In Spandrels of Truth, Beall concisely presents and defends a modest, so-called dialetheic theory of transparent truth.

Consequence is at the heart of logic, and an account of consequence offers a vital tool in the evaluation of arguments. This text presents what the authors term as 'logical pluralism' arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them.

In The Fold Deleuze proposes a new and radical way of understanding philosophy and art.

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

Graham Priest presents an original exploration of questions concerning the one and the many. He covers a wide range of issues in metaphysics--unity, identity, grounding, mereology, universals, being, intentionality and nothingness--and draws on Western and Asian philosophy as well as paraconsistent logic to offer a radically new treatment of unity.

Translated and with an Introduction by Daniel W. Smith Afterword by Tom Conley Gilles Deleuze had several paintings by Francis Bacon hanging in his Paris apartment, and the painter’s method and style as well as his motifs of seriality, difference, and repetition influenced Deleuze’s work. This first English translation shows us one of the most original and important French philosophers of the twentieth century in intimate confrontation with one of that century’s most original and important painters. In considering Bacon, Deleuze (...) offers implicit and explicit insights into the origins and development of his own philosophical and aesthetic ideas, ideas that represent a turning point in his intellectual trajectory. First published in French in 1981, _Francis Bacon_ has come to be recognized as one of Deleuze’s most significant texts in aesthetics. Anticipating his work on cinema, the baroque, and literary criticism, the book can be read not only as a study of Bacon’s paintings but also as a crucial text within Deleuze’s broader philosophy of art. In it, Deleuze creates a series of philosophical concepts, each of which relates to a particular aspect of Bacon’s paintings but at the same time finds a place in the “general logic of sensation.” Illuminating Bacon’s paintings, the nonrational logic of sensation, and the act of painting itself, this work—presented in lucid and nuanced translation—also points beyond painting toward connections with other arts such as music, cinema, and literature. _Francis Bacon_ is an indispensable entry point into the conceptual proliferation of Deleuze’s philosophy as a whole. Gilles Deleuze was professor of philosophy at the University of Paris, Vincennes–St. Denis. He coauthored _Anti-Oedipus_ and _A Thousand Plateaus_ with Félix Guattari. These works, as well as _Cinema 1, Cinema 2, The Fold, Proust and Signs_, and others, are published in English by Minnesota. Daniel W. Smith teaches in the Department of Philosophy at Purdue University. (shrink)

This book offers a clear, analytic, and innovative interpretation of Heidegger's late work. This period of Heidegger's philosophy remains largely unexplored by analytic philosophers, who consider it filled with inconsistencies and paradoxical ideas, particularly concerning the notions of Being and nothingness. This book takes seriously the claim that the late Heidegger endorses dialetheism--namely the position according to which some contradictions are true--and shows that the idea that Being is both an entity and not an entity is neither incoherent nor logically (...) trivial. The author achieves this by presenting and defending the idea that reality has an inconsistent structure. In doing so, he takes one of the most discussed topics in current analytic metaphysics, grounding theory, into a completely unexplored area. Additionally, in order to make sense of Heidegger's concept of nothingness, the author introduces an original axiomatic mereological system that, having a paraconsistent logic as a base logic, can tolerate inconsistencies without falling into logical triviality. This is the first book to set forth a complete and detailed discussion of the late Heidegger in the framework of analytic metaphysics. It will be of interest to Heidegger scholars and analytic philosophers working on theories of grounding, mereology, dialetheism, and paraconsistent logic. (shrink)

This paper presents a simple but, by my lights, effective argument for a subclassical account of logic—an account according to which logical consequence is (properly) weaker than the standard, so‐called classical account. Alas, the vast bulk of the paper is setup. Because of the many conflicting uses of ‘logic’ the paper begins, following a disclaimer on logic and inference, by fixing the sense of ‘logic’ in question, and then proceeds to rehearse both the target subclassical account of logic and its (...) well‐known relative (viz., classical logic). With background in place the simple argument—which takes up less than five pages—is advanced. My hope is that the minimal presentation will help to get ‘the simple argument’ plainly on the table, and that subsequent debate can move us forward. (shrink)

Initially proposed as rivals of classical logic, alternative logics have become increasingly important in areas such as computer science and artificial intelligence. Fuzzy logic, in particular, has motivated major technological developments in recent years. Susan Haack's Deviant Logic provided the first extended examination of the philosophical consequences of alternative logics. In this new volume, Haack includes the complete text of Deviant Logic , as well as five additional papers that expand and update it. Two of these essays critique fuzzy logic, (...) while three augment Deviant Logic 's treatment of deduction and logical truth. Haack also provides an extensive new foreword, brief introductions to the new essays, and an updated bibliography of recent work in these areas. Deviant Logic, Fuzzy Logic will be indispensable to students of philosophy, philosophy of science, linguistics, mathematics, and computer science, and will also prove invaluable to experienced scholars working in these fields. (shrink)

In this paper I advance and defend a very simple position according to which logic is subclassical but is weaker than the leading subclassical-logic views have it.

