Change and local spatial variation are missing in Hamiltonian general relativity according to the most common definition of observables as having 0 Poisson bracket with all first-class constraints. But other definitions of observables have been proposed. In pursuit of Hamiltonian–Lagrangian equivalence, Pons, Salisbury and Sundermeyer use the Anderson–Bergmann–Castellani gauge generator G, a tuned sum of first-class constraints. Kuchař waived the 0 Poisson bracket condition for the Hamiltonian constraint to achieve changing observables. A systematic combination of the two reforms might (...) use the gauge generator but permit non-zero Lie derivative Poisson brackets for the external gauge symmetry of General Relativity. Fortunately one can test definitions of observables by calculation using two formulations of a theory, one without gauge freedom and one with gauge freedom. The formulations, being empirically equivalent, must have equivalent observables. For de Broglie-Proca non-gauge massive electromagnetism, all constraints are second-class, so everything is observable. Demanding equivalent observables from gauge Stueckelberg–Utiyama electromagnetism, one finds that the usual definition fails while the Pons–Salisbury–Sundermeyer definition with G succeeds. This definition does not readily yield change in GR, however. Should GR’s external gauge freedom of general relativity share with internal gauge symmetries the 0 Poisson bracket, or is covariance sufficient? A graviton mass breaks the gauge symmetry, but it can be restored by parametrization with clock fields. By requiring equivalent observables, one can test whether observables should have 0 or the Lie derivative as the Poisson bracket with the gauge generator G. The latter definition is vindicated by calculation. While this conclusion has been reported previously, here the calculation is given in some detail. (shrink)

Here I propose a coherent way of preserving the identity of material objects with the matter that constitutes them. The presentation is formal, and intended for RSL. An informal presentation is in preliminary draft! -/- Relative-sameness relations—such as being the same person as—are like David Lewis's "counterpart" relations in the following respects: (i) they may hold between objects that aren't identical (I propose), and (ii) there are a multiplicity of them, different ones of which may be variously invoked in different (...) contexts. They differ from counterpart relations, however, in that they are weak equivalence relations (transitive, symmetric and weakly reflexive). The likenesses to counterpart relations make them suitable for an analysis of de-re temporal and modal predications. The difference renders the resulting counterpart theory immune to standard criticisms of Lewis's Counterpart Theory (e.g., in Hazen 1979, and Fara and Williamson 2005). (shrink)

It will be shown that, in comparison with the pre-relativistic Galileo-invariant conceptions, special relativity tells us nothing new about the geometry of spacetime. It simply calls something else "spacetime", and this something else has different properties. All statements of special relativity about those features of reality that correspond to the original meaning of the terms "space" and "time" are identical with the corresponding traditional pre-relativistic statements. It will be also argued that special relativity and Lorentz theory (...) are completely identical in both senses, as theories about spacetime and as theories about the behavior of moving physical objects. (shrink)

The multiple detections of gravitational waves by LIGO (the Laser Interferometer Gravitational-Wave Observatory), operated by Caltech and MIT, have been acclaimed as confirming Einstein's prediction, a century ago, that gravitational waves propagating as ripples in spacetime would be detected. Yunes and Pretorius (2009) investigate whether LIGO's template-based searches encode fundamental assumptions, especially the assumption that the background theory of general relativity is an accurate description of the phenomena detected in the search. They construct the parametrized post-Einsteinian (ppE) framework (...) in response, which broadens those assumptions and allows for wider testing under more flexible assumptions. Their methods are consistent with work on confirmation and testing found in Carnap (1936), Hempel (1969), and Stein (1992, 1994), with the following principles in common: that confirmation is distinct from testing, and that, counterintuitively, revising a theory's formal basis can make it more broadly empirically testable. These views encourage a method according to which theories can be made abstract, to define families of general structures for the purpose of testing. With the development of the ppE framework and related approaches, multi-messenger astronomy is a catalyst for deep reasoning about the limits and potential of the theoretical framework of general relativity. (shrink)

