This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most (...) striking results are contained in Goedel's work: First, it is possible to give a simple set of rules that suffice to carry out all mathematical proofs; but, second, these rules are necessarily incomplete - it is impossible, for example, to prove all true statements of arithmetic. The book begins with an introduction to first-order logic, Goedel's theorem, and model theory. A second part covers extensions of first-order logic and limitations of the formal methods. The book covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem. Fraissé's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic. (shrink)

Using hitherto unpublished manuscripts from the Zermelo Nachlass, I describe the development of the notion of definiteness and the discussion about it, giving a conclusive picture of Zermelo's thoughts up to the late thirties. As it turns out, Zermelo's considerations about definiteness are intimately related to his concept of a Cantorian universe of categorically definable sets that may be considered an inner model of set theory in an ideationally given universe of classes.

Psychology has a long past, yet its real history is short. For thousands of years it has existed and has been growing older; but in the earlier part of this period it cannot boast of any continuous progress toward a riper and richer development. In the fourth century before our era that giant thinker, Aristotle, built it up into an edifice comparing very favorably with any other science of that time. But this edifice stood without undergoing any noteworthy changes or (...) extensions, well into the eighteenth or even the nineteenth century. Only in recent times do we find an advance, at first slow but later increasing in rapidity, in the development of psychology. The general causes which checked the progress of this science and thus made it fall behind the others can readily be stated:— "The boundaries of the Soul you cannot find, though you pace off all its streets, so deep a foundation has it," runs a sentence of Heraclitus, and it hits the truth more fully than its author could ever have expected. The structures and functions of our mental life present the greatest difficulties to scientific investigation, greater even than those presented by the phenomena, in many respects{4} similar, of the bodily life of the higher organisms. These structures and processes change so unceasingly, are so fleeting, so enormously complex, and dependent on so many factors hidden yet undoubtedly influential, that it is difficult even to seize upon them and describe their true substance, still more difficult to gain an insight into their causal connections and to understand their significance. We are just now beginning to recognize the full force of these difficulties. (shrink)

El presente texto traduce por primera vez al castellano «La ley de la humanidad y los límites del poder estatal», a partir de la edición de la editorial Bouvier: Julius Ebbinghaus, Sittlichkeit und Recht. Praktische Philosophie 1929-1954. La traducción está antecedida por un estudio sobre Julius Ebbinghaus y su interpretación de la filosofía del derecho de Kant. En este ensayo clásico de 1953, Julius Ebbinghaus ofrece una clara articulación de las líneas fundamentales de la doctrina del derecho (...) de Kant. Por un lado, hace patente que el sistema de la libertad política en Kant sólo puede garantizarse con un sistema legal positivo; por otro lado, y frente al positivismo jurídico, sitúa los límites de la dominación política en la ley de la humanidad. Las consecuencias normativas de dicho derecho se ponen de manifiesto en caso de injustica extrema, cuyo ejemplo paradigmático lo ofrece la Alemania Nacionalsocialista. A partir la ley de la humanidad, Julius Ebbinghaus ofrece una justificación kantiana del concepto de delitos de lesa humanidad. (shrink)

On montre comment, dans le Cogito ergo sum, l’idée de mon existence, en tant que je pense, est liée à l’idée de mon existence en tant qu'être pensant. Ainsi se fait voir la compatibilité du caractère originaire de cette connaissance d’une existence avec la prééminence de la proposition universelle : pour pouvoir penser, il faut exister. De la recherche sur le rapport du cogito ergo sum avec le principe de clarté et de distinction il résulte que le cercle reproché à (...) la démonstration cartésienne n’existe pas. Un développement critique sur le spiritualisme cartésien reste réservé. (shrink)

Towards the end of his 1930 paper on boundary numbers and domains of sets Zermelo briefly discusses the questions of consistency and of the existence of an unbounded sequence of strongly inaccessible cardinals, deferring a detailed discussion to a later paper which never appeared. In a report to the Emergency Community of German Science from December 1930 about investigations in progress he mentions that some of the intended extensions of these topics had been worked out and were nearly ready for (...) publication. Using manuscripts from his Nachlass, we exhibit essential features of these extensions. (shrink)