Graham Priest presents an expanded edition of his exploration of the nature and limits of thought. Embracing contradiction and challenging traditional logic, he engages with issues across philosophical borders, from the historical to the modern, Eastern to Western, continental to analytic.

In this book, Livingston develops the political implications of formal results obtained over the course of the twentieth century in set theory, metalogic, and computational theory. He argues that the results achieved by thinkers such as Cantor, Russell, Godel, Turing, and Cohen, even when they suggest inherent paradoxes and limitations to the structuring capacities of language or symbolic thought, have far-reaching implications for understanding the nature of political communities and their development and transformation. Alain Badiou's analysis of logical-mathematical structures forms (...) the backbone of his comprehensive and provocative theory of ontology, politics, and the possibilities of radical change. Through interpretive readings of Badiou's work as well as the texts of Giorgio Agamben, Jacques Lacan, Jacques Derrida, Gilles Deleuze, and Ludwig Wittgenstein, Livingston develops a formally based taxonomy of critical positions on the nature and structure of political communities. These readings, along with readings of Parmenides and Plato, show how the formal results can transfigure two interrelated and ancient problems of the One and the Many: the problem of the relationship of a Form or Idea to the many of its participants, and the problem of the relationship of a social whole to its many constituents. (shrink)

This paper scrutinizes the debate over logical pluralism. I hope to make this debate more tractable by addressing the question of motivating data: what would count as strong evidence in favor of logical pluralism? Any research program should be able to answer this question, but when faced with this task, many logical pluralists fall back on brute intuitions. This sets logical pluralism on a weak foundation and makes it seem as if nothing pressing is at stake in the debate. The (...) present paper aims to improve this situation by looking at a promising case study and drawing general lessons about the kind of evidence that would support logical pluralism. I argue that the best motivation for logical pluralism will ultimately be rooted in certain kinds of performative data. (shrink)

This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. The point of departure is the general constructivist line of argument that Michael Dummett has offered over the last decades. From there, the author examines the ways in which falsifications can enter into a constructivist semantics, displays the full spectrum of options, and discusses the logical systems most suitable to each one of them. While the idea of introducing falsifications into (...) the semantic account is Dummett's own, the many ways in which falsificationism departs quite radically from verificationism are here spelled out in detail for the first time. The volume is divided into three large parts. The first part provides important background information about Dummett’s program, intuitionism and logics with gaps and gluts. The second part is devoted to the introduction of falsifications into the constructive account and shows that there is more than one way in which one can do this. The third part details the logical effects of these various moves. In the end, the book shows that the constructive path may branch in different directions: towards intuitionistic logic, dual intuitionistic logic and several variations of Nelson logics. The author argues that, on balance, the latter are the more promising routes to take. "Kapsner’s book is the first detailed investigation of how to incorporate the notion of falsification into formal logic. This is a fascinating logico-philosophical investigation, which will interest non-classical logicians of all stripes." Graham Priest, Graduate Center, City University of New York and University of Melbourne. (shrink)

Twentieth-century philosophy has often been pictured as divided into two camps, analytic and continental. This study challenges this depiction by examining encounters between some of the leading representatives of either side. Starting with Husserl and Frege's fin-de-siècle turn against psychologism, it turns to Carnap's 1931 attack on Heidegger's metaphysics (together with its background in the Cassirer-Heidegger dispute of 1929), moving on to Ayer's 1951 meeting with Bataille and Merleau-Ponty at a Parisian bar, followed by the 'dialogue of the deaf' between (...) Oxford linguistic philosophers and phenomenologists at the 1951 Royaumont colloquium, leading up to the Derrida-Searle controversy. Careful study shows that it is implausible to assume the existence of a century-old 'gulf' between two sides of philosophy. Vrahimis argues that miscommunication and ignorance over the exact content of the above encounters must to a large extent be held accountable for any perceived gap. (shrink)

