The fundamental problem of Christology is the apparent contradiction of Christ as recorded at Chalcedon. Christ is human and Christ is divine. Being divine entails being immutable. Being human entails being mutable. Were Christ two different persons there’d be no apparent contradiction. But Chalcedon rules as much out. Were Christ only partly human or only partly divine there’d be no apparent contradiction. But Chalcedon rules as much out. Were the very meaning of ‘mutable’ and/or ‘immutable’ other than what they are, (...) there’d be no apparent contradiction. But the meaning is what it is, and changing the meaning of our terms to avoid the apparent contradiction of Christ is an apparent flight from reality. What, in the end, is the explanation of the apparent contradiction of Christ? Theologians and philosophers have long advanced many consistency-seeking answers, all of which increase the metaphysical or semantical complexity of the otherwise strikingly simple but radical core of Christianity’s GodMan. In this paper, I put the simplest explanation on the theological table: namely, Christ appears to be contradictory because Christ is contradictory. This explanation may sound complicated to the many who are steeped in the mainstream account of logic according to which logic precludes the possibility of true contradictions. But the mainstream account of logic can and should be rejected. Ridding theology of the dogma of mainstream logic illuminates the simple though striking explanation of the apparent contradiction of Christ — namely, that Christ is a contradictory being. Just as the simplest explanation to the apparent roundness of the earth has earned due acceptance, so too should the simplest explanation of the apparent contradiction of Christ. (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)

Three leading philosopher-logicians present a clear and concise overview of formal theories of truth, explaining key logical techniques. Truth is as central topic in philosophy: formal theories study the connections between truth and logic, including the intriguing challenges presented by paradoxes like the Liar.

Traditional monotheism has long faced logical puzzles. We argue that such puzzles rest on the assumed logical truth of the Law of Excluded Middle, which we suggest there is little theological reason to accept. By way of illustration we focus on God's alleged stone problem, and present a simple but plausible ‘gappy’ framework for addressing this puzzle. We assume familiarity with the proposed logic but an appendix is offered as a brief review.

This chapter attempts to give a brief overview of nonclassical (-logic) theories of truth. Due to space limitations, we follow a victory-through-sacrifice policy: sacrifice details in exchange for clarity of big-picture ideas. This policy results in our giving all-too-brief treatment to certain topics that have dominated discussion in the non-classical-logic area of truth studies. (This is particularly so of the ‘suitable conditoinal’ issue: §4.3.) Still, we present enough representative ideas that one may fruitfully turn from this essay to the more-detailed (...) cited works for further study. Throughout – again, due to space – we focus only on the most central motivation for standard non-classical-logic-based truth theories: namely, truth-theoretic paradox (specifically, due to space, the liar paradox). (shrink)

In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn’t automatically solved by solving c-curry. A unified treatment of curry paradox thus calls for a unified treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via non-classical logic, then v-Curry may require a lesson about the structure—indeed, the substructure—of the validity relation itself.

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)

I believe that, for reasons elaborated elsewhere (Beall, 2009; Priest, 2006a, 2006b), the logic LP (Asenjo, 1966; Asenjo & Tamburino, 1975; Priest, 1979) is roughly right as far as logic goes.1 But logic cannot go everywhere; we need to provide nonlogical axioms to specify our (axiomatic) theories. This is uncontroversial, but it has also been the source of discomfort for LP-based theorists, particularly with respect to true mathematical theories which we take to be consistent. My example, throughout, is arithmetic; but (...) the more general case is also considered. (shrink)

The first sentence in this essay is a lie. There is something odd about saying so, as has been known since ancient times. To see why, remember that all lies are untrue. Is the first sentence true? If it is, then it is a lie, and so it is not true. Conversely, suppose that it is not true. As we (viz., the authors) have said it, presumably with the intention of you believing it when it is not true, it is (...) a lie. But then it is true! (shrink)

