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)

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)

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.

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)

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)

I argue that reflection on philosophers who could have been working among us but aren’t can lead us to give up our philosophical beliefs.

Aristotle is said to have held that any kind of actual infinity is impossible. I argue that he was a finitist (or "potentialist") about _magnitude_, but not about _plurality_. He did not deny that there are, or can be, infinitely many things in actuality. If this is right, then it has implications for Aristotle's views about the metaphysics of parts and points.

The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined even if it is not sufficiently formal and precise to belong to mathematics proper (in a narrow sense)—and even if (as many have asserted) for that reason the Church–Turing thesis is unprovable. It is proved logically that the class of effective procedures is not decidable, i.e., that no effective procedure is possible for ascertaining whether a given procedure is effective. This (...) undecidability result is proved directly from the notion itself of an effective procedure, without reliance on any (partly) mathematical lemma, conjecture, or thesis invoking recursiveness or Turing-computability. In fact, there is no reliance on anything very mathematical. The proof does not even appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of an effective procedure. Though the result that effectiveness is undecidable is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure invariably terminates with the correct verdict. (shrink)

Stanley Rosen's book is the first full-length study of the Sophist in English and one of the most complete in any language. He follows the stages of the dialogue in sequence and offers an exhaustive analysis of the philosophical questions that come to light as Theaetetus and the Eleatic Stranger pursue the sophist through philosophical debate. Rosen finds the central problem of the dialogue in the relation between original and image; he shows how this distinction underlies all subsequent (...) technical themes and analyzes in detail such problems as non-being or negation and false statement. Arguing that the dialogue must be treated as a dramatic unity, he pays careful attention throughout to the setting, the events, the language used, and the relations between the natures of the speakers and the topics under discussion. (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)

Combining exemplary scholarship and analytic precision, Stanley Rosen illuminates the underpinnings of post-modernist thought, providing valuable insight as he pursues two arguments: first, that post-modernism, which regards itself as an attack upon the Enlightenment, is in fact the penultimate stage of the Enlightenment itself; and second, that the extraordinary contemporary emphasis upon hermeneutics is the latest consequence of the triumph of history over mathematics within the unstable essence of the Enlightenment. Hermeneutics is consequently at bottom a political phenomenon. In (...) developing these arguments, Rosen demonstrates the paradigmatic status of Kant for a proper understanding of post-modernism, analyzes Derrida's influential critique of Platonism as well as his defense of writing, explains the political dimension of the quarrel between the ancients and moderns by studying the hermeneutics of Leo Strauss and Alexander Kojhve, and shows how the modern notion of "theory" is intrinsically relativized by the triumph of history over mathematics into the notion of interpretation. A wide-ranging exploration into current critical thinking, Hermeneutics as Politics will generate considerable debate among scholars interested in post-modernism, the Enlightenment, hermeneutics, the relation of philosophy and politics, deconstruction, and the history of philosophy. (shrink)

Alonzo Church famously provided three principal competing criteria for “strict synonymy,” i.e., sameness of semantic content. These are his Alternatives (0), (1), and (2)—numbered in order of increasing course-grainedness of content. On Alternative (2), expressions are deemed strictly synonymous iff they are logically equivalent. This criterion seems hopeless as an account of the objects of propositional attitude. On Alternative (1), expressions are deemed synonymous iff they are λ-convertible. Alternative (1) also evidently conflicts with discourse about the attitudes. On Alternative (0), (...) expressions are deemed strictly synonymous iff they are “synonymously isomorphic” in Church’s sense. On Alternative (0), semantic content is so fine-grained that not even “Romeo loves Juliet” and “Juliet is loved by Romeo” qualify as strictly synonymous. A fourth alternative, here called “Alternative (3),” deems expressions strictly synonymous iff they are co-intensional, i.e., they have the same semantic extension with respect to the same possible worlds. This criterion’s notion of content is even more course grained than that of Alternative (2). Several objections to Alternative (3) are considered. (This article is contained within the author’s more definitive essay, “Singular Concepts”.). (shrink)

