Independent of his international renown as a humanitarian, Albert Schweitzer is well known as a great musicologist; a reputation that rests largely upon this book. Schweitzer's \"J. S. Bach\" is one of the great full-length studies of the composer, his life, and his work. Its influence on the subsequent performace of Bach's music was enormous, and there is scarcely a later work on Bach which does not acknowledge a deep debt to Schweitzer's. Grove's Dictionary says of the book, \"Schweitzer (...) has probably been more quoted than any authority since Spitta.\". (shrink)

The Comprehensibility of the Universe puts forward a radically new conception of science. According to the orthodox conception, scientific theories are accepted and rejected impartially with respect to evidence, no permanent assumption being made about the world independently of the evidence. Nicholas Maxwell argues that this orthodox view is untenable. He urges that in its place a new orthodoxy is needed, which sees science as making a hierarchy of metaphysical assumptions about the comprehensibility and knowability of the universe, these (...) assumptions asserting less and less as one ascends the hierarchy. This view has significant implications: that it is part of scientific knowledge that the universe is physically comprehensible; that metaphysics and philosophy are central to scientific knowledge; that science possesses a rational, if fallible, method of discovery; that a new understanding of scientific method and rationality is required. Maxwell argues that this new conception makes possible a natural resolution of long-standing philosophical problems about science, regarding simplicity, induction, and progress. His goal is the reform not just of the philosophy of science but of science itself, and the healing of the rift between the two. (shrink)

_'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.'_ _– The Guardian_ In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system. The importance of Godel's Proof rests upon its radical implications and has echoed throughout many fields, from (...) maths to science to philosophy, computer design, artificial intelligence, even religion and psychology. While others such as Douglas Hofstadter and Roger Penrose have published bestsellers based on Godel’s theorem, this is the first book to present a readable explanation to both scholars and non-specialists alike. A gripping combination of science and accessibility, _Godel’s Proof_ by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity. _Kurt Godel_ Born in Brunn, he was a colleague of physicist Albert Einstein and professor at the Institute for Advanced Study in Princeton, N.J. (shrink)