We put forward a new view of relativity theory that makes the existence of a flow of time compatible with the four-dimensional block universe. To this end, we apply the creation-discovery view elaborated for quantum mechanics to relativity theory and in such a way that time and space become creations instead of discoveries and an underlying non temporal and non spatial reality comes into existence. We study the nature of this underlying non temporal and non spatial (...) reality and reinterpret many aspects of the theory within this new view. We show that data of relativistic measurements are sufficient to derive the three-dimensionality of physical space. The nature of light and massive entities is reconsidered, and an analogy with human cognition is worked out. (shrink)

Change and local spatial variation are missing in canonical General Relativity's observables as usually defined, an aspect of the problem of time. Definitions can be tested using equivalent formulations of a theory, non-gauge and gauge, because they must have equivalent observables and everything is observable in the non-gauge formulation. Taking an observable from the non-gauge formulation and finding the equivalent in the gauge formulation, one requires that the equivalent be an observable, thus constraining definitions. For massive photons, the (...) de Broglie-Proca non-gauge formulation observable A_{\mu} is equivalent to the Stueckelberg-Utiyama gauge formulation quantity A_{\mu} + \partial_{\mu} \phi, which must therefore be an observable. To achieve that result, observables must have 0 Poisson bracket not with each first-class constraint, but with the Rosenfeld-Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first-class constraints, in accord with the Pons-Salisbury-Sundermeyer definition of observables. The definition for external gauge symmetries can be tested using massive gravity, where one can install gauge freedom by parametrization with clock fields X^A. The non-gauge observable g^{\mu\nu} has the gauge equivalent X^A,_{\mu} g^{\mu\nu} X^B,_{\nu}. The Poisson bracket of X^A,_{\mu} g^{\mu\nu} X^B,_{\nu} with G turns out to be not 0 but a Lie derivative. This non-zero Poisson bracket refines and systematizes Kuchař's proposal to relax the 0 Poisson bracket condition with the Hamiltonian constraint. Thus observables need covariance, not invariance, in relation to external gauge symmetries. The Lagrangian and Hamiltonian for massive gravity are those of General Relativity + \Lambda + 4 scalars, so the same definition of observables applies to General Relativity. Local fields such as g_{\mu\nu} are observables. Thus observables change. Requiring equivalent observables for equivalent theories also recovers Hamiltonian-Lagrangian equivalence. (shrink)

We give a “direction for use” of the scale relativity theory and apply it to an example of spontaneous multiscale integration including four embedded levels of organization (intracellular, cell, tissue and organism-like levels). We conclude by an update of our analysis of the arctic sea ice melting.

(2007). Relativity Theory between Structural and Dynamical Explanations. International Studies in the Philosophy of Science: Vol. 21, No. 1, pp. 95-102.

It is widely believed that the principal difference between Einstein's special relativity and its contemporary rival Lorentz-type theories was that while the Lorentz-type theories were also capable of “explaining away” the null result of the Michelson-Morley experiment and other experimental findings by means of the distortions of moving measuring-rods and moving clocks, special relativity revealed more fundamental new facts about the geometry of space-time behind these phenomena. I shall argue that special relativity tells us nothing new about (...) the geometry of space-time, in comparison with the pre-relativistic Galileo-invariant conceptions; it simply calls something else "space-time", and this something else has different properties. All statements of special relativity about those features of reality that correspond to the original meaning of the terms "space" and "time" are identical with the corresponding traditional pre-relativistic statements. It will be also argued that special relativity and Lorentz theory are completely identical in both senses, as theories about space-time and as theories about the behavior of moving physical objects. (shrink)

This survey article is divided into two parts. In the first (section 2), I give a brief account of the structure of classical relativity theory. In the second (section 3), I discuss three special topics: (i) the status of the relative simultaneity relation in the context of Minkowski spacetime; (ii) the ``geometrized" version of Newtonian gravitation theory (also known as Newton-Cartan theory); and (iii) the possibility of recovering the global geometric structure of spacetime from its ``causal (...) structure". (shrink)

Weyl symmetry of the classical bosonic string Lagrangian is broken by quantization, with profound consequences described here. Reimposing symmetry requires that the background space-time satisfy the equations of general relativity: general relativity, hence classical space-time as we know it, arises from string theory. We investigate the logical role of Weyl symmetry in this explanation of general relativity: it is not an independent physical postulate but required in quantum string theory, so from a certain point of (...) view it plays only a formal role in the explanation. (shrink)

