In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational (...) axiomatization. A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation. In contrast to RAs, FAs are representable by proper ones and their equational theory has the expressive power of full first-order logic. A square semantics (the set of arrows is ᵎ x ᵎ for some set ᵎ) for arrow logic was defined by Y. Venema. Due to the negative results about the finite axiomatizability of representable RAs, Venema provided a non-orthodox finite axiomatization for arrow logic by adding a new rule governing the applications of a difference operator. We address here the question of extending the type of relational structures to define orthodox axiomatizations for the class of squares. Given the connections between this problem and the finitization problem addressed by I. Németi, we suspect that this cannot be done by using only logical operations. The modal version of the FA equations provides an orthodox axiomatization for FAL which is complete in view of the representability of FAs. Here we review this result and carry it further to prove that this orthodox axiomatization for FAL also axiomatizes the class of fork squares. (shrink)

In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational (...) axiomatization. A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation. In contrast to RAs, FAs are representable by proper ones and their equational theory has the expressive power of full first-order logic. A square semantics (the set of arrows is U×U for some set U) for arrow logic was defined by Y. Venema. Due to the negative results about the finite axiomatizability of representable RAs, Venema provided a non-orthodox finite axiomatization for arrow logic by adding a new rule governing the applications of a difference operator. We address here the question of extending the type of relational structures to define orthodox axiomatizations for the class of squares. Given the connections between this problem and the finitization problem addressed by I. Németi, we suspect that this cannot be done by using only logical operations. The modal version of the FA equations provides an orthodox axiomatization for FAL which is complete in view of the representability of FAs. Here we review this result and carry it further to prove that this orthodox axiomatization for FAL also axiomatizes the class of fork squares. (shrink)

We compare fork arrow logic, an extension of arrow logic, and its natural first-order counterpart (the correspondence language) and show that both have the same expressive power. Arrow logic is a modal logic for reasoning about arrow structures, its expressive power is limited to a bounded fragment of first-order logic. Fork arrow logic is obtained by adding to arrow logic the fork modality (related to parallelism and synchronization). As a result, fork arrow logic attains the expressive power of its first-order (...) correspondence language, so both can express the same input–output behavior of processes. (shrink)

We compare fork arrow logic, an extension of arrow logic, and its natural first-order counterpart (the correspondence language) and show that both have the same expressive power. Arrow logic is a modal logic for reasoning about arrow structures, its expressive power is limited to a bounded fragment of first-order logic. Fork arrow logic is obtained by adding to arrow logic the fork modality (related to parallelism and synchronization). As a result, fork arrow logic attains the expressive power of its first-order (...) correspondence language, so both can express the same input-output behavior of processes. (shrink)

This collection of essays, written on four continents by scientists, philosophers and humanists, was initially presented to Karl R. Popper on his sixtieth birthday as a token of critical admiration and in recognition of his work. But the volume also stands on its own as a remarkable series of statements utilizing Popper's critical vision in the study of philosophy proper, logic, mathematics, science as method and theory, and finally to the study of society and history. What is remarkable is that (...) Popper worked in all of these areas, not in a cursory or discursive way, but with the utmost clarity and rigor.. The core position of this volume and its contributors is that the progress of knowledge is not a linear accumulation of definitive acquisitions but a zigzagging process in which counterexamples and unfavorable evidence ruin generalizations and prompt the invention of more comprehensive and sometimes deeper generalizations, to be criticized in their turn. A critical approach to problems, procedures, and results in every field of inquiry is therefore a necessary condition for the continuance of progress. The title of this volume then is, in a sense, an homage to Popper's critical rationalism and critical empiricism. The essays are a tribute to his unceasing and uncompromising quest, not for final certainty, but for closer truth and increased clarity. Among the contributors are outstanding figures in philosophy and the exact sciences in their own right, including Herbert Feigl, R. M. Hare, J.O. Wisdom, Nicholas Rescher, David Bohm, Paul K. Feyerabend, F. A. Hayek, and Adolf Grunbaum. Social science contributions include Hans Albert on social science and moral philosophy, W. B. Gallie, on the critical philosophy of history, Pieter Geyl on The Open Society and its Enemies, and George H. Nadel on the philosophy of History. (shrink)