Introduction -- 1. Problem of the New -- 2. Problem of Relations -- 3. Problem of Emergence -- 4. Problem of One and Many -- 5. Plato and the Third Man Argument -- 6. Bradley and the Problem of Relations -- 7. Moore, Russell and the Birth of Analytic Philosophy -- 8. Russell and Deleuze on Leibniz -- 9. On Problematic Fields -- 10. Kant and Problematic Ideas -- 11. Armstrong and Lewis on the Problem of One and Many -- (...) 12. Determinables and Determinates -- 13. The Limits of Representational Thought -- 14. Learning from a Cup of Coffee -- 15. Carnap and the Fate of Metaphysics -- 16. Truth and Relevance -- Conclusion. (shrink)

_Logic: The Basics_ is an accessible introduction to several core areas of logic. The first part of the book features a self-contained introduction to the standard topics in classical logic, such as: · mathematical preliminaries · propositional logic · quantified logic · English and standard ‘symbolic translations’ · tableau procedures. Alongside comprehensive coverage of the standard topics, this thoroughly revised second edition also introduces several philosophically important nonclassical logics, free logics, and modal logics, and gives the reader an idea of (...) how they can take their knowledge further. With its wealth of exercises, _Logic: The Basics _is a useful textbook for courses ranging from the introductory level to the early graduate level, and also as a reference for students and researchers in philosophical logic. (shrink)

The topic of exemplarity has attracted considerable interest in philosophy, legal theory, literary studies and art recently. There is broad consensus that exemplary cases mediate between singular instances and general concepts or norms. The aim of this article is to provide an additional perspective on the logic of exemplarity. First, inspired by Jacques Derrida’s discussion of exemplarity, I shall argue that there is a kind of différance between (singular) examples and (general) exemplars. What an example exemplifies, the exemplarity of the (...) example, eludes any fixed identity and follows a logic of supplement. Second, I shall present the so-called logic of exemplarity. The received paraconsistent view has it that the exemplar of X is an X and, at the same time, is not an X. Inspired by Ludwig Wittgenstein’s discussion of the standard metre, I would like to present an alternative paracomplete view whereby we can say of an exemplar of X neither that it is an X nor that it is not an X. (shrink)

ABSTRACTIt is well known that, from the beginning to the end of his philosophical trajectory, Martin Heidegger tries to develop a fundamental ontology which aims at answering the so-called question...

"Arguing that debates over legitimacy, political violence, freedom, and justice would benefit greatly from cross-tradition theorizing, this book shows how putting analytic and continental political theory in conversation would help us to overcome these intractable problems"--.

Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in (...) simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy. (shrink)

In this sweeping volume, Christopher Norris challenges the view that there is no room for productive engagement between mainstream analytic philosophers and thinkers in the post-Kantian continental line of descent. On the contrary, he argues, this view is simply the product of a limiting perspective that accompanied the rise of logical positivism. Norris reveals the various shared concerns that have often been obscured by parochial interests or the desire to stake out separate philosophical territory. He examines the problems that emerged (...) within the analytic tradition as a result of its turn against Husserlian phenomenology and its outright rejection of what came to be seen as a merely "psychologistic" approach to issues of meaning, knowledge, and truth. Norris shows how these problems have resurfaced in various forms from the heyday of logical empiricism to the present. He provides critical readings of such philosophers as Willard Quine, Thomas Kuhn, Donald Davidson, Hilary Putnam, Richard Rorty, Michael Dummett, Thomas Nagel, and John McDowell. He also offers a running discussion of Wittgenstein's influence and its harmful effect in promoting a placidly consensus-based theory of knowledge. On the continental side, Norris argues for a reassessment of Husserl's phenomenological project and its potential contribution to present-day Anglo-American debates in epistemology and philosophy of science. He discusses Bachelard, Canguilhem, and the French tradition of rationalisme applique as an alternative to Kuhnian conceptions of scientific paradigm change. This leads him to suggest a non-Wittgensteinian way around the problems that have dogged more traditional theories of knowledge andtruth. In two chapters on the work of Jacques Derrida, Norris explores the "supplementary" logic of deconstruction and compares it with other recent proposals for a nonstandard logic. Here again he stresses the community of interests between the two philosophical cultures and the extent to which continental thinking has engaged certain issues with a rigor largely ignored by Anglophone writers. By bringing a fresh perspective to questions that have often been considered the exclusive preserve of analytic philosophy, Norris offers an overview of current debates that is at once refreshingly open-minded and sure of its own argumentative bearings. (shrink)