L’une des plus notoires limites en droit international est la possibilité pour les États parties d’émettre des réserves afin de diminuer leur obligation de mettre en œuvre les droits enchâssés dans un traité. Les réserves formulées lors de la ratification de la Convention relative aux droits de l’enfant au regard du droit à l’éducation sont particulièrement notables et seront le sujet d’analyse de cet article. Nous allons dans un premier temps considérer le sens, l’intention sous-jacente, et la portée des réserves (...) en droit international, dans le cadre de la théorie de la « signifique» élaborée par l’éminente sémioticienne Victoria Lady Welby. Dans un deuxième temps, nous allons étudier le contenu des réserves au droit à l’éducation, l’intention des États lors de la rédaction des dispositions en nous référant aux travaux préparatoires de la CDE, et enfin leur « signification». Nous tenterons de répondre à la question suivante: les réserves au droit à l’éducation ont-elles des limites? Finalement, nous effectuerons une analyse sémioéthique de la Convention afin d’identifier des mesures permettant de désamorcer le signe pernicieux que constitue toute réserve au droit à l’éducation. (shrink)

A recent paper suggested that if Galilean covariance was extended to signals and interactions, the resulting theory would contain such anomalies as would have impelled physicists towards special relativity even without empirical prompts. I analyze this claim. Some so-called anomalies turn out to be errors. Others have classical analogs, which suggests that classical physicists would not have viewed them as anomalous. Still others, finally, remain intact in special relativity, so that they serve as no impetus towards this (...) theory. I conclude that Galilean covariance is insufficient to derive special relativity. (shrink)

Withdrawn by the author! The main content of this paper has been moved into "Szabó, László E., Does special relativity theory tell us anything new about space and time? (ID Code:1321)".

Games such as the St. Petersburg game present serious problems for decision theory.1 The St. Petersburg game invokes an unbounded utility function to produce an infinite expectation for playing the game. The problem is usually presented as a clash between decision theory and intuition: most people are not prepared to pay a large finite sum to buy into this game, yet this is precisely what decision theory suggests we ought to do. But there is another problem associated (...) with the St. Petersburg game. The problem is that standard decision theory counsels us to be indifferent between any two actions that have infinite expected utility. So, for example, consider the decision problem of whether to play the St. Petersburg game or a game where every payoff is $1 higher. Let’s call this second game the Petrograd game (it’s the same as St. Petersburg but with a bit of twentieth century inflation). Standard decision theory is indifferent between these two options. Indeed, it might be argued that any intuition that the Petrograd game is better than the St. Petersburg game is a result of misguided and na¨ıve intuitions about infinity.2 But this argument against the intuition in question is misguided. The Petrograd game is clearly better than the St. Petersburg game. And what is more, there is no confusion about infinity involved in thinking this. When the series of coin tosses comes to an end (and it comes to an end with probability 1), no matter how many tails precede the first head, the payoff for the Petrograd game is one dollar higher than the St. Petersburg game. Whatever the outcome, you are better off playing the Petrograd game. Infinity has nothing to do with it. Indeed, a straightforward application of dominance reasoning backs up this line of reasoning.3 Standard decision theory. (shrink)

In classical Newtonian physics there was a clear understanding of “what reality is.≓ Indeed in this classical view, reality at a certain time is the collection of all what is actual at this time, and this is contained in “the present.≓ Often it is stated that three-dimensional space and one-dimensional time hare been substituted by four-dimensional space-time in relativity theory, and as a consequence the classical concept of reality, as that which is “present,≓ cannot be retained. Is reality (...) then the four-dimensional manifold of relativity theory? And if so, what is then the meaning of “change in time?≓ This problem confronts a geometric view (as the Einsteinian interpretation of relativity theory) with a process view (where reality changes constantly in time). In this paper we investigate this problem, taking into account our insight into the nature of reality as it came by analyzing the problems of quantum mechanics. We show that with an Einsteinian interpretation of relativity theory, reality is indeed four-dimensional, but there is no contradiction with the process view, where this reality changes in time. (shrink)

