Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the (...) explanation of the rules. (shrink)

In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, known as reduction and expansion . We propose (...) a construction of the E-rules (in GE-form) from given I-rules, and prove that the constructed rules satisfy also local intrinsic harmony. The construction is based on a classification of I-rules, and constitute an implementation to Gentzen’s (and Pawitz’) remark, that E-rules can be “read off” I-rules. (shrink)

That every first-order theory has a coherent conservative extension is regarded by some as obvious, even trivial, and by others as not at all obvious, but instead remarkable and valuable; the result is in any case neither sufficiently well-known nor easily found in the literature. Various approaches to the result are presented and discussed in detail, including one inspired by a problem in the proof theory of intermediate logics that led us to the proof of the present paper. It can (...) be seen as a modification of Skolem’s argument from 1920 for his “Normal Form” theorem. “Geometric” being the infinitary version of “coherent”, it is further shown that every infinitary first-order theory, suitably restricted, has a geometric conservative extension, hence the title. The results are applied to simplify methods used in reasoning in and about modal and intermediate logics. We include also a new algorithm to generate special coherent implications from an axiom, designed to preserve the structure of formulae with relatively little use of normal forms. (shrink)

The paper briefly surveys the sentential proof-theoretic semantics for fragment of English. Then, appealing to a version of Frege’s context-principle (specified to fit type-logical grammar), a method is presented for deriving proof-theoretic meanings for sub-sentential phrases, down to lexical units (words). The sentential meaning is decomposed according to the function-argument structure as determined by the type-logical grammar. In doing so, the paper presents a novel proof-theoretic interpretation of simple type, replacing Montague’s model-theoretic type interpretation (in arbitrary Henkin models). The domains (...) of derivations are collections of derivations in the associated “dedicated” natural-deduction proof-system, and functions therein (with no appeal to models, truth-values and elements of a domain). The compositionality of the semantics is analyzed. (shrink)

By considering the new notion of theinversesof syllogisms such asBarbaraandCelarent, we show how the rule ofIndirect Proof, in the form (no multiple or vacuous discharges) used by Aristotle, may be dispensed with, in a system comprising four basic rules of subalternation or conversion and six basic syllogisms.

The paper presents a proof-theoretic semantics (PTS) for a fragment of natural language, providing an alternative to the traditional model-theoretic (Montagovian) semantics (MTS), whereby meanings are truth-condition (in arbitrary models). Instead, meanings are taken as derivability-conditions in a dedicated natural-deduction (ND) proof-system. This semantics is effective (algorithmically decidable), adhering to the meaning as use paradigm, not suffering from several of the criticisms formulated by philosophers of language against MTS as a theory of meaning. In particular, Dummett’s manifestation argument does not (...) obtain, and assertions are always warranted, having grounds of assertion. The proof system is shown to satisfy Dummett’s harmony property, justifying the ND rules as meaning conferring. The semantics is suitable for incorporation into computational linguistics grammars, formulated in type-logical grammar. (shrink)

We describe a sequent calculus, based on work of Herbelin, of which the cut-free derivations are in 1-1 correspondence with the normal natural deduction proofs of intuitionistic logic. We present a simple proof of Herbelin's strong cut-elimination theorem for the calculus, using the recursive path ordering theorem of Dershowitz.

This paper shows that, for the Hertz–Gentzen Systems of 1933, extended by a classical rule T1 and using certain axioms, all derivations are analytic: every cut formula occurs as a subformula in the cut’s conclusion. Since the Stoic cut rules are instances of Gentzen’s Cut rule of 1933, from this we infer the decidability of the propositional logic of the Stoics. We infer the correctness for this logic of a “relevance criterion” and of two “balance criteria”, and hence that a (...) particular derivable sequent has no derivation that is “normal” in the sense that the first premiss of each cut is cut-free. We also infer that Cut is not admissible in the Stoic system, based on the standard Stoic axioms, the T1 rule and the instances of Cut with just two antecedent formulae in the first premiss. OPEN ACCESS. (shrink)

We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs. i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.

We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs. i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.

The decision problem for positively quantified formulae in the theory of linearly ordered Heyting algebras is known, as a special case of work of Kreisel, to be solvable; a simple solution is here presented, inspired by related ideas in Gödel-Dummett logic.