What is the meaning of life? Does anything really matter? In the past few decades these questions, perennially associated with philosophy in the popular consciousness, have rightly retaken their place as central topics in the academy. In this major contribution, Nicholas Waghorn provides a sustained and rigorous elucidation of what it would take for lives to have significance. Bracketing issues about ways our lives could have more or less meaning, the focus is rather on the idea of ultimate meaning, the (...) issue of whether a life can attain meaning that cannot be called into question. Waghorn sheds light on this most fundamental of existential problems through a detailed yet comprehensive examination of the notion of nothing, embracing classic and cutting-edge literature from both the analytic and Continental traditions. Central figures such as Heidegger, Carnap, Wittgenstein, Nozick and Nagel are drawn upon to anchor the discussion in some of the most influential discussion of recent philosophical history. In the process of relating our ideas concerning nothing to the problem of life's meaning, Waghorn's book touches upon a number of fundamental themes, including reflexivity and its relation to our conceptual limits, whether religion has any role to play in the question of life's meaning, and the nature and constraints of philosophical methodology. A number of major philosophical traditions are addressed, including phenomenology, poststructuralism, and classical and paraconsistent logics. In addition to providing the most thorough current discussion of ultimate meaning, it will serve to introduce readers to philosophical debates concerning the notion of nothing, and the appendix engaging religion will be of value to both philosophers and theologians. (shrink)

Belonging together of the foreign -- Hermeneutic circularity: tradition as genuine repetition of futural past -- Inceptual thinking and nonsystematic atonality -- Heidegger's Seyn/Nichts and Kabbalistic Ein Sof -- Simsum, Lichtung, and bestowing refusal -- Autogenesis, nihilating leap, and otherness of the not-other -- Temporalizing and granting time-space -- Disclosive language: poiesis and apophatic occlusion of occlusion -- Ethnolinguistic enrootedness and invocation of historical destiny.

Olkowski proposes a model of phenomenology, both scientific and philosophical, that helps make sense of reality and composes an ethics for dealing with unpredictability in our world.

In their paper ‘Zilch’, Oliver and Smiley claim that the word ‘nothing’ can be used as a singular term and that ‘nothing’ as a singular term and the word ‘zilch’ are empty terms, which fail to refer to anything. In this paper, we propose that ‘nothing’ as a singular term and ‘zilch’ can be used to denote null things such as absences, null objects or nothingness. We also claim that, pace their interpretation of Heidegger’s ‘das Nichts’ as an empty term, (...) it should be understood as such a singular term that refers to nothingness. (shrink)

This paper attempts to provide an account of what is philosophically distinctive about what has come to be known as 'Continental philosophy'. In the early parts of the paper I give a historical and cultural analysis of the emergence of Continental philosophy and consider objections to the latter and some stereotypical representations of the analytic-Continental divide. In the philosophically more substantial part of the paper, I seek to redraw the distinction between analytic and Continental philosophy by focusing on a number (...) of themes: (i) the centrality of tradition and history for Continental philosophy and the way this affects philosophical practices of argumentation and interpretation, (ii) the way in which the concept of Continental philosophy emerges out of the German idealist reception of the Kantian critique of metaphysics and the significant way this is continued in Nietzsche with his concept of nihilism, (iii) the centrality of the concepts of critique, emancipation and praxis for the Continental tradition, (iv) the importance of the theme of crisis that runs through the Continental tradition, (v) an explanation and justification of the pervasive anti-scientism of the Continental tradition. I conclude by explaining and criticizing the professionalization of philosophy that has produced the analytic-Continental divide, insofar as this divide disguises a deeper possible debate about the identity of philosophy itself outside of its professional confines. (shrink)

Propositional logic -- Propositions and arguments -- Connectives and argument forms -- Truth tables -- Trees -- Vagueness and bivalence -- Conditionality -- Natural deduction -- Predicate logic -- Predicates, names, and quantifiers -- Models for predicate logic -- Trees for predicate logic -- Identity and functions -- Definite descriptions -- Some things do not exist -- What is a predicate? -- What is logic?

Truth, Christopher Norris reminds us, is very much out of fashion at the moment whether at the hands of politicians, media pundits, or purveyors of postmodern wisdom in cultural and literary studies. Across a range of disciplines the idea has taken hold that truth-talk is either redundant or the product of epistemic might. Questions of truth and falsehood are always internal to some specific language-game; history is just another kind of fiction; philosophy is only a kind of writing; law is (...) a wholly rhetorical practice. In _Reclaiming Truth_, Norris critiques these fashionable trends of thought and mounts a specific challenge to cultural relativist doctrines in epistemology, philosophy of science, ethics, and political theory. Norris presents his case in a series of closely argued chapters that take issue with the relativist position. He attempts to rehabilitate the value of truth in philosophy of science by restoring a lost distinction between concept and metaphor and argues that theoretical discourse, so far from being an inconsequential activity, has very real consequences, particularly in ethics and politics. This debate has become skewed, he suggests, through the widespread and typically postmodern idea that truth-claims must always go along with a presumptive or authoritarian bid to silence opposing views. On the contrary, there is nothing as dogmatic—or as silencing—as a relativism that acknowledges no shared truth conditions for valid or responsible discourse. Norris also offers a timely reassessment of several thinkers—Althusser and Derrida among them—whose reception history has been distorted by the vagaries of short-term intellectual fashion. _Reclaiming Truth _will be welcomed by readers concerned with the uses and abuses of theory at a time when such questions are in urgent need of sustained and serious debate. (shrink)

