We review the decoherent histories approach to the interpretation of quantum mechanics. The Everett relative-state theory is reformulated in terms of decoherent histories. A model of evolutionary adaptation is shown to imply decoherence. A general interpretative framework is proposed: probability and value-definiteness are to have a similar status to the attribution of tense in classical spacetime theory.

Everett's relative-state formulation of quantum mechanics is an attempt to solve the measurement problem by dropping the collapse dynamics from the standard von Neumann-Dirac theory of quantum mechanics. The main problem with Everett's theory is that it is not at all clear how it is supposed to work. In particular, while it is clear that he wanted to explain why we get determinate measurement results in the context of his theory, it is unclear how he intended to do this. (...) There have been many attempts to reconstruct Everett's no-collapse theory in order to account for the apparent determinateness of measurement outcomes. These attempts have led to such formulations of quantum mechanics as the many-worlds, many-minds, many-histories, and relative-fact theories. Each of these captures part of what Everett claimed for his theory, but each also encounters problems. (shrink)

The consensus problem is presented for the switched multiagent system, where the MAS is switched between continuous- and discrete-time systems with relative state constraints. With some standard assumptions, we obtain the fact that the switched MAS with relative state constraints can achieve consensus under both fixed undirected graphs and switching undirected graphs. Furthermore, based on the absolute average value of initial states, we propose sufficient conditions for consensus of the switched MAS. The challenge of this study is (...) that relative state constraints are considered, which will make the consensus problem much more complex. One of the main contributions is that, for the switched MAS with relative state constraints, we explore the solvability of the consensus problem. Finally, we present two simulation examples to show the effectiveness of the results. (shrink)

This paper connects the hard problem of consciousness to the interpretation of quantum mechanics. It shows that constitutive Russellian pan(proto)psychism (CRP) is compatible with Everett’s relative-state (RS) interpretation. Despite targeting different problems, CRP and RS are related, for they both establish symmetry between micro- and macrosystems, and both call for a deflationary account of Subject. The paper starts from formal arguments that demonstrate the incompatibility of CRP with alternative interpretations of quantum mechanics, followed by showing that RS entails Russellian (...) pan(proto)psychism. Therefore, CRP and RS are mutually supportive. It then provides a unified ontological picture by combining CRP and RS. The challenge faced by CRP, the combination problem, can be resolved by adopting a RS version of quantum mechanics. Technically, this is achieved by a co-consciousness relation capable of explaining the difference between first-person and third-person perspectives. The hierarchical structure of the relation removes any concern on the structural mismatch between the physical and the phenomenal. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough (...) to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The main purpose of this study was to investigate the impact of perceived HR practices on affective commitment and turnover intention. This study explored which HR practices were relatively more important in predicting affective commitment and turnover intention. A total of 302 employees from the United States and 317 from South Korea completed the same questionnaires for assessing the aforementioned relationships. The results illustrated that among perceived HR practices, internal mobility had the most significant association with turnover intention in (...) both the US and South Korea. While internal mobility was a stronger predictor of affective commitment for the US sample, training was the most important variable for predicting affective commitment in South Korea. The second purpose of the study was to examine whether individuals’ positive affect influences the relationship between perceived HR practices and affective commitment and turnover intention. In the US, positive affect moderated the relationship between perceived HR practices and affective commitment and turnover intention such that the relationships were stronger for individuals reporting high positive affect relative to those reporting low positive affect. However, these relationships were not significant in South Korea. We discuss the implications of these results, study limitations, and practical suggestions for future research. (shrink)

Researchers in psychology have focused a great deal of attention on the potential greater predisposition to achievement among first-born children relative to their siblings. Focusing on the United States as an example, a time series of the first birth ratio is used to show how the changing prevalence of first births relative to higher order births has altered the composition of birth cohorts, and the ratio is decomposed into four factors. Results show that the ratio increased significantly (...) in the 1960s and early 1970s, but changed only slightly in the following decades. While more recent birth cohorts are composed of larger proportions of first-born children, the majority of children are still born as siblings. Contrary to expectations, the primary source of change was the proportion childless rather than decreasing higher order birth rates. (shrink)