We investigate the possibility to characterize (multi) functions that are Σ b i -definable with small i (i = 1, 2, 3) in fragments of bounded arithmetic T 2 in terms of natural search problems defined over polynomial-time structures. We obtain the following results: (1) A reformulation of known characterizations of (multi)functions that are Σ b 1 - and Σ b 2 -definable in the theories S 1 2 and T 1 2 . (2) New characterizations of (multi)functions that are (...) Σ b 2 - and Σ b 3 -definable in the theory T 2 2 . (3) A new non-conservation result: the theory T 2 2 (α) is not ∀Σ b 1 (α)-conservative over the theory S 2 2 (α). To prove that the theory T 2 2 (α) is not ∀Σ b 1 (α)-conservative over the theory S 2 2 (α), we present two examples of a Σ b 1 (α)-principle separating the two theories: (a) the weak pigeonhole principle WPHP (a 2 , f, g) formalizing that no function f is a bijection between a 2 and a with the inverse g, (b) the iteration principle Iter (a, R, f) formalizing that no function f defined on a strict partial order ( $\{0,\dots,a\}$ , R) can have increasing iterates. (shrink)

Historical materialism I take to be the view expressed in the well-known Preface to the Critique of Political Economy and exemplified in Capital and in many other writings by Marx and by Marxists. I shall begin with a few introductory remarks, next sketch in the theory, and finally contend that, despite real attractions, it too far limits the scope of legitimate historical enquiry to be ultimately acceptable.

Reading the _Republic_ without reference to the less familiar _Laws_ can lead to a distorted view of Plato's political theory. In the _Republic_ the philosopher describes his ideal city; in his last and longest work he deals with the more detailed considerations involved in setting up a second-best 'practical utopia.' The relative neglect of the _Laws_ has stemmed largely from the obscurity of its style and the apparent chaos of its organization so that, although good translations now exist, students of (...) philosophy and political science still find the text inaccessible. This first full-length philosophical introduction to the Laws will therefore prove invaluable. The opening chapters describe the general character of the dialogue and set it in the context of Plato's political philosophy as a whole. Each of the remaining chapters deals with a single topic, ranging over material scattered through the text and so drawing together the threads of the argument in a stimulating and readily comprehensible way. Those topics include education, punishment, responsibility, religion, virtue and pleasure as well as political matters and law itself. Throughout, the author encourages the reader to think critically about Plato's ideas and to see their relevance to present-day philosophical debate. No knowledge of Greek is required and only a limited background in philosophy. Although aimed primarily at students, the book will also be of interest to more advanced readers since it provides for the first time a philosophical, as opposed to linguistic or historical, commentary on the _Laws_ in English. (shrink)

This volume has 41 chapters written to honor the 100th birthday of Mario Bunge. It celebrates the work of this influential Argentine/Canadian physicist and philosopher. Contributions show the value of Bunge’s science-informed philosophy and his systematic approach to philosophical problems. The chapters explore the exceptionally wide spectrum of Bunge’s contributions to: metaphysics, methodology and philosophy of science, philosophy of mathematics, philosophy of physics, philosophy of psychology, philosophy of social science, philosophy of biology, philosophy of technology, moral philosophy, social and (...) political philosophy, medical philosophy, and education. The contributors include scholars from 16 countries. Bunge combines ontological realism with epistemological fallibilism. He believes that science provides the best and most warranted knowledge of the natural and social world, and that such knowledge is the only sound basis for moral decision making and social and political reform. Bunge argues for the unity of knowledge. In his eyes, science and philosophy constitute a fruitful and necessary partnership. Readers will discover the wisdom of this approach and will gain insight into the utility of cross-disciplinary scholarship. This anthology will appeal to researchers, students, and teachers in philosophy of science, social science, and liberal education programmes. 1. Introduction Section I. An Academic Vocation Section II. Philosophy Section III. Physics and Philosophy of Physics Section IV. Cognitive Science and Philosophy of Mind Section V. Sociology and Social Theory Section VI. Ethics and Political Philosophy Section VII. Biology and Philosophy of Biology Section VIII. Mathematics Section IX. Education Section X. Varia Section XI. Bibliography. (shrink)

The idea of absolute goodness and the idea of an absolute requitement tend nowadays to be viewed with suspicion in the world of English-speaking philosophy. The tendency is well rooted and has not just arisen by osmosis from the temper of the times. There are various lines of thought, all of them attractive, by which a recent or contemporary academic practitioner of the subject could have been induced into scepticism about an ethics of absolute conceptions.