It is known that Maxwell’s electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these (...) bodies is in motion. For if the magnet is in motion and the conductor at rest, there arises in the neighbourhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise—assuming equality of relative motion in the two cases discussed—to electric currents of the same path and intensity as those produced by the electric forces in the former case. Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.1 We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reply to Russell's letter of 16 May 1960 by Albert Shalom EDITORIAL NOTE To illustrate a list ofrecent acquisitions in Russell (Summer 1981), we printed in facsimile Russell's letter of 16 May 1960 to Professor Albert Shalom concerning the interpretation of Wittgenstein's Tractatus LogicoPhilosophicus. The correspondence between Russell and Shalom began when Shalom wrote on I May 1960 asking whether Russell had the time and inclination to (...) read a translation of a lecture which Shalom had given the previous December in Paris. The paper was entitled "The Metaphysical Thinking Underlying Wittgenstein's Tractatus". Shalom had received "different and even contradictory appraisals" of his paper, and he very much wanted to have Russell's opinion of it. Close to the age ofninety, Russell was entering a hectic period in his life in which he worked assiduouslyfor the Campaign for Nuclear Disarmament. He had published three books in 1959 and had produced prefaces and introductions for other people. As usual, he was besieged with mail including numerous requests to read unsolicited manuscripts sent to him quite regularly. Yet he had managed to answer correspondence in a very personal way. In November 1959, he had been involved in a controversy regarding the refusal ofthe editor of Mind to review Ernest Gellner's Words and Things, a book which attacked the then prevalent philosophy of linguistic analysis and for which Russell had written the introduction. In the early months of1960, he took time out from his usual writing on the nuclear threat to reply to several articles devoted to his theory of descriptions and his ethical theory in the journal Philosophy. Russell's reply (4 May 1960) to Shalom's first letter states: "Thank you for your letter ofMay I. I shall be interested to see your paper on Wittgenstein's Tractatus, but, as I am very busy, it may be some time before I can read it carefully." On 8 May Shalom wrote back in appreciation enclosing his paper and an offprint of an article, "Qu'est-ce qu'un concept?", Revue internationale dephilosophie, 50 (1959): I-IS. The main objection raised against his paper, Shalom admitted, was that Wittgenstein was not concerned with problems of epistemology at the time of his writing the Tractatus. Nonetheless, Shalom felt that the "picture theory" of reality implies an epistemology, and he was unable to see a fallacy in his paper: "Perhaps the fact that I'm not a logician has something to do with the matter. Ifyou could enlighten me on this point I should be most grateful to you." 45 28th April 1982. 46 Russell winter 1982-83 Russell's letter of 16 May followed. On 25 May Shalom challenged Russell's interpretation. Far /rom underestimating the notion of structure, Shalom claimed that he had emphasized the notion as the key to understanding the Tractatus. "In fact, my main point is that Wittgenstein's analyses of various concepts are unintelligible unless understood as arguments in terms of the dominating idea ofstructure or form. And that is what I understand as a metaphysical argument." Shalom went on to say that his interest in any philosopher was to try to discover the chief concepts employed in the philosopher's analysis and to examine the manner in which the analysis was performed. For this reason, the later Wittgenstein was not devoid ofinterest. In a postscript, he asked Russell whether he would be in London in July ofthat year, and ifso, whether a meeting was possible. Russell replied on 18June as follows: "Thank you for your letter ofMay 25. I am sorry that at present my time and thought are so occupied with matters very remote from those with whichyour letter deals that I cannot offeryou a reasoned reply. Unfortunately, I do not expect to be in London in July so that I am afraid a meeting will hardly be possible." On 14 Shalom requested the return of his paper, and Russell complied on 19 July. Shalom is now Professor ofPhilosophy at McMaster. We invited him to comment on his exchange with Russell, particularly Russell's letter of16 May 1960. His comments take the form ofa further (and no doubtfinal) letter in the exchange.-Carl... (shrink)

An homage to the men and women of science, and an exposition of Einstein's place in scientific history In this fascinating collection of articles and speeches, Albert Einstein reflects not only on the scientific method at work in his own theoretical discoveries, but also eloquently expresses a great appreciation for his scientific contemporaries and forefathers, including Johannes Kepler, Isaac Newton, James Clerk Maxwell, Max Planck, and Niels Bohr. While Einstein is renowned as one of the foremost innovators of (...) modern science, his discoveries uniquely his own, through his own words it becomes clear that he viewed himself as only the most recent in a long line of scientists driven to create new ways of understanding the world and to prove their scientific theories. Einstein's thoughtful examinations explain the "how" of scientific innovations both in his own theoretical work and in the scientific method established by those who came before him. This authorized Philosophical Library book features a new introduction by Neil Berger, PhD, and an illustrated biography of Albert Einstein, which includes rare photos and never-before-seen documents from the Albert Einstein Archives at the Hebrew University of Jerusalem. "What place does the theoretical physicist's picture of the world occupy among all these possible pictures? It demands the highest possible standard of rigorous precision in the description of relations, such as only the use of mathematical language can give" -Albert Einstein, "Principles of Research" Albert Einstein (1879-1955) was born in Germany and became an American citizen in 1934. A world-famous theoretical physicist, he was awarded the 1921 Nobel Prize for Physics and is renowned for his Theory of Relativity. In addition to his scientific work, Einstein was an influential humanist who spoke widely about politics, ethics, and social causes. After leaving Europe, Einstein taught at Princeton University. His theories were instrumental in shaping the atomic age. Neil Berger, an associate professor emeritus of mathematics, taught at the University of Illinois at Chicago in the Mathematics, Statistics, and Computer Science department from 1968 until his retirement in 2001. He was the recipient of the first Monroe H. Martin Prize (1975), which is now awarded by the University of Maryland every five years for a singly authored outstanding applied mathematics research paper. He has published numerous papers and reviews in his fields of expertise, which include elasticity, tensor analysis, scattering theory, and fluid mechanics. (shrink)