We present a complete axiomatisation of the operator of projection onto state in the Duration Calculus relative to validity in DC without extending constructs. Projection onto state was introduced and studied extensively in our earlier works. We first establish the completeness of a system of axioms and proof rules for the operator relative to validity in the extension of DC by neighbourhood formulas, which express the neighbourhood values of boolean DC state expressions. By establishing a relatively complete axiomatisation (...) for the neighbourhood formulas in DC, we then achieve completeness of our system relative to basic DC. (shrink)

For Knobe, observers evaluate mental states by comparing agents' statements with the attitudes they are expected to hold. In our analysis, Knobe's model relies primarily on what agents should think, and little on expectancies of what they would think. We show the importance and complexity of including descriptive and prescriptive norms if one is to take expectancies seriously.

Background Changes in policies and practices related to repeat cesareans and home birth in the U.S. have been influenced by different interpretations of the risk of poor outcomes. Methods This article examines two cases—vaginal birth after cesarean (VBAC) and home birth to illustrate how an emphasis on relative over absolute risk has been used to characterize outcomes associated with these practices. The case studies will rely on reviews of the research literature and examination of data on birth trends and (...) outcomes. Results Childbirth involves some unique challenges in assessing health risks, specifically the issues of: (1) timing of risks (lowering health risk in a current birth can increase it in subsequent births); (2) the potential weighing of risks to the mother’s versus the infant’s health; (3) the fact that birth is a condition of health and many of the feared outcomes (for example, symptomatic uterine rupture) involve very low absolute risk of occurrence; and (4) a malpractice environment that seizes upon those rare poor outcomes in highly publicized lawsuits that receive widespread attention in the clinical community. In the cases of VBAC and home birth, the result has been considerable emphasis on relative risks, typically an adjusted odds ratio, with little consideration of absolute risks. Conclusion Assessments of the safety of interventions in childbirth should involve careful consideration and communication of the multiple dimensions of risk, particularly a balancing of relative and absolute risks of poor health outcomes. (shrink)

The paper re-evaluates Prior's tenets about indeterminism and relativity from the point of view of the current state of the debate. We first discuss Prior's claims about indeterministic tense logic and about relativity separately and confront them with new technical developments. Then we combine the two topics in a discussion of indeterministic approaches to space-time logics. Finally we show why Prior would not have to "dig his heels in" when it comes to relativity: We point out a way of combining (...) the existential import of the distinction between past, present, and future with a frame-relative notion of the present. (shrink)

The United States Court of Appeals for the Third Circuit held that when quitam relators file a multi-claim complaint under the Fraudulent Claims Act, their share of the proceeds must be based on an individual analysis of each claim. More importantly, the court held that relators are not entitled to any portion of the settlement of a specific claim if that claim was subject to dismissal under section 3730 Relator Merena filed a quitam suit against his employer, SmithKline Beecham, (...) claiming, among other things, that SKB defrauded the government by billing for laboratory tests that were not performed, paying illegal kickbacks to health care providers, and participating in an “automated chemistry” scheme. Soon thereafter, additional relators filed suit. (shrink)

The United States Court of Appeals for the Third Circuit held that when quitam relators file a multi-claim complaint under the Fraudulent Claims Act, their share of the proceeds must be based on an individual analysis of each claim. More importantly, the court held that relators are not entitled to any portion of the settlement of a specific claim if that claim was subject to dismissal under section 3730 Relator Merena filed a quitam suit against his employer, SmithKline Beecham, (...) claiming, among other things, that SKB defrauded the government by billing for laboratory tests that were not performed, paying illegal kickbacks to health care providers, and participating in an “automated chemistry” scheme. Soon thereafter, additional relators filed suit. (shrink)