This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditionalω. Namely, the equivalence between normal transfinite recursion scheme and newdependent transfinite recursionscheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universeVof sets is treated as (...) the given totality. (shrink)

It is common to distinguish moral rules, reasons, or values that are agent-relative from those that are agent-neutral. One can also distinguish moral rules, reasons, or values that are moment-relative from those that are moment-neutral. In this article, I introduce a third distinction that stands alongside these two distinctions—the distinction between moral rules, reasons, or values that are patient-relative and those that are patient-neutral. I then show how patient-relativity plays an important role in several moral theories, gives us a (...) better understanding of agent-relativity and moment-relativity, and provides a novel objection to Derek Parfit’s “appeal to full relativity” argument. (shrink)

This white paper aims to identify an open problem in 'Quantum Physics and the Nature of Reality' -namely whether quantum theory and special relativity are formally compatible-, to indicate what the underlying issues are, and put forward ideas about how the problem might be addressed.

It is shown that the combination of unitary quantum theory and special relativity may lead to a contradiction when considering the EPR correlations in different inertial frames in a Gedankenexperiment. This result seems to imply that either unitary quantum theory is wrong or if unitary quantum theory is right then there must exist a preferred Lorentz frame.

In this paper I expound an argument which seems to establish that probabilism and special relativity are incompatible. I examine the argument critically, and consider its implications for interpretative problems of quantum theory, and for theoretical physics as a whole.

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, we (...) discuss some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to systems biology. (shrink)

We discuss the meaning and prove the accordance of general relativity, wave mechanics, and the quantization of Einstein's gravitation equations themselves. Firstly, we have the problem of the influence of gravitational fields on the de Broglie waves, which influence is in accordance with Eeinstein's weak principle of equivalence and the limitation of measurements given by Heisenberg's uncertainty relations. Secondly, the quantization of the gravitational fields is a “quantization of geometry.” However, classical and quantum gravitation have the same physical meaning (...) according to limitations of measurements given by Einstein's strong principle of equivalence and the Heisenberg uncertainties for the mechanics of test bodies. (shrink)

A theory is agent neutral if it gives every agent the same set of aims and agent relative otherwise. Most philosophers take act-consequentialism to be agent-neutral, but I argue that at the heart of consequentialism is the idea that all acts are morally permissible in virtue of their propensity to promote value and that, given this, it is possible to have a theory that is both agent-relative and act-consequentialist. Furthermore, I demonstrate that agent-relative act-consequentialism can avoid the counterintuitive (...) implications associated with utilitarianism while maintaining the compelling idea that it is never wrong to bring about the best outcome. (shrink)

This chapter discusses the roles of ether and electrons in relativity theory. One of the most radical moves made by Albert Einstein was to dismiss the ether from electrodynamics. His fellow physicists felt challenged by Einstein’s view, and they came up with a variety of responses, ranging from enthusiastic approval, to dismissive rejection. Among the naysayers were the electron theorists, who were unanimous in their affirmation of the ether, even if they agreed with other aspects of Einstein’s (...) class='Hi'>theory of relativity. The eventual success of the latter theory (circa 1911) owed much to Hermann Minkowski’s idea of four-dimensional spacetime, which was portrayed as a conceptual substitute of sorts for the ether. (shrink)

We continue to explore the consequences of Thermal Relativity Theory to the physics of black holes. The thermal analog of Lorentz transformations in the tangent space of the thermodynamic manifold are studied in connection to the Hawking evaporation of Schwarzschild black holes and one finds that there is no bound to the thermal analog of proper accelerations despite the maximal bound on the thermal analog of velocity given by the Planck temperature. The proper entropic infinitesimal interval corresponding to (...) the Kerr–Newman black hole involves a \ non-Hessian metric with diagonal and off-diagonal terms of the form \^2 = g_{ ab } d Z^a dZ^b\), where \ are the mass, charge and angular momentum, respectively. Since the computation of the scalar curvature associated to this metric is very elaborate, to simplify matters, we focused on the singularities of the metric and found that they correspond to the extremal Kerr–Newman black hole case \ with vanishing temperature. Black holes in asymptotically Anti de Sitter spacetimes are more subtle to study since the mass turns out to be related to the enthalpy rather that the internal energy. We finalize with some remarks about the thermal-relativistic analog of proper force, the need to extend our analysis of Gibbs-Boltzmann entropy to the case of Reny and Tsallis entropies, and to complexify spacetime. (shrink)