Jung was intrigued from early in his career with coincidences, especially those surprising juxtapositions that scientific rationality could not adequately explain. He discussed these ideas with Albert Einstein before World War I, but first used the term "synchronicity" in a 1930 lecture, in reference to the unusual psychological insights generated from consulting the I Ching. A long correspondence and friendship with the Nobel Prize-winning physicist Wolfgang Pauli stimulated a final, mature statement of Jung's thinking on synchronicity, originally published in 1952 (...) and reproduced here. Together with a wealth of historical and contemporary material, this essay describes an astrological experiment Jung conducted to test his theory. Synchronicity reveals the full extent of Jung's research into a wide range of psychic phenomena. This paperback edition of Jung's classic work includes a new foreword by Sonu Shamdasani, Philemon Professor of Jung History at University College London. (shrink)

In the present philosophical climate of opinion many are inclined to respond to this question in the spirit of the cynical comment concerning Christian Science, that it is neither Christian nor scientific. So it might be affirmed of Christian philosophy. It is neither Christian nor philosophical. It is customary these days to find both theologians and positivistic philosophers agreeing on this point. Theologians of a certain persuasion wish to keep theology free from any taint of the bacillus metaphysicus. Philosophers of (...) a certain school are equally anxious to keep philosophy free of any entanglement with theological questions which involve problems incapable of linguistic clarification and precise meaning. Nevertheless, there is mounting evidence that this kind of intellectual apartheid is becoming less and less possible in practice and less attractive in principle. Even those who wish to separate rigidly theology and philosophy seem in practice to find it impossible to let each other alone. Each exercises a kind of morbid fascination for the other, and even if real dialogue is refused, the sniping still goes on, in reluctant acknowledgement of the existence of the other. The time would appear to be ripe, therefore, for a fresh and bold re-opening of the question which forms the title of this paper. (shrink)

Originally published in 1920, this title wrestles with the critical conflict in modern philosophy of whether philosophers should employ pure reason in a world of abstracts or, rather, should rely upon experience and rationality to examine the actual world. Hoernlé argues for the latter and emphasises the importance of metaphysics in the intellectual quest for knowing reality. This title is ideal for students of philosophy and provides insightful background into the diverging philosophical views of the early 20th century.

Considered one of Jung's most controversial works, Answer to Job also stands as Jung's most extensive commentary on a biblical text. Here, he confronts the story of the man who challenged God, the man who experienced hell on earth and still did not reject his faith. Job's journey parallels Jung's own experience--as reported in The Red Book: Liber Novus--of descending into the depths of his own unconscious, confronting and reconciling the rejected aspects of his soul. This paperback edition of Jung's (...) classic work includes a new foreword by Sonu Shamdasani, Philemon Professor of Jung History at University College London. Described by Shamdasani as "the theology behind The Red Book," Answer to Job examines the symbolic role that theological concepts play in an individual's psychic life. (shrink)

Dream analysis is a distinctive and foundational part of analytical psychology, the school of psychology founded by C. G. Jung and his successors. This volume collects Jung's most insightful contributions to the study of dreams and their meaning. The essays in this volume, written by Jung between 1909 and 1945, reveal Jung's most essential views about dreaming--especially regarding the relationship between language and dream. Through these studies, Jung grew to understand that dreams are themselves a language, a language through which (...) the soul communicates with the body. The essays included are "The Analysis of Dreams," "On the Significance of Number Dreams," "General Aspects of Dream Psychology," "On the Nature of Dreams," "The Practical Use of Dream Analysis," and "Individual Dream Symbolism in Relation to Alchemy". New to this edition is a foreword by Sonu Shamdasani, Philemon Professor of Jung History at University College London. (shrink)

One of Jung's most influential ideas has been his view, presented here, that primordial images, or archetypes, dwell deep within the unconscious of every human being. The essays in this volume gather together Jung's most important statements on the archetypes, beginning with the introduction of the concept in "Archetypes and the Collective Unconscious." In separate essays, he elaborates and explores the archetypes of the Mother and the Trickster, considers the psychological meaning of the myths of Rebirth, and contrasts the idea (...) of Spirits seen in dreams to those recounted in fairy tales.This paperback edition of Jung's classic work includes a new foreword by Sonu Shamdasani, Philemon Professor of Jung History at University College London. (shrink)

In the autumn of 1912, C. G. Jung, then president of the International Psychoanalytic Association, set out his critique and reformulation of the theory of psychoanalysis in a series of lectures in New York, ideas that were to prove unacceptable to Freud, thus creating a schism in the Freudian school. Jung challenged Freud's understandings of sexuality, the origins of neuroses, dream interpretation, and the unconscious, and Jung also became the first to argue that every analyst should themselves be analyzed. Seen (...) in the light of the subsequent reception and development of psychoanalysis, Jung's critiques appear to be strikingly prescient, while also laying the basis for his own school of analytical psychology. This volume of Jung's lectures includes an introduction by Sonu Shamdasani, Philemon Professor of Jung History at University College London, and editor of Jung's Red Book. (shrink)

pt. 1. A critique of current educational aims.--pt. 2. Reason.--pt. 3. Education and reason.