On October 4, 1937, Zermelo composed a small note entitled “Der Relativismus in der Mengenlehre und der sogenannte Skolemsche Satz” in which he gives a refutation of “Skolem's paradox”, i.e., the fact that Zermelo-Fraenkel set theory—guaranteeing the existence of uncountably many sets—has a countable model. Compared with what he wished to disprove, the argument fails. However, at a second glance, it strongly documents his view of mathematics as based on a world of objects that could only be grasped adequately by (...) infinitary means. So the refutation might serve as a final clue to his epistemological credo.Whereas the Skolem paradox was to raise a lot of concern in the twenties and the early thirties, it seemed to have been settled by the time Zermelo wrote his paper, namely in favour of Skolem's approach, thus also accepting the noncategoricity and incompleteness of the first-order axiom systems. So the paper might be considered a late-comer in a community of logicians and set theorists who mainly followed finitary conceptions, in particular emphasizing the role of first-order logic. However, Zermelo never shared this viewpoint: In his first letter to Gödel of September 21, 1931, he had written that the Skolem paradox rested on the erroneous assumption that every mathematically definable notion should be expressible by a finite combination of signs, whereas a reasonable metamathematics would only be possible after this “finitistic prejudice” would have been overcome, “a task I have made my particular duty”. (shrink)

The article investigates Cassirer's developing interest in the cultural sciences to display how his Philosophy of Symbolic Forms constitutes a philosophy of culture. The core concept in such a philosophy of culture is the symbolic formation that both possesses a structured-structuring dimension and appears as an historical process in which culture shows itself as a temporal creation. The philosophy of culture displays 'life in meaning', that is reality as it exhibits human reality manifested in and through the medium of linguistic, (...) artistic, religious, scientific "and so on" action and behaviour. This reality, therefore, is mediation between culture and nature through human spirit. Cassirer's philosophy of culture connects back to Kant's transcendental idealism by emphasizing that any concept of reality establishes itself through a modalization of reality, e.g. that reality constitutes itself in the mode of interpretation. This makes the basis for Cassirer's characteristic understanding of hermeneutics where cultural development is regarded as drama. (shrink)

Ernst Cassirer and Ernst Bloch are considered from the standpoint of the philosophy of culture as the object of comparative study. Instead of considering possible mutual correlative influences, their work is considered with regard to a possible systematic comparison. Bloch's Materialism, like Cassirer's Philosophy of symbolic Forms, can be read as a kind of philosophy of media, if we take »medium« to mean the dimension in which meaning is generated. Against this background Cassirer and Bloch make use of (...) different means to thematize the mediality of culture. (shrink)

The concept of philosophy as a philosophical problem.--Critical idealism as a philosophy of culture.--Descartes, Leibniz, and Vico.--Hegel's theory of the State.--The philosophy of history.--Language and art I.--Language and art II.--The educational value of art.--Philosophy and politics.--Judaism and the modern political myths.--The technique of our modern political myths.--Reflections on the concept of group and the theory of perception.

The geometric shapes and natural forms, captured with exceptional precision in Ernst Haeckel's prints, still influence artists and designers to this day. This volume highlights the research and findings of this natural scientist. Powerful modern microscopes have confirmed the accuracy of Haeckel's prints, which even in their day, became world famous. Haeckel's portfolio, first published between 1899 and 1904 in separate installments, is described in the opening essays. The plates illustrate Haeckel's fundamental monistic notion of the "unity of all (...) living things" and the wide variety of forms are executed with utmost delicacy. Incipient microscopic organisms are juxtaposed with highly developed plants and animals. The pages, ordered according to geometric and "constructive" aspects, document the oness of the world in its most diversified forms. This collection of plates was not only well-received by scientists, but by artists and architects as well. Rene Binet, a pioneer of glass and iron constructions, Emile Galle, a renowned Art Nouveau designer, and the photographer Karl Blossfeld all make explicit reference to Haeckel in their work. (shrink)

In the Preface of Animal Species and Evolution (1963), I wrote that it was "an attempt to summarize and review critically what we know about the biology and genetics of animal species and their role in evolution." The result was a volume of XIV ...