This is a collection of Paul Hoffman's wide-ranging essays on Descartes composed over the past twenty-five years. The essays in Part I include his celebrated "The Unity of Descartes' Man," in which he argues that Descartes accepts the Aristotelian view that soul and body are related as form to matter and that the human being is a substance; a series of subsequent essays elaborating on this interpretation and defending it against objections; and an essay on Descartes' theory of distinction. (...) In the essays in Part II he argues that Descartes retains the Aristotelian theory of causation according to which an agent's action is the same as the passion it brings about, and explains the significance of this doctrine for understanding Descartes' dualism and physics. In the essays in Part III he argues that Descartes accepts the Aristotelian theory of cognition according to which perception is possible because things that exist in the world are also capable of a different way of existing in the soul, and he shows how this theory figures in Descartes' account of misrepresentation and in the controversy over whether Descartes is a direct realist or a representationalist. The essays in Part IV examine Descartes' theory of the passions of the soul: their definition; their effect on our happiness, virtue, and freedom; and methods of controlling them. (shrink)

This paper explores some interconnections between the business and environmental ethics movements. The first section argues that business has obligations to protect the environment over and above what is required by environmental law and that it should cooperate and interact with government in establishing environmental regulation. Business must develop and demonstrate environmental moral leadership. The second section exposes the danger of using the rationale of "good ethics is good business" as a basis for such business moral leadership in both the (...) business and environmental ethics movements. The third section cautions against the moral shallowness inherent in the position or in the promotional strategy of ecological homocentrism which claims that society, including business, ought to protect the environment solely because of harm done to human beings and human interests. This paper urges business and environmental ethicists to promote broader and deeper moral perspectives than ones based on mere self-interest or human interest. Otherwise both movements will come up ethically short. (shrink)

A very common twofold view in contemporary philosophy is that classical logic is the correct view of logical consequence and that possibility conforms to classical logic in the sense that ‘possible worlds’ — whatever else they may be — are closed under classical logic. These two views are assumed in this paper. My aim in this paper is to show that a very natural ‘paraconsistent’ consequence relation is involved in the given view of possible worlds and logical consequence.

Logic: the Basics is an accessible introduction to the core philosophy topic of standard logic. Focussing on traditional Classical Logic the book deals with topics such as mathematical preliminaries, propositional logic, monadic quantified logic, polyadic quantified logic, and English and standard ‘symbolic transitions’. With exercises and sample answers throughout this thoroughly revised new edition not only comprehensively covers the core topics at introductory level but also gives the reader an idea of how they can take their knowledge further and the (...) philosophical questions around logic. -/- Logic: the Basics is essential reading for first-year undergraduate philosophy students on standard introductory logic courses. (shrink)

Can a corporation have a conscience? What is wrong with reverse discrimination? Can ethical management and managed care coexist? Hoffman, Frederick, and Schwartz address these and many other current, intriguing, often complex issues in corporate morality. This introductory business ethics text contains a thorough general introduction on ethical theory, 54 readings, and 25 cases. Divided into five parts, each with an introduction that presents the major themes of its articles and cases, the text contains an impartial, point-counterpoint presentation of (...) different perspectives on the most important issues being debated in business ethics. Each chapter ends with questions that can be used for student discussion, review, tests/quizzes, or for student assignments. The fourth edition has 27 new readings, 15 new cases, and 10 new mini-cases. (shrink)

This paper offers a new and very simple alternative to Bochvar's well known nonsense -- or meaninglessness -- interpretation of Weak Kleene logic. To help orient discussion I begin by reviewing the familiar Strong Kleene logic and its standard interpretation; I then review Weak Kleene logic and the standard interpretation. While I note a common worry about the Bochvar interpretation my aim is only to give an alternative -- and I think very elegant -- interpretation, not necessarily a replacement.

This paper presents, in a more general setting, a simple approach to ‘relevant restricted generalizations’ advanced in previous work. After reviewing some desiderata for restricted generalizations, I present the target route towards achieving the desiderata. An objection to the approach, due to David Ripley, is presented, followed by three brief replies, one from a dialetheic perspective and the others more general.

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.

This paper advances and defends a new solution to the so-called fundamental problem in christology (the problem being the apparent contradiction entailed by the christian doctrine of divine incarnation).

