_ have suggested a new system of taxation coined as ‘VaxTax’ that would force higher-income countries to fund the access of low-income and middle-income countries (LMICs) to new vaccines in times of pandemic. I will argue that this idea faces numerous challenges of ethical, sociopolitical and economical nature that may hinder any effort to solve the numerous health challenges that LMICs face. I argue (...) that while it is an interesting idea, it is neither sufficient nor will it ever be easily implemented because of socioeconomic or practical reasons. (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 book argues that Hume is a radical epistemic skeptic who gives only practical reasons for retaining belief in sensory beliefs and the deliverances of reason. He advises us to take a moderate approach to the demands of philosophy, since they sometimes diverge from the demands of life.

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)

The concept of a proposition is important in several areas of philosophy and central to the philosophy of language. This collection of readings investigates many different philosophical issues concerning the nature of propositions and the ways they have been regarded through the years. Reflecting both the history of the topic and the range of contemporary views, the book includes articles from Bertrand Russell, Gottlob Frege, the Russell-Frege Correspondence, Alonzo Church, David Kaplan, John Perry, Saul Kripke, Hilary Putnam, Mark Richard, Scott (...) Soames, and Nathan Salmon. (shrink)

Alan Weir: Quine's Naturalism: Starting with the distinction between epistemological and ontological naturalism, this chapter focuses most on Quine's epistemological naturalism, not the ontological anti‐naturalism he thought it leads to. It is argued that naturalized epistemology is not central to Quine's epistemology. Quine's key epistemological principle is: follow the methods of science, and only those. Can Quine demarcate scientific methods from non‐scientific ones? The problems which have been raised here, for example in the case of mathematics, are considered. A main (...) theme is the relationship between Quine's naturalism and reductionist forms of “scientistic” naturalism. Quine is generally taken to be an anti‐reductionist, unsurprisingly given his explicit anti‐reductionist pronouncements from “Two Dogmas” onward. It is argued that the situation is more complex than this and that key Quinean arguments are driven by a positivistic reductionism he never entirely broke free from. (shrink)

The non-lover -- The concealed lover -- The lover -- The language of love.

A thesis (“weak BCP”) nearly universally held among philosophers of probability connects the concepts of objective chance and metaphysical modality: Any prospect (outcome) that has a positive chance of obtaining is metaphysically possible—(nearly) equivalently, any metaphysically impossible prospect has zero chance. Particular counterexamples are provided utilizing the monotonicity of chance, one of them related to the four world paradox. Explanations are offered for the persistent feeling that there cannot be chancy metaphysical necessities or chancy metaphysical impossibilities. Chance is objective but (...) contrary to popular opinion it is also largely epistemic. Chancy necessities are analogous to necessary a posteriori truths. Philosophy and Phenomenological Research, Volume 99, Issue 3, Page 644-662, November 2019. (shrink)

A new philosophical analysis is provided of the notorious Sleeping Beauty Problem. It is argued that the correct solution is one-third, but not in the way previous philosophers have typically meant this. A modified version of the Problem demonstrates that neither self-locating information nor amnesia is relevant to the core Problem, which is simply to evaluate the conditional chance of heads given an undated Monday-or-Tuesday awakening. Previous commentators have failed to appreciate the significance of the information that Beauty gains upon (...) waking, and which is relevant to the conditional chance of heads: de re acquaintance with the awakening itself and the non-locating knowledge that it is an experimental awakening. David Lewis and company are committed to several unjustifiable and unacceptable probability assessments. Previous commentators have in effect confused the information that Beauty undergoes this particular experimental awakening for the information that she undergoes some experimental awakening or other. Lewis in particular thereby illegitimately tips the scales both in favor of heads and in favor of Monday. The Sleeping Beauty Problem is equivalent to a ball-in-urn word problem in elementary probability theory. (shrink)

Tom Regan argues that human beings and some non-human animals have moral rights because they are “subjects of lives,” that is, roughly, conscious, sentient beings with an experiential welfare. A prominent critic, Carl Cohen, objects: he argues that only moral agents have rights and so animals, since they are not moral agents, lack rights. An objection to Cohen’s argument is that his theory of rights seems to imply that human beings who are not moral agents have no moral rights, but (...) since these human beings have rights, his theory of rights is false, and so he fails to show that animals lack rights. Cohen responds that this objection fails because human beings who are not moral agents nevertheless are the “kind” of beings who are moral agents and so have rights, but animals are not that “kind” of being and so lack rights. Regan argues that Cohen’s “kind” arguments fail: they fail to explain why human beings who are not moral agents have rights and they fail to show that animals lack rights. Since Cohen’s “kind” arguments are influential, I review and critique Regan’s objections . I offer suggestions for stronger responses to arguments like Cohen’s. (shrink)

What makes for a good education? What does one need to count as well-educated? Knowledge, to be sure. But knowledge is easily forgotten, and today's knowledge may be obsolete tomorrow. Skills, particularly in critical thinking, are crucial as well. But absent the right motivation, graduates may fail to put their skills to good use. In this book, Nathan King argues that intellectual virtues-traits like curiosity, intellectual humility, honesty, intellectual courage, and open-mindedness-are central to any education worthy of the name. (...) Further, such virtues are crucial to our functioning well in everyday life, in areas as diverse as personal relationships, responsible citizenship, civil discourse, and personal success. Our struggles in these areas often result from a failure to think virtuously. Drawing upon recent work in philosophy and psychology, King paints a portrait of virtuous intellectual character-and of the vices such a character opposes. Filled with examples and applications, this book introduces readers to the intellectual virtues: what they are, why they matter, and how we can grow in them. (shrink)