A common and much-explored thought is Łukasiewicz's idea that the future is ‘indeterminate’—i.e., ‘gappy’ with respect to some claims—and that such indeterminacy bleeds back into the present in the form of gappy ‘future contingent’ claims. What is uncommon, and to my knowledge unexplored, is the dual idea of an overdeterminate future—one which is ‘glutty’ with respect to some claims. While the direct dual, with future gluts bleeding back into the present, is worth noting, my central aim is simply to sketch (...) and briefly explore an alternative glutty-future view, one that is conservative—indeed, entirely classical—with respect to the present. The structure of the paper runs as follows. §1 briefly sketches the target gap picture of an indeterminate future yielding gappy claims at the present. §2 presents the direct dual idea—a glut picture of an overdeterminate future yielding glutty claims at present. §3 sketches the central idea, a more interesting glut picture in which the future contains contradictory states but the present remains entirely classical. §4 contains a general defence of the idea, leaving it open as to whether the gappy-future view enjoys substantive virtues over the proposed glutty-future view of §3. (shrink)

Martin Heidegger is a towering figure in the history of continental philosophy, but his work has recently been brought into productive engagement with analytic philosophy. This paper introduces and explores two channels along which such engagement has been taking place. The first is in metaphysics, where Heideggerian thought has been interpreted either as making the metaphysical concept of being literally senseless or as mandating a revision to classical logic. The second is in philosophy of mind, and more particularly in philosophy (...) of cognitive science, where Heideggerian thought has been used to mount a challenge to representational theories of mind. (shrink)

This paper intends to offer a new assessment of the “Ontological Difference”, one of Martin Heidegger’s mainstays, in the light of the metaphysical view called “dialetheism”. In the first paragraph I briefly summarize the main argument of Heidegger’s contradiction of Being, where OD is present as a premise. In the second paragraph I introduce dialetheism, indicate two kinds of dialetheic solutions to the paradox and explain why they face comeback troubles from OD. The third paragraph is devoted to a review (...) of Heidegger’s uses of OD and underlines the crucial role of negation in it. In the fourth paragraph I investigate the philosopher’s account of negation and show similarities with the account provided by the paraconsistent logic called “Logic of Paradox”. The fifth paragraph puts forward two possible readings of OD, the first based on the classical notion of negation and the second on the notion of negation pointed out in the previous paragraph. The second reading is proved suitable for dialetheists and in accordance with the exegesis of some textual passages from Heidegger’s late works. (shrink)

Martin Heidegger's philosophy is famous for being unusually rich. It ranges over technology, poetry, theology, history, and many other subjects. In this paper, I focus my attention on two topics which are particularly close to the hearts of analytic philosophers: logic and language. I show that Heidegger faces two different kinds of paradoxes: an ontic paradox and an ontological paradox. Moreover, for each one of these paradoxes, I give an overview of how both Heidegger and the philosophers who engage with (...) his thought have tried to overcome them by challenging either a certain account of language or the authority of logic in philosophical discourse. (shrink)

Jean-Pierre Dupuy argues that our failure to prevent the looming climate catastrophe results from a faulty metaphysics of time: because we believe the present can proceed down one of the many branches that extend into the future, some of which bypass the catastrophe, we do not think it is absolutely urgent to take drastic action now. His solution to this problem of demotivation is “enlightened doomsaying” in “projected time”, which means that we affirm the coming catastrophe as something real in (...) the future rather than being a mere possibility; thus, we regard it seriously enough that we are motivated to take the needed actions to prevent it. One potential obstacle to this proposal is that it requires the forming of consensus and coordination with the powerful players who benefit from our current path and whose apparently near-total grip on this catastrophic future may itself discourage action. We then consider an alternative model based on Gilles Deleuze’s philosophy of the present–future relation. Although it has the branching structure that Dupuy is wary of, it may not suffer from the same problem of demotivation on account of the way it conceives the complex structure of the present event. For this reason, the Deleuzian model may be more suited to motivating action in a world where the future must be fought for rather than unanimously agreed upon. (shrink)