Born in 1838, Mach was a pioneer in the field of physics, having even made an impression on Einstein in his younger life who credited him with being the "Philosophical forerunner of relativity theory." His name is also associated with the speed of sound (as in traveling at Mach "insert-number-here") as well as the Doppler effect. Throughout his career, he was particularly interested in the biological and sensory relationship to physics and science, and naturally, this interest expanded to that of (...) the world of psychological perception and physiological psychology as well as philosophy. The Analysis of Sensations is about just that, the nature of the relationship of physics and the physical sciences to psychological phenomena of sense and perception. It's a fascinating read for anyone looking to expand their knowledge of how the two sides of the same coin meld harmoniously. (shrink)

Excerpt from Substanzbegriff und Funktionsbegriff: Untersuchungen Uber die Grundfragen der Erkenntniskritik Die erste Anregung zu den Untersuchungen, die dieser Band enthalt, ist mir aus Studien zur Philosophie der Mathe matik erwachsen. Indem ich versuchte, von Seiten der Logik aus einen Zugang zu den Grundbegriffen der Mathematik zu gewinnen, erwies es sich vor allem als notwendig, die B e g r i f f s f u n k t i 0 n e'lhsimaher zu zergliedern und auf ihre Voraussetzungen zuruckzufuhren. Hier (...) aber machte sich alsbald eine eigentumliche Schwierigkeit geltend: die her kommliche logische Lehre vom Begriff zeigte sich in ihren bekannten Hauptzugen als unzureichend, die Probleme, zu denen die Prinzipienlehre der Mathematik hinfuhrt, auch nur vollstandig z u b e z e i c h n e n. Die exakte Wissenschaft war hier, wie sich mir immer deutlicher zu ergeben schien, zu Fragen gelangt, fur welche die Formensprache der tradi tionellen Logik kein genaues Correlat besitzt. Der sachliche Gehalt der mathematischen Erkenntnisse wies auf eine Grund form des Begriffs zuruck, die in der Logik selbst nicht zu klarer Bezeichnung und Anerkennung gekommen war. Ins besondere waren es Untersuchungen jiber den Reihenbegriff und den Grenzbegriff (deren spezielles Ergebnis in die allgemeineren Erorterungen dieses Buches nich? 3iffge nommen werden konnte), die diese Uberzeugung in mir be festigten und damit zu einer erneuten Analyse der Prinzipien der Begriffsbildung selbsfhindrangten. 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)

Ernst Troeltsch's essay on socialism presents a summary account of his views on the prospects for a socialist economic order within the Weimar Republic. Troeltsch attempts to formulate a compromise that incorporates the proposals of both social conservatism and communism. Such a compromise, he insists, is possible on the basis of a realistic assessment of socialism supported by "an act of faith in the future" based upon explicitly religious resources. This essay is significant not only in relation to the (...) "religious socialism" then discussed in Germany, but also for the development of "political theology" today. (shrink)

Conventional wisdom situates the historical origins of social movements in the eighteenth and nineteenth centuries by attributing their emergence to the rise of democracy, capitalism, and the nation-state. In this article, I challenge this scholarly orthodoxy by presenting primary sources and historical scholarship that demonstrate how the German Peasants’ Revolt of 1524 and 1525 meets Charles Tilly’s criteria for a modern social movement. By challenging the standard narrative of social movements as a product of modernity, this article breaks with the (...) dichotomy between modern and premodern social movements and encourages us to rethink the concept of social movements. (shrink)

This paper provides strong evidence challenging the self-interest assumption that dominates the behavioral sciences and much evolutionary thinking. The evidence indicates that many people have a tendency to voluntarily cooperate, if treated fairly, and to punish noncooperators. We call this behavioral propensity “strong reciprocity” and show empirically that it can lead to almost universal cooperation in circumstances in which purely self-interested behavior would cause a complete breakdown of cooperation. In addition, we show that people are willing to punish those who (...) behaved unfairly towards a third person or who defected in a Prisoner’s Dilemma game with a third person. This suggests that strong reciprocity is a powerful device for the enforcement of social norms involving, for example, food sharing or collective action. Strong reciprocity cannot be rationalized as an adaptive trait by the leading evolutionary theories of human cooperation (in other words, kin selection, reciprocal altruism, indirect reciprocity, and costly signaling theory). However, multilevel selection theories of cultural evolution are consistent with strong reciprocity. (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)