Imre Lakatos and Paul Feyerabend initially both accepted Popper's philosophy of science, but then reacted against it, and developed it in different directions. Lakatos sought to reconcile Kuhn and Popper by characterizing science as a process of competing research programmes, competing fragments of Kuhn's normal science. Feyerabend emphasized the need to develop rival theories to facilitate severe empirical testing of accepted theories, but then, as a result of a disastrous mistake, came to hold that theories that are incompatible with one (...) another cannot be compared empirically. He ended up rejecting method in science. All four philosophers, Popper, Kuhn, Lakatos and Feyerabend missed the decisive defect in Popper's philosophy of science: persistent acceptance of unified theories only when endlessly many empirically more successful disunified rivals are available means that physics makes a big, highly problematic metaphysical assumption about the nature of the universe: it is such that some kind of underlying unity exists in nature. We need to adopt a new conception of science. In order to subject this implicit metaphysical conjecture to sustained critical assessment in an attempt to improve it, we need to see science as making a hierarchy of metaphysical assumptions about the knowability and comprehensibility of the universe, these assumptions becoming less substantial and more likely to be true as we ascend the hierarchy. Elements of Popper, Kuhn and Lakatos are to be found in this picture, but it also differs radically from all three. It more closely resembles Einstein's mature views about the nature of science. (shrink)

In this paper, I argue that the recent discussion on the time - reversal invariance of classical electrodynamics (see (Albert 2000: ch.1), (Arntzenius 2004), (Earman 2002), (Malament 2004),(Horwich 1987: ch.3)) can be best understood assuming that the disagreement among the various authors is actually a disagreement about the metaphysics of classical electrodynamics. If so, the controversy will not be resolved until we have established which alternative is the most natural. It turns out that we have a paradox, namely that (...) the following three claims are incompatible: the electromagnetic fields are real, classical electrodynamics is time-reversal invariant, and the content of the state of affairs of the world does not depend on whether it belongs to a forward or a backward sequence of states of the world. (shrink)

The theories of cultural anthropologist Ernest Becker arise from an existential and psychological analysis of the death terror/anxiety deep in the unconscious of every human. Becker details how this anxiety governs the ideologies and behaviors of our species—something now confirmed by thousands of experiments performed by psychologists engaged in contemporary terror management theory (TMT). Humans manage their anxiety through what Becker terms “hero systems”—concepts, beliefs, and myths we create to give us a sense of significance and meaning during, and (...) even beyond our mortal lives. Today, many dominant economic, technological, and religious hero systems seek to confirm our significance by denying that we are—like all other species—animals who must exist in a decaying, mortal body. Becker shows how this attempt to deny our “creatureliness” (basic biological nature) causes humans to stand against the natural world we are embedded in, leading to an assault on the planet and nonhuman animals. As a result, Becker believed pacifism was the only hero system capable of keeping humankind from destroying itself and the earth. Pacifism is the precursor to the more encompassing ethical concept of “reverence for life,” advocated by Dr. Albert Schweitzer. By respecting the will-to-live in all sentient beings, reverence for life transcends concern for humans alone and extends moral and physical safeguards to life as such. Confronting the fact that humans are increasingly alienated from their commodified world and their own being, reverence for life stands as a vital solution to many of our modern problems. And following contemporary TMT research, reverencing life can also expand one’s self-esteem, which research shows lowers death anxiety, reduces aggression, and offers authentic meaning to life itself. (shrink)

Recently Albert and Hemmo and Shenker have argued that, contrary to what is sometimes suggested, Liouville's theorem does not prohibit a Maxwellian demon from operating but merely places certain restrictions on its ability to operate. There are two main claims made in this article. First, that the restrictions Liouville's theorem places on Maxwell's demon's ability to operate depend on which notion of entropy one adopts. Second, that when one operates with the definition of entropy that is usual in (...) this debate, the restrictions put on Maxwell's demon are not even as severe as Albert and Hemmo and Shenker argue. (shrink)