Excerpt from Relativity: The Electron Theory and Gravitation The first edition of this book was published while the General Principle of Relativity was being worked out, before it seemed possible to arrive at any confirmation from observation. Shortly after, however, it was shown that the new theory explained the motion of the perihelion of Mercury, and now the result of the Solar Eclipse expedition has clinched matters. It seemed best to leave practically untouched the account of the special principle as (...) the natural avenue of approach to the broader view, which is described at length in Part II. Acknowledgment is due to the authors friends, Prof. H. F. Baker and Mr. E. V. Appleton, who kindly read through the proofs of the new matter. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Excerpt from Relativity The four chapters which follow are four lectures delivered before the Edinburgh Mathematical Colloquium on the subject of Relativity. As many of the audience had their chief interests in other branches of mathematical science, it was necessary to start ab initio. The best method appeared to be to treat the subject in the historical order; I have brought it down to the stage in which it was left by Minkowski. If I have stimulated any of my audience (...) to pursue the matter further, I shall be amply repaid for any trouble that I have taken. I wish to express my thanks to the Edinburgh Mathematical Society for the honour that they have conferred on me in inviting me to give these lectures. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

In this article I pose a challenge for attempts to ground all reasons in considerations of value. Some believe that all reasons for action are grounded in considerations of value. Some also believe that there are agent-relative restrictions, which provide us with agent-relative reasons against bringing about the best state of affairs, on an impartial ranking of states of affairs. Some would like to hold both of these beliefs. That is, they would like to hold that such (...) agent-relative restrictions are compatible with a teleological theory, one that grounds all reasons for action in considerations of value. This is what I will argue is problematic. I will argue that agent-centered restrictions will not fit into a teleological theory. If the correct moral theory is a teleological one, then there are no agent-relative restrictions. If there are agent-relative restrictions, then teleology is false. My argument challenges a particular project, of showing that all ethical theories are broadly consequentialist. The attraction of this project is that it promises to preserve what is thought to be compelling about consequentialism—its teleology and maximizing—while also preserving elements of commonsense morality—such as agent-relative restrictions—that have typically been thought of as distinctly non-consequentialist in nature. If my argument is correct, then this promise cannot be fulfilled. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The General Theory of Relativity (GR) and the Dynamic Universe (DU) are evaluated in how they explain frequencies of atomic clocks. DU and GR predict the frequencies with equal accuracy, but their explanations, the postulates they apply in the explanations and the word-views that come along with them are entirely different. The central argument is that if unified and under- standable physics is appreciated, then DU deserves to be taken as a viable alternative to GR. In GR different frequencies of (...) identical atomic clocks are explained by letting rates of the flow of time in their frames of reference vary as functions of the clocks’ states of motion and gravitation. The GR- based world-view is nonunderstandable because GR violates absolute simultaneity, and disunified because quantum mechanics is built on different postulates than GR. In DU different frequencies of identical atomic clocks are explained by letting their frequencies vary as functions of their states of motion and gravitation. As DU commits to absolute simultaneity and as the postulates of DU suffice as the ontological ground of quantum mechanics at least partially, DU provides an under- standable and unified scientific world-view. -/- Résumé: La théorie de la relativité générale (RG) et de l’univers dynamique (UD) sont évalués sur la fac ̧on dont ils expliquent les fréquences des horloges atomiques. La RG et l’UD prédisent les fréquences avec une précision égale, mais leurs explications, les postulats qu’ils appliquent aux explications et les visions du monde qui les accompagnent sont entie`rement différents. L’argument central est que si l’on reconnaˆıt la physique unifiée et compréhensible, alors l’UD mérite d’ être considéré comme une alternative viable à la RG. En RG, différentes fréquences d’horloges atomiques identiques sont expliquées en faisant varier les vitesses de l’écoulement du temps dans leurs cadres de référence en fonction des états de mouvement et de la gravitation des horloges. La vue du monde basée sur la RG est incompréhensible parce que la RG viole la simultanéité absolue, et est désunifiée parce que la mécanique quantique est construite sur des postulats différents de ceux de la RG. Dans l’UD, différentes fréquences d’horloges atomiques identiques sont expliquées en laissant leurs fréquences varier en fonction de leurs états de mouvement et de gravitation. Comme l’UD s’engage à la simultanéité absolue et que les postulats de l’UD suffisent, au moins en partie, comme fondements ontologiques de la mécanique quantique, l’UD fournit une vision du monde scientifique compréhensible et unifiée. (shrink)