In this double-volume work, a great modern philosopher propounds a system of thought in which Einstein's theory of relativity represents only the latest (albeit the most radical) fulfillment of the motives inherent to mathematics and the physical sciences. In the course of its exposition, it touches upon such topics as the concept of number, space and time, geometry, and energy; Euclidean and non-Euclidean geometry; traditional logic and scientific method; mechanism and motion; Mayer's methodology of natural science; Richter's definite proportions; relational (...) concepts and the activity of the ego; Einstein's relativity and "reality"; and the philosophical concept of truth and its role in relativity theory. 1923 edition. (shrink)

Erkenntnis und Irrtum. Skizzen zur Psychologie der Forschung. Von E. MACH Emer. Professor an der Unlversltlt Wlen. LEIPZIG Verlag von Johann Ambrosius Barth 1905. INTRODUCTION XIII On a number of occasions Mach expressed the sentiment, especially in his correspondence, that America was the land of intellectual freedom and opportunity, the coming frontier for a new radical empiricism that would help to wash metaphysics out of philosophy. In 1901 he sponsored the German edition of Concepts and Theories of Modern Physics (1881) (...) 2 by J. B. Stallo, Cincinnati lawyer and philosopher. Mach warmly endorsed Stallo's book because his scientific aims so closely approximated his own, and because Stallo rejected the latent metaphysical elements and concealed ontological assumptions of the mechanical-atomistic inter­ pretation of the world. The second edition of Wiirmelehre was dedicated to Stallo in 1900. The fourth edition of Populiir-wissenschaftliche Vorlesungen (1910), containing seven new essays, was dedicated to Harvard Professor of physiology, philosophY, and psychology, William James. Mach had a strong intellectual affinity for James' pragmatism because, like himself, he recognized that James had come to radically empirical views from science. Both men took pure pre-conceptualized experience, from which the mental and physical predicates of experience are composed, to be neutral rather than real, unreal, objective or subjective. (shrink)

Ernst Cassirer occupies a unique space in Twentieth-century philosophy. A great liberal humanist, his multi-faceted work spans the history of philosophy, the philosophy of science, intellectual history, aesthetics, epistemology, the study of language and myth, and more. Cassirer's thought also anticipates the renewed interest in the origins of analytic and continental philosophy in the Twentieth Century and the divergent paths taken by the 'logicist' and existential traditions, epitomised by his now legendary debate in 1929 with the philosopher Martin Heidegger, (...) over the question "What is the Human Being?" The Philosophy of Symbolic Forms is Cassirer's most important work. It was first published in German in 1923, the third and final volume appearing in 1929. In it Cassirer presents a radical new philosophical worldview - at once rich, creative and controversial - of human beings as fundamentally "symbolic animals," placing signs and systems of expression between themselves and the world. This major new translation of all three volumes, the first for over fifty years, brings Cassirer's magnum opus to a new generation of students and scholars. Taken together, the three volumes of The Philosophy of Symbolic Forms are a vital treatise on human beings as symbolic animals and a monumental expression of neo-Kantian thought. Correcting important errors in previous English editions, this translation reflects the contributions of significant advances in Cassirer scholarship over the last twenty to thirty years. Each volume includes a new introduction and translator's notes by S. G. Lofts, a foreword by Peter Gordon, a glossary of key terms, and a thorough index. (shrink)

Bloch's The Spirit of Utopia, here presented for the first time in English translation, is one of the great historic books from the beginning of the twentieth-century. A peculiar amalgam of biblical, Marxist, and Expressionist turns, drawing on both Hegel and Schopenhauer for the groundwork of its metaphysics of music, but consistently interpreting the cultural legacy in the light of a certain Marxism, The Spirit of Utopia is a unique attempt to rethink the history of Western civilizations as a process (...) of revolutionary disruptions and to reread the artworks, religions, and philosophies of this tradition as incentives to continue disrupting. The first part concerns a mode of 'self-encounter' which presents itself in the history of music from Mozart through Mahler as an encounter with the problem of a community to come. The second part is entitled 'Karl Marx, Death and the Apocalypse'. (shrink)

This new translation of The Logic of the Cultural Sciences _ _makes Ernst Cassirer’s classic study, long out of print, available to English readers. A German Jew living in exile at the beginning of the Second World War, Cassirer wrote this book—one of his clearest and most concise—in response to the crises besetting his era. It represented to him a rethinking and completion of his magnum opus _The Philosophy of Symbolic Forms. _S. G. Lofts’s translation stays close to the (...) original German and accurately reflects the echoes of the philosophical debates of Cassirer’s day. In the book’s five linked studies, Cassirer considers the intellectual structure of the disciplines we commonly refer to as the humanities. He defines and justifies the basic philosophical perspective of the philosophy of symbolic forms, and he contributes a wealth of ideas to continuing debates about culture and what is unique in human nature. (shrink)

Discusses the nature of time, suggests a hierarchical model of human temporal experience, and proposes a new definition of consciousness.