Résumé En 1880 fut créée au Collège de France une chaire d’Histoire des religions. Il s’agissait là d’un des moments forts de l’institutionnalisation de cette discipline en France. Il n’y eut pas alors d’élection, mais une nomination par le ministère. La presse rendit largement compte de l’affrontement entre les deux candidats. Jules Soury était alors le représentant d’un anticléricalisme virulent qui allait bien au-delà du catholicisme et qui affirmait que les religions étaient un archaïsme dont les sociétés évoluées finiraient par (...) se débarrasser. Le pasteur Albert Réville, qui l’emporta, était quant à lui le représentant du protestantisme libéral. On conserve aux Archives Nationales deux rapports défendant l’opportunité de cette création. L’un est de Jules Soury lui-même. Quant à l’autre, anonyme, nous pensons pouvoir l’attribuer à Ernest Renan. Nous publions ces deux textes inédits avec des notes explicatives. (shrink)

Albert Einstein was the most influential physicist of the twentieth century. Less well-known is that fundamental philosophical problems, such as concept formation, the role of epistemology in developing and explaining the character of physical theories, and the debate between positivism and realism, played a central role in his thought as a whole. Thomas Ryckman shows that already at the beginning of his career, at a time when the twin pillars of classical physics, Newtonian mechanics and Maxwell’s electromagnetism, were (...) known to have but limited validity, Einstein sought to advance physical theory by positing certain physical principles as secure footholds. That philosophy produced his greatest triumph, the general theory of relativity, and his greatest failure, an unwillingness to accept quantum mechanics. This book shows that Einstein’s philosophy grew from a lifelong aspiration for a unified theoretical representation encompassing all physical phenomena. It also considers how Einstein’s theories of relativity and criticisms of quantum theory have shaped the course of twentieth-century philosophy of science. Including a chronology, glossary, chapter summaries, and suggestions for further reading, _Einstein_ is an ideal introduction to this iconic figure in twentieth-century science and philosophy. It is essential reading for students of philosophy of science, and also suitable for those working in related areas such as physics, history of science, or intellectual history. (shrink)

The relationship between Albert Einstein’s special theory of relativity and Hendrik A. Lorentz’s ether theory is best understood in terms of competing interpretations of Lorentz invariance. In the 1890s, Lorentz proved and exploited the Lorentz invariance of Maxwell’s equations, the laws governing electromagnetic fields in the ether, with what he called the theorem of corresponding states. To account for the negative results of attempts to detect the earth’s motion through the ether, Lorentz, in effect, had to assume that (...) the laws governing the matter interacting with the fields are Lorentz invariant as well. This additional assumption can be seen as a generalization of the well-known contraction hypothesis. In Lorentz’s theory, it remained an unexplained coincidence that both the laws governing fields and the laws governing matter should be Lorentz invariant. In special relativity, by contrast, the Lorentz invariance of all physical laws directly reflects the Minkowski space-time structure posited by the theory. One can use this observation to produce a common-cause argument to show that the relativistic interpretation of Lorentz invariance is preferable to Lorentz’s interpretation. (shrink)

The United States, along with other nations and international organizations, has developed an elaborate system of ethical norms and legal rules to govern biomedical research using human subjects. These policies govern research that might provide direct health benefits to participants and research in which there is no prospect for participant health benefits. There has been little discussion, however, about how well these rules would apply to research designed to improve participants’ capabilities or characteristics beyond the goal of good health. When (...) mentioned at all in the literature, this so-called enhancement research, as opposed to research aimed at diagnosing, preventing, curing, or treating illnesses or medical conditions, is usually dismissed without explanation. (shrink)

This paper is a preliminary exploration of the connections between the statistical style of reasoning and the research practices of statistical mechanics in the early period of the long quantum revolution. It suggests that before 1925 the instantiations of the statistical style in physics went through two phases. The first phase consisted of the formulation of the Maxwell‐Boltzmann statistics on the basis of the population‐gas analogy. The second phase was characterized by the generalization of the Maxwell‐Boltzmann statistics through (...) analogies between ideal gas molecules and other microphysical entities, analogies that shaped and were shaped by the rise of quantum theory. Einstein's invention of the Bose‐Einstein statistics started a third phase and created the conditions of possibility for a new classification of microphysical entities according to their different statistics. (shrink)