One of the most significant challenges in the application of brain-computer interfaces is the large performance variation, which often occurs over time or across users. Recent evidence suggests that the physiological states may explain this performance variation in BCI, however, the underlying neurophysiological mechanism is unclear. In this study, we conducted a seven-session motor-imagery experiment on 20 healthy subjects to investigate the neurophysiological mechanism on the performance variation. The classification accuracy was calculated offline by common spatial pattern and support (...) vector machine algorithms to measure the MI performance of each subject and session. Relative Power values from different rhythms and task stages were used to reflect the physiological states and their correlation with the BCI performance was investigated. Results showed that the alpha band RP from the supplementary motor area within a few seconds before MI was positively correlated with performance. Besides, the changes of RP between task and pre-task stage from theta, alpha, and gamma band were also found to be correlated with performance both across time and subjects. These findings reveal a neurophysiological manifestation of the performance variations, and would further provide a way to improve the BCI performance. (shrink)

This paper compares two ‘relativist’ theories about deliciousness: truth-relativism, and Kit Fine’s non-factualism about a subject-matter. Contemporary truth-relativism is presented as a linguistic thesis; its metaphysical underpinning is often neglected. I distinguish three views about the obtaining of worldly states of affairs concerning deliciousness, and argue that none yields a satisfactory version of truth-relativism. Finean non-factualism about deliciousness is not subject to the problems with truth-relativism. I conclude that Finean non-factualism is the better relativist theory. As I explain, non-facualism (...) about deliciousness is happily combined with an invariantist semantics for the word “delicious”. On this approach, relativism is a matter for a metaphysical theory, not a linguistic one. (shrink)

The articles included in this Volume represent a broad and highly qualified view on the present state of general relativity, quantum gravity, and their cosmological and astrophysical implications. As such, it may serve as a valuable source of knowledge and inspiration for experts in these fields, as well as an advanced source of information for young researchers. The occasion to gather together so many leading experts in the field was to celebrate the centenary of Einstein's stay in Prague in 1911-1912. (...) It was in fact during his stay in Prague that Einstein started in earnest to develop his ideas about general relativity that fully developed in his paper in 1915. Approaching soon the centenary of his famous paper, this volume offers a precious overview of the path done by the scientific community in this intriguing and vibrant field in the last century, defining the challenges of the next 100 years. The content is divided into four broad parts: (i) Gravity and Prague, (ii) Classical General Relativity, (iii) Cosmology and Quantum Gravity, and (iv) Numerical Relativity and Relativistic Astrophysics. (shrink)

The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete as the Lebesgue one. Its unit is a quantum bit (qubit) and can be considered as a generalization of the unit of classical information, a bit. It allows quantum mechanics to be interpreted in terms of quantum information, and all physical processes to be seen as informational in a generalized (...) sense. This implies a fundamental connection between the physical and material, on the one hand, and the mathematical and ideal, on the other hand. Quantum measure unifies them by a common and joint informational unit. Furthermore the approach clears up philosophically how quantum mechanics and general relativity can be understood correspondingly as the holistic and temporal aspect of one and the same, the state of a quantum system, e.g. that of the universe as a whole. The key link between them is the notion of the Bekenstein bound as well as that of quantum temperature. General relativity can be interpreted as a special particular case of quantum gravity. All principles underlain by Einstein (1918) reduce the latter to the former. Consequently their generalization and therefore violation addresses directly a theory of quantum gravity. Quantum measure reinterprets newly the “Bing Bang” theories about the beginning of the universe. It measures jointly any quantum leap and smooth motion complementary to each other and thus, the jump-like initiation of anything and the corresponding continuous process of its appearance. Quantum measure unifies the “Big Bang” and the whole visible expansion of the universe as two complementary “halves” of one and the same, the set of all states of the universe as a whole. It is a scientific viewpoint to the “creation from nothing”. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough (...) to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The purpose of the study is to introduce a new economic index, the "relative productivity exponent in the global economy g", which characterizes the deviation of the economic productivity index of a given country from some ideal productivity determined by the shape of the axial line of the swarm of the global economy in the three-dimensional space of economic indices EPI, BLI, CPI. To determine the values of the relative productivity exponent g, the shape of the axial line (...) of the global economy of 2019, established earlier by the authors, is used. The article examines the distribution of countries according to the exponent g and the index of socio-economic equilibrium of countries, and also investigates the relationship between the exponent g and the index of economic productivity EPI. The scientific novelty of the research lies in the introduction of a new economic index g and the calculation of its values for countries based on economic data from 2019. The distribution of countries according to the value of g allows us to reveal, as a result, a certain range of the exponent g, indicating a balanced state of the economy. (shrink)