Relativistic quantum field theories (RQFTs) are invariant under the action of the Poincaré group, the symmetry group of Minkowski spacetime. Non-relativistic quantum field theories (NQFTs) are invariant under the action of the symmetry group of a classical spacetime; i.e., a spacetime that minimally admits absolute spatial and temporal metrics. This essay is concerned with cashing out two implications of this basic difference. First, under a Received View, RQFTs do not admit particle interpretations. I will argue that the concept of particle (...) that informs this view is motivated by nonrelativistic intuitions associated with the structure of classical spacetimes, and hence should be abandoned. Second, the relations between RQFTs and NQFTs also suggest that routes to quantum gravity are more varied than is typically acknowledged. The second half of this essay is concerned with mapping out some of this conceptual space. (shrink)

We consider the following question within both Newtonian physics and relativity theory. "Given two point particles X and Y, if Y is rotating relative to X, does it follow that X is rotating relative to Y?" As it stands the question is ambiguous. We discuss one way to make it precise and show that, on that reading at least, the answers given by the two theories are radically different. The relation of relative orbital rotation turns out to be (...) symmetric in Newtonian physics, but not in relativity theory. (shrink)

Special relativity theory is generalized to two or more “maximal” signalling speeds. This framework is discussed in three contexts: (i) as a scenario for superluminal signalling and motion, (ii) as the possibility of two or more “light” cones due to the a “birefringent” vacuum, and (iii) as a further extension of conventionality beyond synchrony.

SummaryThis essay explores analogies between classical notions of pyrrhonist skepticism and reflexive phenomena of twentieth‐century metamathematics. In a theoretical framework T, for example, one may interpret1T's appearances () as its axioms;2evident and inevident assertions () in the language L of T as sentences 0 which are decidable and undecidable in T; and3skeptical self ‐doubt about T in L as T's Godel‐sentence γ .These analogies complement another one, between pyrrhonist ‘modes’() of indefinite semantic regress (), and recurrent appeals to ‘new’ metatheories (...) T', T., to consider ‘new’, identify alternate interpretations, and adjudicate claims of consistency.These analogies are also reflexive in a wider sense. ‐ are stated for theories T, T', T., in some unspecified metatheory t̄–to which they also apply. This wider reflexivity suggests that ‘problems' of skeptical self‐doubt are not vicious or otiose, but significant aspects of the phenomena of indefinite semantic regress.RésuméCet essai explore quelques analogies entre les notions classiques du scepticisme pyrrhonien et les phénomenes réflexifs de la métamathématique du vingtième siècle. Dans un cadre théorique T du premier ordre, par exemple, on peut interpréter les apparences de T (), comme des axiomes; les assertions évidentes et non évidentes (), dans la langue L de T, comme les énoncés ø decidables et indecidables dans L; et le doute sceptique de ‘soi au sujet de T dans L, come ľénoncé ‐γ de Gödel de T .Ces analogies en complèment une autre, entre les ‘modes' pyrrhoniens() dela régression sémantique indéfinie(), et les appels récurrents à de ‘nouvelles' métathéories T', T., pour considérer de ‘nou‐veaux’, identifier des interpretations alternatives et juger des questions de consistance.Ces analogies sont aussi réflexives dans un sense plus large. ‐ se constatent pour les théories T, T T., dans une métathéorie indéterminée T –aG laquelle ilss'appliquent à nouveau. Cette réflexivité plus étendue suggère que les problèmes de doute sceptique de soi‘ ne sont pas vicieux ou vides, mais représentent au contraire des aspects signifiants des phénomènes de régression sémantique indéfinie.ZusammenfassungIn der vorliegenden Arbeit werden einige Analogien zwischen klassischen Begriffen des pyrrhonischen Skeptizismus und reflexiven Phänomenen der Metamathematik des zwanzigsten Jahrhunderts untersucht. In einem theoretischen Rahmenwerk T kann man die folgenden Interpretationen geben:1die Erscheinungen () von T als dessen Axiome;2evidente und nicht‐evidente Aussagen () in der Sprache L von T als Sätze ø, die entscheidbar, bzw. unentscheidbar sind; und3den skeptischen Selbst zweifel über T in L als den Güdel‐Satz γ für T .Diese Analogien sind complementär zu einer anderen, nämlich derjenigen zwischen den Pyrrhonischen Modi () des semantischen regresssus in indefinitum (), und dem wiederholten Rekurs auf ‘neue’ Metatheorien T', T, …, in denen man ‘neue’ berücksichtigt, alternative Deutungen erwägt und Fragen der Widerspruchsfreiheit beurteilt.Diese Analogien sind auch reflexiv in einem weiteren Sinne. ‐ werden für T, T, T, …, in einer Metatheorie T – bestimmt, für die sie auch gelten. Diese weitere Reflexivität legt nahe, dass ‘Probleme’ des skeptischen ‘Selbsf zweifels weder zu circuit vitiosi führen noch Scheinprobleme sind, sondern beachtenswerte Aspekte der Phänomene des indefiniten semantischen Regresses darstellen. (shrink)