This Companion provides a fresh and comprehensive account of this outstanding work, which remains among the most frequently read works of Greek philosophy, indeed of Classical antiquity in general. The sixteen essays, by authors who represent various academic disciplines, bring a spectrum of interpretive approaches to bear in order to aid the understanding of a wide-ranging audience, from first-time readers of the Republic who require guidance, to more experienced readers who wish to explore contemporary currents in the work’s interpretation. The (...) three initial chapters address aspects of the work as a whole. They are followed by essays that match closely the sequence in which topics are presented in the ten books of the Republic. Since the Republic returns frequently to the same topics by different routes, so do the authors of this volume, who provide the readers with divergent yet complementary perspectives by which to appreciate the Republic’s principal concerns. (shrink)

This volume critically and constructively discusses philosophical questions which have particular bearing on the formulation of educational aims. The book is divided into three major parts: the first deals with the nature of education, and discusses the various general aims, such as 'mental health', 'socialization' and 'creativity' which have been thought to characterize it; the second section is concerned with the nature of reason and its relationship to feeling, will and action; finally the development of different aspects of reason in (...) an educational context is considered. (shrink)

Designed to fill a large gap in American philosophy scholarship, this bibliography covers the first four decades of the pragmatic movement. It references most of the philosophical works by the twelve major figures of pragmatism: Charles S. Peirce, William James, John Dewey, George H. Mead, F.C.S. Schiller, Giovanni Papini, Giovanni Vailati, Guiseppe Prezzolini, Mario Calderoni, A.W. Moore, John E. Boodin, and C.I. Lewis. It also includes writings of dozens of minor pragmatic writers, along with those by commentators and critics (...) of pragmatism. It encompasses literature not only concerning pragmatism as an alliance of philosophical theories of meaning, inquiry, belief, knowledge, logic, truth, ontology, value, and morality, but also as an intellectual and cultural force impacting art, literature, education, the social and natural sciences, religion, and politics.This bibliography contains 2,794 main entries and more than 2,000 additional references, organized by year of publication. 2,101 of the references include annotation. Its international scope is focused on writings in English, French, German, and Italian, though many other languages are also represented. Peter H. Hare contributed the Guest Preface. The introduction contains an historical orientation to pragmatism and guides to recent studies of pragmatic figures. This work is extensively cross-referenced, and it has exhaustive and lengthy author and subject indexes. (shrink)

First published in 2000, this translation of one of the great works of Western political thought is based on the assumption that when Plato chose the dialogue form for his writing, he intended these dialogues to sound like conversations - although conversations of a philosophical sort. In addition to a vivid, dignified and accurate rendition of Plato's text, the student and general reader will find many aids to comprehension in this volume: an introduction that assesses the cultural background to the (...) Republic, its place within political philosophy, and its general argument; succinct notes in the body of the text; an analytical summary of the work's content; a full glossary of proper names; a chronology of important events; and a guide to further reading. The result is an accomplished and accessible edition of this seminal work, suitable for philosophers and classicists as well as historians of political thought at all levels. (shrink)

ALTHOUGH THE IDEA OF A VIOLATION OF NATURAL LAW IS NOT NECESSARILY INVOLVED IN THE IDEA OF THE MIRACULOUS, THERE IS "ONE KIND" OF MIRACLE WHICH SEEMS TO INVOLVE IT. HUME’S DISCUSSION OF THE EVIDENCE FOR MIRACLES RELATES TO THIS KIND AND IS INTERPRETABLE AS AN ARGUMENT AGAINST ITS POSSIBILITY. ALSO THERE IS AN ARGUMENT THAT THE EXPRESSION "VIOLATION OF NATURAL LAW" SIGNIFIES A CONFUSION IN WHICH THE IDEAS OF NATURAL LAW AND LEGAL LAW COLLAPSE INTO EACH OTHER. NEITHER OF (...) THESE ARGUMENTS IS EFFICACIOUS. FURTHERMORE, THE CONTENTION THAT THERE CAN BE NO SUCH THING AS ESTABLISHING THE "ABSENCE" OF A NATURAL CAUSE IS OPEN TO OBJECTION. HOWEVER, TO BE CONCEIVED AS A VIOLATION OF NATURAL LAW, A MIRACLE MUST BE THOUGHT OF AS AN OCCURRENCE WHICH IS BOTH EMPIRICALLY CERTAIN AND CONCEPTUALLY IMPOSSIBLE--WHICH OUGHT TO MAKE THE NOTION RIDICULOUS. AND YET IT NEED NOT. (shrink)