The problem of statistical inference based on a partial measurement (“coarse-graining”) requires the specification of an a priori distribution. We reformulate the ordinary theory such as to encompass systematically a wide range of a priori distributions (“relative coarse-graining”). This is done in a mathematical setting which admits an interpretation in both classical probability and quantum mechanics. The formalism is illustrated in a few simple examples, such as the die whose geometrical shape is known, the spin in thermal equilibrium with (...) an unknown reservoir, and the position measurement of a one-dimensional particle. It is shown that some of the limitations of the usual theory are a consequence of the fact that it is restricted to “equidistributed” (symmetric) a priori states. (shrink)

Agent-relativity, as an attribute of principles for moral decision, reasons for action, and values, has been a topic of discussion in recent ethical theory primarily in the context of objections to act-consequentialism. Thus, Samuel Scheffler explains that act-consequentialist theories “first specify some principle for ranking overall states of affairs from best to worst from an impersonal point of view.” These rankings are not agent-relative, i.e., “they do not vary from person to person, depending on what one’s particular situation (...) is.” Scheffler notes that this is because “they do not embody judgements about which overall states of affairs are best for particular individuals, but rather judgements about which states of affairs are best, all things considered, from an impartial standpoint.” Act-consequentialism then directs each agent always to bring about the highest-ranked state of affairs that he or she can. (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 paper examines public accountants' perceptions of the relative importance of business ethics as a selection criterion for entry-level public accounting positions. Also, it seeks to determine whether gender differences do exist with respect to these perceptions. The data were collected through a survey of 335 professional accountants in four southeastern states. The results show that, among the eight selection factors that were studied, technical competence in accounting, communication skills, and interpersonal skills were the most influential, while professionalism (...) and leadership abilities were the least important. Ethics was ranked fourth by the females and sixth by the males. A multivariate analysis of variance revealed significant differences between the genders with respect to five of the eight factors. The females' scores were higher for ethics and interpersonal skills and lower for conceptual aptitude, strategic thinking, and leadership abilities. Implications for accounting educators and practitioners are discussed. (shrink)

In this paper, I argue that maximizing act-consequentialism (MAC)—the theory that holds that agents ought always to act so as to produce the best available state of affairs—can accommodate both agent-centered options and supererogatory acts. Thus I will show that MAC can accommodate the view that agents often have the moral option of either pursuing their own personal interests or sacrificing those interests for the sake of the impersonal good. And I will show that MAC can accommodate the idea that (...) certain acts are supererogatory in the sense of not being morally required even though they are what the agent has most moral reason to do. These two theses are surprising in themselves, but even more surprising is how I arrive at them. I argue that anyone generally concerned to accommodate, in some coherent fashion, our pre-theoretical moral intuitions at both the normative and meta-ethical levels will have to give a certain account of agent-centered options and supererogatory acts and that this account is the very one that allows for the maximizing act-consequentialist to accommodate both. So my paper will not only be of interest to those concerned with the tenability of consequentialism, but also to anyone interested in giving a coherent account of our pre-theoretical moral intuitions. (shrink)

Most philosophers believe that qualitative states must be explained in terms of physical states of the brain in order to resolve the mind/ body problem. But the severe difficulties involved in deriving the mental from the physical or, even more bizarrely, eliminating the mental altogether, have caused some to seriously investigate Russell's longstanding ideas about the intrinsic nature of physical entities. The resulting microphenomenal approaches, however, are of necessity extremely vague and complicated. Consequently, a macrophenomenal theory of mind (...) may well be a more plausible alternative than microphenomenal ones -- especially if it takes into account the relative aspect of experience and thereby avoids reifying qualia. (shrink)