The apparent underdetermination of the formalism of quantum field theory (QFT) as between a particle and a field interpretation is studied in this paper through a detour over the problem of unifying QFT with general relativity. All we have at present is a partial or approximate unification, QFT in non-Minkowskian spaces. The nature of this hybrid and the problem of its internal consistency are discussed. One of its most striking implications is that particles do not have an observer-independent (...) existence. We trace the ways in which physicists reacted to this at first highly implausible ontological consequence. We conclude that quantum fields rather than particles are after all the basic entities in QFT. (shrink)

The conventionalistic aspects of physical world perception are reviewed with an emphasis on the constancy of the speed of light in relativity theory and the irreversibility of measurements in quantum mechanics. An appendix contains a complete proof of Alexandrov's theorem using mainly methods of affine geometry.

Relativity Theory by Albert Einstein has been so far littleconsidered by cognitive scientists, notwithstanding its undisputedscientific and philosophical moment. Unfortunately, we don't have adiary or notebook as cognitively useful as Faraday's. But physicshistorians and philosophers have done a great job that is relevant bothfor the study of the scientist's reasoning and the philosophy ofscience. I will try here to highlight the fertility of a `triangulation'using cognitive psychology, history of science and philosophy of sciencein starting answering a clearly very (...) complex question:why did Einstein discover Relativity Theory? Here we arenot much concerned with the unending question of precisely whatEinstein discovered, that still remains unanswered, for we have noconsensus over the exact nature of the theory's foundations. We are mainly interested in starting to answer the`how question', and especially the following sub-question: what were his goals and strategies in hissearch? I will base my argument on fundamental publications ofEinstein, aiming at pointing out a theory-specific heuristic, settingboth a goal and a strategy: covariance/invariance.The result has significance in theory formation in science, especiallyin concept and model building. It also raises other questions that gobeyond the aim of this paper: why was he so confident in suchheuristic? Why didn't many other scientists use it? Where did he keep? such a heuristic? Do we have any other examples ofsimilar heuristic search in other scientific problemsolving? (shrink)

Exponential mappings into an imaginary space or number field for the axioms of a theory, which are in the form of propositional constants and variables, make possible: (a) an understanding of the meaning and differences between the Lorentz transformation constants, such that their product is still equal to one, but the axioms at each end of the transformations are logically inverse and separately consistent; (b) an interpretation of the psi function phase factor which is part of the axiomE=hf; (c) (...) the unification of the quantum-mechanical psi function and the electromagnetic wave function. Thus, those statements whose mechanisms are unknown (the axioms of the theory) are to be assigned the axiom propositional number symbol ϑ and are to be associated with the complex probability eiϑ, which is a uniform factor of the energy equations expressing the physical state. Such probabilistic axiom functions can be associated with both the special theory of relativity and the quantum-electromagnetic theory. (shrink)