This paper applies what I call the shrieking method (a refined version of an idea with roots in Priest's work) to one of – if not the – issues confronting glut-theoretic approaches to paradox (viz., the problem of ‘just true’ or, what comes to the same, ‘just false’). The paper serves as a challenge to formulate a problem of ‘just true’ that isn't solved by shrieking (as advanced in this paper), if such a problem be thought to exist.

_The Divine Attributes_is an engaging analysis of the God of Judaism, Christianity, and Islam from the perspective of rational theology.

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)

This book argues that the standard (orthodox) doctrine of incarnation (of "God enfleshed") is best understood along glut-theoretic lines: the incarnate God is a contradictory being. Example: because God, the Christ figure is all-knowing; but because human, ignorant. And so on. Standard theological theory in the tradition recognizes the apparent contradiction in its core doctrines; Beall argues that the appearance should be accepted as veridical.

Book Information Truth and the Absence of Fact. By Hartry Field. Clarendon Press. Oxford. 2001. Pp. xi + 401. Hardback, 45.00, US$65.00. Paperback, 16.99, $24.95.

Substance has been a leading idea in the history of Western philosophy. _Joshua Hoffman and Gary S. Rosenkrantz_ explain the nature and existence of individual substances, including both living things and inanimate objects. Specifically written for students new to this important and often complex subject, _Substance_ provides both the historical and contemporary overview of the debate. Great Philosophers of the past, such as Aristotle, Descartes, Spinoza, Leibnitz, Locke, and Berkeley were profoundly interested in the concept of substance. And, the (...) authors argue, a belief in the existence of substances is an integral part of our everyday world view. But what constitutes substance? Was Aristotle right to suggest that artefacts like tables and ships don't really exist? _Substance: Its Nature and Existence_ is one of the first non-technical, accessible guides to this central problem and will be of great use to students of metaphysics and philosophy. (shrink)

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1. In both Benedetto Croce's and Hegel's own terminology, dialectics can be understood as dottrina degli opposti (the doctrine of the opposites – Lehre der Gegensätze).1 In the dialectical process,...

Recent articles in Religious Studies have underscored the questions of whether Buddhism presents any empirical doctrines, and whether, if it does, such doctrines are false or vacuous. In what follows I want to sketch an interpretation of Buddhism according to which it does not offer doctrines which are empirically false, on the one hand, or trivially true on the other. In doing so I take my cue from an earlier, and by now classic, paper by H. H. Price. For the (...) exposition of Buddhism I take the Pali Nikāyas, the single most significant collection of texts in the Buddhist tradition. The particular doctrine which is the focus of discussion here is the kammavāda or ‘karma view’ of early Indian Buddhism, for it is the focus of much of the recent literature cited above and a doctrine which some have thought amenable to statement in empirical terms. (shrink)

Philosophical applications of familiar paracomplete and paraconsistent logics often rely on an idea of . With respect to the paraconsistent logic LP (the dual of Strong Kleene or K3), such is standardly cashed out via an LP-based nonmonotonic logic due to Priest (1991, 2006a). In this paper, I offer an alternative approach via a monotonic multiple-conclusion version of LP.

Face perception, perhaps the most highly developed visual skill in humans, is mediated by a distributed neural system in humans that is comprised of multiple, bilateral regions. We propose a model for the organization of this system that emphasizes a distinction between the representation of invariant and changeable aspects of faces. The representation of invariant aspects of faces underlies the recognition of individuals, whereas the representation of changeable aspects of faces, such as eye gaze, expression, and lip movement, underlies the (...) perception of information that facilitates social communication. The model is also hierarchical insofar as it is divided into a core system and an extended system. The core system is comprised of occipitotemporal regions in extrastriate visual cortex that mediate the visual analysis of faces. In the core system, the representation of invariant aspects is mediated more by the face-responsive region in the fusiform gyrus, whereas the representation of changeable aspects is mediated more by the face-responsive region in the superior temporal sulcus. The extended system is comprised of regions from neural systems for other cognitive functions that can be recruited to act in concert with the regions in the core system to extract meaning from faces. (shrink)