Charles Sanders Peirce is generally regarded as the founder of pragmatism, and one of the greatest ever American philosophers. Peirce is also widely known for his work on truth, his foundational work in mathematical logic, and an influential theory of signs, or semiotics. Albert Atkin introduces the full spectrum of Peirce’s thought for those coming to his work for the first time. The book begins with an overview of Peirce’s life and work, considering his early and long-standing interest in (...) logic and science, and highlighting important views on the structure of philosophical thought. Atkin then explains Peirce’s accounts of pragmatism and truth examining important later developments to these theories. He then introduces Peirce’s full accounts of semiotics, examines his foundational work on formal and graphical logic, and introduces Peirce’s account of metaphysics, the least understood aspect of his philosophy. The final chapter considers Peirce’s legacy and influence on the thought of philosophers such as John Dewey and Richard Rorty, as well as highlighting areas where Peirce’s ideas could still provide important insights for contemporary philosophers. Including chapter summaries, suggestions for further reading and a glossary, this invaluable introduction and guide to Peirce’s philosophy is essential reading for those new to his work. (shrink)

History of Cognitive Neuroscience documents the major neuroscientific experiments and theories over the last century and a half in the domain of cognitive neuroscience, and evaluates the cogency of the conclusions that have been drawn from them. Provides a companion work to the highly acclaimed Philosophical Foundations of Neuroscience – combining scientific detail with philosophical insights Views the evolution of brain science through the lens of its principal figures and experiments Addresses philosophical criticism of Bennett and Hacker?s previous book Accompanied (...) by more than 100 illustrations. (shrink)

A Companion to Donald Davidson presents newly commissioned essays by leading figures within contemporary philosophy. Taken together, they provide a comprehensive overview of Davidson’s work across its full range, and an assessment of his many contributions to philosophy. Highlights the breadth of Davidson's work across philosophy Demonstrates the continuing influence his work has on the philosophical community Includes newly commissioned contributions from leading figures in contemporary philosophy Provides an in-depth exposition and analysis of Davidson's work across the range of areas (...) to which he contributed, including philosophy of action, epistemology, metaphysics, philosophy of language, and philosophy of mind. (shrink)

"In preparing this remarkable book, Ernest Hook persuaded an eminent group of scientists, historians, sociologists and philosophers to focus on the problem: why are some discoveries rejected at a particular time but later seen to be valid? The interaction of these experts did not produce agreement on 'prematurity' in science but something more valuable: a collection of fascinating papers, many of them based on new research and analysis, which sometimes forced the author to revise a previously-held opinion. The book (...) should be enthusiastically welcomed by all readers who are interested in how science works."—Stephen G. Brush, co-author of Physics, The Human Adventure: From copernicus to Einstein and Beyond "Prematurity and Scientific Discovery contains interesting and insightful papers by numerous well-known scientists and scholars. It will be of wide interest, not only to science studies scholars but also to working scientists and to science-literate general readers."—Thomas Nickles, editor of Scientific Discovery, Logic, and Rationality. (shrink)

The series MISCELLANEA MEDIAEVALIA was founded by Paul Wilpert in 1962 and since then has presented research from the Thomas Institute of the University of Cologne. The cornerstone of the series is provided by the proceedings of the biennial Cologne Medieval Studies Conferences, which were established over 50 years ago by Josef Koch, the founding director of the Institute. The interdisciplinary nature of these conferences is reflected in the proceedings. The MISCELLANEA MEDIAEVALIA gather together papers from all disciplines represented in (...) Medieval Studies - medieval history, philosophy, theology, together with art and literature, all contribute to an overall perspective of the Middle Ages. (shrink)