"The papers in this volume are extended versions of presentations at the fourth International Workshop on Extensions of Logic Programming, held at the University of St Andrews, March/April 1993. Among the topics covered in the volume are: defintional reflection and completion, modules in lambda-Prolog, representation of logics as partial inductive definitions, non-procedural logic programming, knowledge representation, contradiction avoidance, disjunctive databases, strong negation, linear logic programming, proof theory and regular search spaces, finite sets and constraint logic programming, search-space pruning and universal (...) algebra, and implementation on transputer networks."--PUBLISHER'S WEBSITE. (shrink)

A major strategy to reduce transport congestion and other social costs of transport is to ensure that travellers make the best decisions, based on real time information. A wide range of technological systems have been developed to provide this information, but little is known about how travellers actually respond to it. This book offers an overview of various transport telematics options and provides an appropriate methodological framework, followed by a presentation of results from actual applications of these telematics systems from (...) a range of European countries in various transport sectors. The empirical results are supplemented by analytical models and geographic information systems representations with a view on generalizing these findings and identifying the key parameters which determine user response. (shrink)

The eclipse riddle -- Seeing surfaces -- The disappearing act -- Spinning shadows -- Berkeley's shadow -- Para-reflections -- Para-refractions : shadowgrams and the black drop -- Goethe's colored shadows -- Filtows -- Holes in the light -- Black and blue -- Seeing in black and white -- We see in the dark -- Hearing silence.

In a brilliant series of studies, Roy Bhaskar, the originator of the influential, multi-disciplinary and international philosophy of critical realism, presents for the first time in published form, his new philosophy of Meta-Reality. The philosophy of Meta-Reality confirms many aspects of the great philosophical traditions of the past, while correcting their one-sidedness and transcending their dualism and dichotomies, representing what is valid in them in a radically new way, apt for our contemporary times of global crisis.

This unique collection of studies, based for the most part on transcripts of talks in India, Europe and America over the last five years, covers the period in which Roy Bhaskar was developing out of the seeds of the most radical phase of critical realism, his new philosophy of meta-Reality. Because of the spontaneous and informal nature of these talks and discussions, this book provides probably the most immediately accessible introduction to his thought, both for those new to it and (...) those already familiar with it alike. (shrink)

In his most audacious and radical book to date, Bhaskar develops his existing philosophy of dialectical critical realism into a philosophy of and for universal self-realization (which he also terms a transcendental critical realism). In a general theoretical introduction, Bhaskar establishes the existence of God as the fundamental categorical structure of the world and unconditional love as the cement of the universe. This system of thought is followed by a narrative novella designed to render plausible the ideas of reincarnation, karma (...) and moksha, or liberation, and to support an ethic of engaged but unattached activity in the world. (shrink)

Can God create a stone too heavy for him to lift? Can time have a beginning? Which came first, the chicken or the egg? Riddles, paradoxes, conundrums--for millennia the human mind has found such knotty logical problems both perplexing and irresistible. Now Roy Sorensen offers the first narrative history of paradoxes, a fascinating and eye-opening account that extends from the ancient Greeks, through the Middle Ages, the Enlightenment, and into the twentieth century. When Augustine asked what God was doing before (...) He made the world, he was told: "Preparing hell for people who ask questions like that." A Brief History of the Paradox takes a close look at "questions like that" and the philosophers who have asked them, beginning with the folk riddles that inspired Anaximander to erect the first metaphysical system and ending with such thinkers as Lewis Carroll, Ludwig Wittgenstein, and W.V. Quine. Organized chronologically, the book is divided into twenty-four chapters, each of which pairs a philosopher with a major paradox, allowing for extended consideration and putting a human face on the strategies that have been taken toward these puzzles. Readers get to follow the minds of Zeno, Socrates, Aquinas, Ockham, Pascal, Kant, Hegel, and many other major philosophers deep inside the tangles of paradox, looking for, and sometimes finding, a way out. Filled with illuminating anecdotes and vividly written, A Brief History of the Paradox will appeal to anyone who finds trying to answer unanswerable questions a paradoxically pleasant endeavor. (shrink)

'As an introduction to early modern thinking and the impact of past ideas on present lives, this book can find few equals and no superiors. Porter is a witty, humane writer with an extraordinary vocabulary and a sparkling sense of fun. Whether he is quoting from obscure medical texts or analysing scabrous diaries, dishing the dirt on long-dead bigwigs or evoking sympathy for human suffering, his grasp is masterly and his erudition appealing. I wish I could read it again for (...) the first time: you can.' Times Educational Supplement, Book of the Week In this startlingly brilliant sequel to the prize-winning ENLIGHTENMENT Roy Porter completes his lifetime's work, offering a magical, enthusiastic and charming account of the writings of some of the most attractive figures ever to write English. (shrink)

In this book, Roy Bhaskar sets out to revindicate ontology, critiquing the reduction of being in favor of knowledge, which he calls the "epistemic fallacy".