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)

LetCbe an axiom system formalized within the first order functional calculus, and letC′ be related toCas the Bernays-Gödel set theory is related to the Zermelo-Fraenkel set theory. Ilse Novak [5] and Mostowski [8] have shown that, ifCis consistent, thenC′ is consistent. Mostowski has also proved the stronger result that any theorem ofC′ which can be formalized inCis a theorem ofC.The proofs of Novak and Mostowski do not provide a direct method for obtaining a contradiction inCfrom a contradiction inC′. We could, (...) of course, obtain such a contradiction by proving the theorems ofCone by one; the above result assures us that we must eventually obtain a contradiction. A similar process is necessary to obtain the proof of a theorem inCfrom its proof inC′. The purpose of this paper is to give a new proof of these theorems which provides a direct method of obtaining the desired contradiction or proof.The advantage of the proof may be stated more specifically by arithmetizing the syntax ofCandC′. (shrink)

PREFACE. THE Author of this very practical treatise on Scotch Loch - Fishing desires clearly that it may be of use to all who had it. He does not pretend to have written anything new, but to have attempted to put what he has to say in as readable a form as possible. Everything in the way of the history and habits of fish has been studiously avoided, and technicalities have been used as sparingly as possible. The writing of this (...) book has afforded him pleasure in his leisure moments, and that pleasure would be much increased if he knew that the perusal of it would create any bond of sympathy between himself and the angling community in general. This section is interleaved with blank shects for the readers notes. The Author need hardly say that any suggestions addressed to the case of the publishers, will meet with consideration in a future edition. We do not pretend to write or enlarge upon a new subject. Much has been said and written-and well said and written too on the art of fishing but loch-fishing has been rather looked upon as a second-rate performance, and to dispel this idea is one of the objects for which this present treatise has been written. Far be it from us to say anything against fishing, lawfully practised in any form but many pent up in our large towns will bear us out when me say that, on the whole, a days loch-fishing is the most convenient. One great matter is, that the loch-fisher is depend- ent on nothing but enough wind to curl the water, -and on a large loch it is very seldom that a dead calm prevails all day, -and can make his arrangements for a day, weeks beforehand whereas the stream- fisher is dependent for a good take on the state of the water and however pleasant and easy it may be for one living near the banks of a good trout stream or river, it is quite another matter to arrange for a days river-fishing, if one is looking forward to a holiday at a date some weeks ahead. Providence may favour the expectant angler with a good day, and the water in order but experience has taught most of us that the good days are in the minority, and that, as is the case with our rapid running streams, -such as many of our northern streams are, -the water is either too large or too small, unless, as previously remarked, you live near at hand, and can catch it at its best. A common belief in regard to loch-fishing is, that the tyro and the experienced angler have nearly the same chance in fishing, -the one from the stern and the other from the bow of the same boat. Of all the absurd beliefs as to loch-fishing, this is one of the most absurd. Try it. Give the tyro either end of the boat he likes give him a cast of ally flies he may fancy, or even a cast similar to those which a crack may be using and if he catches one for every three the other has, he may consider himself very lucky. Of course there are lochs where the fish are not abundant, and a beginner may come across as many as an older fisher but we speak of lochs where there are fish to be caught, and where each has a fair chance. Again, it is said that the boatman has as much to do with catching trout in a loch as the angler. Well, we dont deny that. In an untried loch it is necessary to have the guidance of a good boatman but the same argument holds good as to stream-fishing... (shrink)

We approach the physics of \emph{minimal coupling} in general relativity, demonstrating that in certain circumstances this leads to violations of the \emph{strong equivalence principle}, which states that, in general relativity, the dynamical laws of special relativity can be recovered at a point. We then assess the consequences of this result for the \emph{dynamical perspective on relativity}, finding that potential difficulties presented by such apparent violations of the strong equivalence principle can be overcome. Next, we draw upon our discussion of (...) the dynamical perspective in order to make explicit two `miracles' in the foundations of relativity theory. We close by arguing that the above results afford us insights into the nature of special relativity, and its relation to general relativity. (shrink)