In this paper we deal with infinitary universal Horn logic both with and without equality. First, we obtain a relative Lyndon-style interpolation theorem. Using this result, we prove a non-standard preservation theorem which contains, as a particular case, a Lyndon-style theorem on surjective homomorphisms in its Makkai-style formulation. Another consequence of the preservation theorem is a theorem on bimorphisms, which, in particular, provides a tool for immediate obtaining characterizations of infinitary universal Horn classes without equality from those with equality. From (...) the theorem on surjective homomorphisms we also derive a non-standard Beth-style preservation theorem that yields a non-standard Beth-style definability theorem, according to which implicit definability of a relation symbol in an infinitary universal Horn theory implies its explicit definability by a conjunction of atomic formulas. We also apply our theorem on surjective homomorphisms, theorem on bimorphisms and definability theorem to algebraic logic for general propositional logic. (shrink)

Agent-relative reasons are an important feature of any nonconsequentialist moral theory. Many authors think that they cannot be accommodated within a value-first theory that understands all value as agent-neutral. In this paper, I offer a novel explanation of agent-relative reasons that accommodates them fully within an agent-neutral value-first view. I argue that agent-relative reasons are to be understood in terms of second-order value responses: when an agent acts on an agent-relative reason, she responds appropriately to the agent-neutral value (...) of her own appropriate response to some agent-neutral value. This view helps reconcile important elements of deontology and consequentialism. (shrink)

In nonstandard mathematics, the predicate ‘x is standard’ is fundamental. Recently, ‘relative’ or ‘stratified’ nonstandard theories have been developed in which this predicate is replaced with ‘x is y -standard’. Thus, objects are not standard in an absolute sense, but standard relative to other objects and there is a whole stratified universe of ‘levels’ or ‘degrees’ of standardness. Here, we study stratified nonstandard arithmetic and the related transfer principle. Using the latter, we obtain the ‘reduction theorem’ which states that arithmetical (...) formulas can be reduced to equivalent bounded formulas. Surprisingly, the reduction theorem is also equivalent to the transfer principle. As applications, we obtain a truth definition for arithmetical sentences and we formalize Nelson's notion of impredicativity. (shrink)

David Chalmers has recently argued that Relativity Theory supports the notion that shapes are Twin-Earthable. In this paper this argument is challenged. I reconstruct the argument in five steps where the last step is the conclusion. I proceed to argue that one step in the argument can be interpreted in two different ways. The problem is that on the first interpretation of the step, the conclusion does not follow. And on the second interpretation of the step, it contradicts (...) a previous step in the argument. I conclude that Relativity Theory does not entail that phenomenal and functional twins could represent different shapes. (shrink)

The first completely geometric approach to relativity theory, based on the space-time geometries of Loedel and Brehme.

I discuss the debate between dynamical versus geometrical approaches to spacetime theories, in the context of both special and general relativity, arguing that the debate takes a substantially different form in the two cases; different versions of the geometrical approach—only some of which are viable—should be distinguished; in general relativity, there is no difference between the most viable version of the geometrical approach and the dynamical approach. In addition, I demonstrate that what have previously been dubbed two ‘miracles’ (...) of general relativity admit of no resolution from within general relativity, on either the dynamical or ‘qualified’ geometrical approaches, modulo some possible hints that the second ‘miracle’ may be resolved by appeal to recent results regarding the ‘geodesic principle’ in GR. (shrink)

Relativity theory is often said to support something called ‘the four-dimensional view of reality’. But there are at least three different views that sometimes go by this name. One is ‘spacetime unitism’, according to which there is a spacetime manifold, and if there are such things as points of space or instants of time, these are just spacetime regions of different sorts: thus space and time are not separate manifolds. A second is the B-theory of time, according (...) to which the past, present, and future are all equally real and there is nothing metaphysically special about the present. A third is perdurantism, according to which persisting material objects are made up of different temporal parts located at different times. We sketch routes from relativity to unitism and to the B-theory. We then discuss some routes to perdurantism, via the B-theory and via unitism. (shrink)