The Indian film’s depiction of rape and sexual violence specifically on women, can provide a glimpse into the wider Indian cultural mores seeping into the thoughts and processes that are in play du...

Following on from Roy Bhaskarâe(tm)s first two books, A Realist Theory of Science and The Possibility of Naturalism, Scientific Realism and Human Emancipation, establishes the conception of social science as explanatoryâe"and thence emancipatoryâe"critique. Scientific Realism and Human Emancipation starts from an assessment of the impasse of contemporary accounts of science as stemming from an incomplete critique of positivism. It then proceeds to a systematic exposition of scientific realism in the form of transcendental realism, highlighting a conception of science as explanatory (...) of a structured, differentiated and changing world. Turning to the social domain, the book argues for a view of the social order as conditioned by, and emergent from, nature. Advocating a critical naturalism, the author shows how the transformational model of social activity together with the conception of social science as explanatory critique which it entails, resolves the divisions and dualisms besetting orthodox social and normative theory: between society and the individual, structure and agency, meaning and behavior, mind and body, reason and cause, fact and value, and theory and practice. The book then goes on to discuss the emancipatory implications of social science and sketches the nature of the depth investigation characteristically entailed. In the highly innovative third part of the book Roy Bhaskar completes his critique of positivism by developing a theory of philosophical discourse and ideology, on the basis of the transcendental realism and critical naturalism already developed, showing how positivism functions as a restrictive ideology of and for science and other social practices. (shrink)

Since its original publication in 1979, The Possibility of Naturalism has been one of the most influential works in contemporary philosophy of science and social science. It is a cornerstone of the critical realist position, which is now widely seen as offering a viable alternative to move positivism and postmodernism. This revised edition includes a new foreword.

Since its inception in the 1970's, critical realism has grown to address a broad range of subjects, including economics, philosophy, science, and religion. It has also gone through a number of key evolutions that have changed its direction, and seen it develop into a complex and mature branch of philosophy. Critical Realism: A Brief Introduction, is the first book to look back over the entire field of critical realism in one concise and accessible volume. As the originator and chief exponent (...) of CR, Roy Bhaskar draws from his experience of countless introductory lectures, seminars, workshops and courses to give a definitive and compelling account of this increasingly influential, international and multi-disciplinary approach. Its eight chapters examine the following topics: Transcendental Realism and the Philosophy of Science Critical Naturalism and the Philosophy of Social Science Explanatory Critique and Ethics Language and Critical Discourse Analysis The Development of Critical Realism Interdisciplinarity and Applied Critical Realism Modernity, Theories of Science and Metacritique The Advantages of Critical Realism Everything from the definition of CR and its applicability to the social sciences, to explanations of dialectical critical realism and the philosophy of meta-reality are addressed in detail, making this the essential introduction for students of CR at all levels. (shrink)

_Dialectic_ is now widely regarded as a classic of contemporary philosophy. This book, first published in 1993, sets itself three main aims: the development of a general theory of dialectic, of which Hegelian dialectic can be seen to be a special case; the dialectical enrichment and deepening of critical realism, viz. into the system of dialectical critical realism; and the outline of the elements of a totalizing critique of Western philosophy. The first chapter clarifies the rational core of Hegelian dialectic. (...) Chapter two then proceeds to develop a general theory of dialectic. Isolating the fallacy of 'ontological monovalence', Roy Bhaskar then shows how absence and other negating concepts such as contradiction have a legitimate and necessary ontological employment. He then goes on to give a synoptic account of key dialectical concepts such as the concrete universal; to sketch the further dialectical development of critical naturalism through an account of what he calls four-planar social being; and following consideration of the dialectical critique of analytical reason, he moves on to the real definition of dialectic as absenting absence and in the human sphere, the axiology of freedom. Chapter three extends and deepens critical realism’s characteristic concerns with ontology, science, social science and emancipation not only into the realms of negativity and totality, but also into the fields of reference and truth, spatio-temporality, tense and process, the logic of dialectical universalizability and on to the plane of ethics, where it articulates a combination of moral realism and ethical naturalism, whereby consideration of elemental desire involves commitment to the eudaimonistic society. This is then followed by a sublime discussion of key moments in the trajectory of Western philosophy, the tradition of which can now be seen to be based on what the author calls the unholy trinity of the epistemic fallacy or the reduction of being to knowledge, primal squeeze or the collapse of structure and alethic truth, and ontological monovalence. (shrink)