Contents Preface General Introduction 1 | Science and Pseudoscience Introduction Karl Popper, Science: Conjectures and Refutations Thomas S. Kuhn, Logic of Discovery or Psychology of Research? Imre Lakatos, Science and Pseudoscience Paul R. Thagard, Why Astrology Is a Pseudoscience Michael Ruse, Creation-Science Is Not Science Larry Laudan, Commentary: Science at the Bar---Causes for Concern Commentary 2 | Rationality, Objectivity, and Values in Science Introduction Thomas S. Kuhn, The Nature and Necessity of Scientific Revolutions Thomas S. Kuhn, Objectivity, Value Judgment, and (...) Theory Choice Ernan McMullin, Rationality and Paradigm Change in Science Larry Laudan, Kuhn’s Critique of Methodology Helen E. Longino, Values and Objectivity Kathleen Okruhlik, Gender and the Biological Sciences Commentary 3 | The Duhem-Quine Thesis and Underdetermination Introduction Pierre Duhem, Physical Theory and Experiment W. V. Quine, Two Dogmas of Empiricism Donald Gillies, The Duhem Thesis and the Quine Thesis Larry Laudan, Demystifying Underdetermination *Colin Howson and Peter Urbach, The Duhem Problem Commentary 4 | Induction, Prediction, and Evidence Introduction Peter Lipton, Induction Karl Popper, The Problem of Induction Wesley C. Salmon, Rational Prediction Carl G. Hempel, Criteria of Confirmation and Acceptability Peter Achinstein, Explanation v. Prediction: Which Carries More Weight? *Nelson Goodman, The New Riddle of Induction Commentary 5 | Confirmation and Relevance: Bayesian Approaches Introduction Wesley C. Salmon, Rationality and Objectivity in Science *Deborah G. Mayo, A Critique of Salmon’s Bayesian Way *Alan Chalmers, The Bayesian Approach Paul Horwich, Therapeutic Bayesianism Commentary 6 | Models of Explanation Introduction Rudolf Carnap, The Value of Laws: Explanation and Prediction Carl G. Hempel, Two Basic Types of Scientific Explanation Carl G. Hempel, The Thesis of Structural Identity Carl G. Hempel, Inductive-Statistical Explanation Peter Railton, A Deductive-Nomological Model of Probabilistic Explanation *Philip Kitcher, Explanatory Unification *James Woodward, The Manipulability Conception of Causal Explanation Commentary 7 | Laws of Nature Introduction A. J. Ayer, What Is a Law of Nature? Fred I. Dretske, Laws of Nature D. H. Mellor, Necessities and Universals in Natural Laws Nancy Cartwright, Do the Laws of Physics State the Facts? Commentary 8 | Intertheoretic Reduction Introduction Ernest Nagel, Issues in the Logic of Reductive Explanations Paul K. Feyerabend, How to Be a Good Empiricist *Jerry A. Fodor, Special Sciences Philip Kitcher, 1953 and All That: A Tale of Two Sciences Commentary 9 | Empiricism and Scientific Realism Introduction Grover Maxwell, The Ontological Status of Theoretical Entities Bas C. van Fraassen, Arguments Concerning Scientific Realism Alan Musgrave, Realism versus Constructive Empiricism Larry Laudan, A Confutation of Convergent Realism *Juha T. Saatsi, On the Pessimistic Induction and Two Fallacies Ian Hacking, Experimentation and Scientific Realism David B. Resnik, Hacking’s Experimental Realism *Martin Carrier, What Is Right with the Miracle Argument Arthur Fine, The Natural Ontological Attitude Alan Musgrave, NOA’s Ark---Fine for Realism Commentary Glossary Bibliography Name Index Subject Index. (shrink)

The von Neumann hierarchy of sets is heavily used as a basic tool in classical set theory, being an underlying ingredient in many proofs and concepts. In constructive set theories like without the powerset axiom however, it loses much of its potency by ceasing to be a hierarchy of sets as its single stages become only classes. This article proposes an alternative cumulative hierarchy which does not have this drawback and provides examples of how it can be used to prove (...) new theorems in. (shrink)