Plato's great attempt to define the nature of the sophist -- the false image of the philosopher -- has perplexed readers from classical times to the present. The dialogue has been central in the ongoing debate about the theory of forms, and it remains a crucial text for Plato scholars in both the analytical and the phenomenological traditions. Stanley Rosen's book is the first full-length study of the Sophist in English and one of the most complete in any language. (...) He follows the stages of the dialogue in sequence and offers an exhaustive analysis of the philosophical questions that come to light as Theaetetus and the Eleatic Stranger pursue the sophist through philosophical debate. Rosen finds the central problem of the dialogue in the relation between original and image; he shows how this distinction underlies all subsequent technical themes and analyzes in detail such problems as non-being or negation and false statement. Arguing that the dialogue must be treated as a dramatic unity, he pays careful attention throughout to the setting, the events, the language used, and the relations between the natures of the speakers and the topics under discussion. Rosen's new approach to the technical issues in the dialogue will be of interest to Plato scholars of all schools, and his analysis of the sophistical dimension of the world will engage all who have puzzled over what it means to be a philosopher. (shrink)

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.

To counter the imbalance in vaccine distribution during the COVID-19 pandemic, Albertsen and more recently Germaniet alhave 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)

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)

Toward a theory of n-tuples of individuals and concepts as surrogates for Russellian singular propositions and singular concepts. Alonzo Church proposed a powerful and elegant theory of sequences of functions and their arguments as singular-concept surrogates. Church’s account accords with his Alternative (0), the strictest of his three competing criteria for strict synonymy. The currently popular objection to strict criteria like (0) on the basis of the Russell-Myhill paradox is here rebutted. As Church recognized, Russell-Myhill is not a problem specifically (...) for Alternative (0). Rather it is a disproof of unrestricted concept comprehension. Unrestricted comprehension is also inconsistent with facts about sets of properties. It is demonstrated furthermore that the principal rival conception of propositions--propositions conceived as classes of possible worlds--is subject to a fatal philosophical collapse: It follows on that conception, given that each of us is fallible, that everyone believes everything. Although it is far superior to its principal rival conception, Church’s proposed theory is vulnerable under (0) to a version of Russell’s notorious Gray’s /Elegy/ objection. Some amendments to Church’s proposal are proffered that address Russell’s objection, including an amendment first proposed in the present author’s /Frege’s Puzzle/ (1986). Church’s response (personal correspondence) is considered. (shrink)

The first part of my hypothesis, then, is simple enough, and would be accepted in principle by most students of Plato: the dramatic structure of the dialogues is an essential part of their philosophical meaning. With respect to the poetic and mathematical aspects of philosophy, we may distinguish three general kinds of dialogue. For example, consider the Sophist and Statesman, where Socrates is virtually silent: the principal interlocutors are mathematicians and an Eleatic Stranger, a student of Parmenides, although one who (...) is not always loyal to his master's teaching of what might be called monadic homogeneity. In these dialogues, the mathematical character of philosophy is not merely emphasized but exaggerated, and any attempt to interpret them must take this fact into account. Otherwise, we shall not be able to understand why the Stranger seems to classify the general's art in the same species of the genus hunting as the louse catcher. The significance of this step, which does not stem from humanitarian considerations, but rather illustrates how the human becomes invisible from the mathematical viewpoint, contributes its share to the obscurity of these two dialogues. Second, there are dialogues like the Phaedrus and Symposium, in which the style, the interlocutors, and even the subject-matter seem to be largely poetic and rhetorical. Here, the overwhelming impression is of enthusiasm, divine madness, and intoxication in speech and deed. Finally, there are dialogues like the Philebus and Republic, in which it is not so easy to say whether poetry or mathematics predominates, if indeed either may be said to do so. (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.

Modeled on the classic Tao Te Ching, this startling and revealing new interpretation of Carl Jung's life and psychology parallels Jung's natural world of the psyche and that of Taoist philosophy, exploring the integration of such opposites as shadow/persona, yin/yang, dark/light, and feminine/masculine. Photos & drawings.