Introduction: Critical realism, hegelian dialectic and the problems of philosophy preliminary considerations -- Objectives of the book -- Dialectic : an initial orientation -- Negation -- Four degrees of critical realism -- Prima facie objections to critical realism -- On the sources and general character of the hegelian dialectic -- On the immanent critique and limitations of the hegelian dialectic -- The fine structure of the hegelian dialectic -- Dialectic : the logic of absence, arguments, themes, perspectives, configurations -- Absence (...) -- Emergence -- Contradiction I : Hegel and Marx -- Contradiction II : misunderstandings -- On the materialist diffraction of dialectic -- Dialectical arguments and the unholy trinity -- Dialectical motifs : tina formation, mediation, concrete universality, etc -- On the generalized theory of the dialectical remark, the failure of detachment, and the presence of the past -- Dialectical critical naturalism -- Towards a real definition of dialectic -- Dialectical critical realism and the dialectic of freedom -- Ontology -- The dialectic of truth -- On the emergence and derivability of dialecticized transcendental realism -- 1m realism : non-identity -- 2e realism : negativity -- Space, time and tense -- Social science, explanatory critique, emancipatory axiology -- 3l realism : totality -- 4d realism : agency -- The dialectic of desire to freedom -- Dialectical critical realism and the dialectics of critical realism -- Metacritical dialectics : irrealism and its consequences -- Irrealism -- The problems of philosophy and their resolution -- Contradictions of the critical philosophy -- Dilemmas of the beautiful soul and the unhappy consciousness -- Master and slave : from dialectics of reconciliation to dialectics of liberation -- The metacritique of the hegelian dialectic -- Marxian dialectic i: the rational kernel in the mystical shell -- Marxian dialectic ii: the mystical shell in the rational kernel -- Metacritical dialectics : philosophical ideologies, their sublation and explanation -- The consequences of irrealism -- Diffracted and retotalized dialectics -- Dialectic as the pulse of freedom. (shrink)

Originally published in 1989, Reclaiming Reality still provides the most accessible introduction to the increasingly influential multi-disciplinary and international body of thought, known as critical realism. It is designed to "underlabour" both for the sciences, especially the human sciences, and for the projects of human emancipation which such sciences may come to inform; and provides an enlightening intervention in current debates about realism and relativism, positivism and poststucturalism, modernism and postmodernism, etc. Elaborating his critical realist perspective on society, nature, science (...) and philosophy itself, Roy Bhaskar shows how this perspective can be used to undermine currently fashionable ideologies of the Right, and at the same time, to clear the ground for a reinvigorated Left. Reclaiming Reality contains powerful critiques of some of the most important schools of thought and thinkers of recent years—from Bachelard and Feyerabend to Rorty and Habermas; and it advances novel and convincing resolutions of many traditional philosophical problems. Now with a new introduction from Mervyn Hartwig, this book continues to provide a straightforward and stimulating introduction to current debates in philosophy and social theory for the interested lay reader and student alike. Reclaiming Reality will be of particular value not only for critical realists but for all those concerned with the revitalization of the socialist emancipatory project and the renaissance of the Marxist theoretical tradition. Roy Bhaskar is the originator of the philosophy of critical realism, and the author of many acclaimed and influential works including A Realist Theory of Science, The Possibility of Naturalism, Scientific Realism and Human Emancipation and Dialectic: The Pulse of Freedom. He is an editor of the recently published Critical Realism: Essential Readings and is currently chair of the Centre for Critical Realism. (shrink)

Now acknowledged as a classic in the philosophy of science, A Realist Theory of Science is one of the very few books to transform not only our understanding of science, but that of the nature of the world it studies. The book has inspired the multi-disciplinary and international movement of thought known as critical realism. Re-issued with a new introduction.