“Here is the first Kant-biography in English since Paulsen’s and Cassirer’s only full-scale study of Kant’s philosophy. On a very deep level, all of Cassirer’s philosophy was based on Kant’s, and accordingly this book is Cassirer’s explicit coming to terms with his own historical origins. It sensitively integrates interesting facts about Kant’s life with an appreciation and critique of his works. Its value is enhanced by Stephen Körner’s Introduction, which places Cassirer’s Kant-interpretation in its historical and contemporary context.”—Lewis White Beck (...) “The first English translation (well done by James Haden) of a 60-year-old classic intellectual biography. Those readers who know Kant only through the first _Critique_ will find their understanding of that work deepened and illuminated by a long explication of the pre-critical writings, but perhaps the most distinctive contribution is Cassirer’s argument that the later _Critiques_, and especially the _Critique of Judgment_, must be understood not as merely applying the principles of the first to other areas but as subsuming the latter into a larger and more comprehensive framework.”—Frederick J. Crown, _The Key Reporter_ “_Kant’s Life and Thought_ is that rare achievement: a lucid and highly readable account of the life and work of one of the world’s profoundest thinkers. Now for the first time available in an admirable English translation, the book introduces the reader to two of the finest minds in the history of philosophy.”—Ashley Montagu. (shrink)

"In his Phenomenology of Cognition, Cassirer provides a comprehensive and systematic account of the dynamic process involved in the whole of human culture as it progresses from the world of myth and its feeling of social belonging to the highest abstractions of mathematics, logic and theoretical physics. Cassirer engages with the most sophisticated and cutting-edge work in fields ranging from ethnology to classics, egyptology and assyriology to ethology, brain science and psychology to logic, mathematics and theoretical physics. His command of (...) philosophy, literature, and the arts is superb. Echoing his work on Kant, Cassirer begins ThePhilosophy of Symbolic Formswith the problem posed by the meaning of being for philosophy since Plato. But Cassirer also shows that this problem gains new significance with Kant and with the development of modern culture. Cassirer weaves his conception of the development of knowledge into a broadly Kantian and German idealist dynamic-historical conception of significance and of experience that refuses to accept a fundamental opposition between literary, philosophical and scientific culture. In consequence of his great vision grounded in careful reflection and argument, Cassirer's systematic conception of the Copernican cosmopolitan-cosmological revolution is still philosophically and scientifically unmatched in contemporary philosophy on both sides of the Atlantic and of the Pacific." - Pierre Keller, Professor of Philosophy, University of California, Riverside, USA. This new translation makes Cassirer's seminal work available to a new generation of scholars. Each volume includes an introduction by Steve Lofts, a foreword by Peter Gordon, a glossary of key terms, and an index. Steve Lofts is Professor of Philosophy at King's University College, Canada. He is the translator of Cassirer's The Logic of the Cultural Sciences and The Warburg Years : Essays on Language, Art, Myth, and Technology. (shrink)

The existence of objective knowledge and the possibility of communicating it by means of language have traditionally been taken for granted by educators. Recent developments in the philosophy of science and the historical study of scientific accomplishments have deprived these presuppositions of their former plausibility. Sooner or later, this must have an effect on the teaching of science. In this paper I am presenting a brief outline of an alternative theory of knowing that takes into account the thinking organism''s cognitive (...) isolation from reality. This orientation was proposed by Vico at the beginning of the 18th century, disregarded for two hundred years, and then propounded independently by Piaget as a developmentally grounded constructivist epistemology. The paper focuses specifically on the adaptive function of cognition, Piaget''s scheme theory, the process of communication, and the subjective perspective on social interaction. In the concluding section it then suggests some of the consequences the shift of epistemological presuppositions might have for the practice of teaching. (shrink)