In ”Formal Problems about Knowledge,” Roy Sorensen examines epistemological issues that have logical aspects. He uses Fitch's proof for unknowables and the surprise test paradox to illustrate the hopes of the modal logicians who developed epistemic logic, and he considers the epistemology of proof with the help of the knower paradox. One solution to this paradox is that knowledge is not closed under deduction. Sorensen reviews the broader history of this maneuver along with the relevant alternatives model of knowledge which (...) assumes that ”know” is an absolute term like ”flat.” Sorensen argues that the difference between epistemic absolute terms and extensional absolute terms gives rise to an asymmetry that undermines recent claims that there is a structural parallel between the supervaluational and epistemicist theories of vagueness, and he suggests that we have overestimated the ability of logical demonstration to produce knowledge. (shrink)

This series of interviews, conducted in the form of exchanges between Roy Bhaskar and Mervyn Hartwig, tells a riveting story of the formation and development of critical realism. Three intersecting and interweaving narratives unfold in the course of this unfinished story: the personal narrative of Roy Bhaskar, born of an Indian father and English mother, a child of post-war Britain and Indian partition and independence; the intellectual narrative of the emergence and growth of critical realism; and a world-historical story, itself (...) theorized by critical realism in its discussion of the development of modernity. This book gives an invaluable account of the development of critical realism, and its consolidation as a leading philosophy of our times. It takes us through the major moments of its formation, the principal objections to and controversies within critical realism, the establishment of its institutions, and considers its limits and future development. Special features of the book include discussion of the genesis of critical realism, and the origins and nature of the so-called dialectical and spiritual turns. The informal dialogical style of The Formation of Critical Realism makes it compelling reading and an invaluable source for students of critical realism as well as all those interested in the intellectual story of our times. (shrink)

Since its original publication in 1979, The Possibility of Naturalism has been one of the most influential works in contemporary philosophy of science and social science. It is one of the cornerstones of the critical realist position, which is now widely seen as offering perhaps the only viable alternative to positivism and post positivism. This fourth edition contains a new foreword from Mervyn Hartwig, who is founding editor of the Journal of Critical Realism and editor and principal author of the (...) Dictionary of Critical Realism. (shrink)

Free will can be understood as a novel form of action control that evolved to meet the escalating demands of human social life, including moral action and pursuit of enlightened self-interest in a cultural context. That understanding is conducive to scientific research, which is reviewed here in support of four hypotheses. First, laypersons tend to believe in free will. Second, that belief has behavioral consequences, including increases in socially and culturally desirable acts. Third, laypersons can reliably distinguish free actions from (...) less free ones. Fourth, actions judged as free emerge from a distinctive set of inner processes, all of which share a common psychological and physiological signature. These inner processes include self-control, rational choice, planning, and initiative. (shrink)

In this concise text, Roy Bhaskar sets out to diagnose, explain and resolve the "problems of philosophy". _Plato Etc._ reviews all the main areas of the subject: the theory of knowledge and philosophy of science; the philosophy of logic and language; the philosophies of space, time and causality; the philosophy of the social and life sciences and of dialectic; ethics, politics and aesthetics; and the history and sociology of philosophy. Among the issues discussed are the problems of induction and universals, (...) the question of relativism, Heidegger’s "scandal of philosophy", the nature of moral truth and the conundrum of free will and determinism. The last two chapters consist of a synoptic account of the development of Western philosophy from the pre-Socratics to poststructuralism. _Plato Etc._ seeks to revindicate the philosophical project, and to demonstrate that the author’s "dialectical critical realism" has the categorical power to remedy the problem fields of philosophy. The book serves both as a critical introduction to philosophy and as an invaluable resource for the scholar. (shrink)

Shankara was born in the eighth century on the west coast of south India. After devoting himself to yoga practices and meditation, Shankara wrote commentaries on the Bhagavad Gita, some of the Upanishads and other scriptures, and travelled throughout India declaring the oneness of a supreme reality and refuting erroneous philosophical doctrines. He reorganized the ancient, renunciate swami order and established permanent monastic centres in four regions of India: Sringeri in the south, Puri in the east, Dwaraka in the west, (...) and Badrinath in the Himalayas. Shankara lived during an era when Sanatana Dharma was beginning to be more widely emphasized, authoritative leadership was lacking, and conflicting religious sects were promoting a variety of philosophical opinions. His emphasis on the oneness of a supreme reality and the divinity of each person was a harmonizing influence. Besides expounding his non-dualistic views as presented in Self-Knowledge, he also wrote poems and composed hymns to reverently honour a variety of gods and goddesses to inspire and encourage people in all walks of life to be devoted to right living and spiritual practices. (shrink)

The author argues that our best hope for addressing world problems (from climate change to violence, to poverty) is to teach critical thinking through the study of language and all symbol systems. This means removing disciplinary boundaries so that we can focus more effectively on solving common problems. Human survival also depends upon our critical analysis of electronic media and our wise uses of technology. Critical thinking via all symbol systems is more likely to generate humane actions. Therefore, education—not governments (...) or armies or institutions or private corporations—is our best hope. (shrink)