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)

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)

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)

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.

My aim here is a modest one: to note another example in which the theory of validity and the theory of ‘inference’ naturally come apart. The setting is multiple-conclusion logic. At least on one philosophy of multiple-conclusion logic, there are very clear examples of where logic qua validity and logic qua normative guide to inference are essentially different things. On the given conception, logic tells us only what follows from what, what our ‘choices’ are given a set of premises; it (...) is simply silent on which, of the given ‘choices’, we select from the (conclusion) set of options. (shrink)

English summary: Criticism is often levelled at Hegel's philosophy of the absolute spirit for its being conceived at the expense of the world. In view of this, Hegel's regular reference to a world in the Phenomenology of Spirit is somewhat puzzling. How then are we to understand the presence of the world, or even numerous worlds? Tereza Matejckova contends that at every stage of its journey, consciousness designs a new world-model, each built on central concepts of the respective form of (...) consciousness. Consciousness thus finds itself in a world of contradiction, of life, of struggle, or one of unhappy diremption. The point of absolute knowledge is not that the world is now derived from consciousness itself, but rather that it conceives a world-model that corresponds with reality, as whose reflection it itself now grasps. German description: Oft wird gegen Hegel der Vorwurf erhoben, seine Philosophie des absoluten Geistes sei auf Kosten der Welt konzipiert. Umso auffallender ist, dass Hegel in der Phanomenologie des Geistes nahezu auf jeder Ebene auf eine Welt zu sprechen kommt. Wie ist diese Gegenwart der Welt, sogar einer Mehrzahl von Welten zu deuten? Tereza Matejckova behauptet, dass das Bewusstsein auf jeder Ebene seiner Genese ein Weltmodell entwirft, in dessen Zentrum Schlusselbegriffe der einschlagigen Bewusstseinsgestalt stehen. Das Bewusstsein findet sich somit in einer Welt des Widerspruchs, des Lebens, des Kampfes oder der unglucklichen Entzweiung wieder. Pointe des absoluten Wissens ist nicht, dass das Bewusstsein nun die Welt aus sich selbst ableitet, sondern dass es ein der Wirklichkeit entsprechendes Weltmodell konzipiert, als dessen Widerschein es sich selbst erfasst. (shrink)

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.

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.

Der Aufsatz schildert den platonisierenden Antipsychologismus welchen Bolzano, der junge Brentano, Twardowski, Meinong, der Husserl der Logischen Untersuchungen, Frege, der Russell der Jahrhundertwende und der junge Wittgenstein philosophisch vertraten, und versucht eine soziologische und ideologiekritische Interpretation sowohl dieser Einstellung als auch derjenigen des traditionellen Psychologismus des achtzehnten Jahrhunderts. Der Platonismus des neunzehnten und zwanzigsten Jahrhunderts wird als ein Ausdruck fiir ? oder vielmehr als eine Reaktion gegen ? den Verfall der klassischen burgerlichen Werte aufgefaBt. In Wittgensteins Tractatus spielen Elemente sowohl (...) eines platonisierenden Antipsychologismus wie auch eines relativistischen, verhaltensphanomenologisch orientierten Antipsychologismus eine Rolle: dieses Werk wird also als eine grelle Manifestation des Uberganges von der klassischen zur spatbiirgerlichen Weltanschauung, als ein Obergang vom Glauben an ewige Wahrheiten zur Hinnahme einer Gebrauchs?Theorie der Bedeutung und deren Konsequenzen interpretiert. (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)

_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)

Austria, by the end of the nineteenth century, clearly lagged behind its more developed Western neighbours in matters of intellect and science. The Empire had witnessed a relatively late process of urbanization, bringing also a late development of those liberal habits and values which would seem to be a presupposition of the modern, scientific attitude. It therefore lacked institutions of scientific research of the sort that had been founded in Germany since the time of von Humboldt. On the other hand, (...) as more liberal ways began to be established in Austria - effectively in the second half of the nineteenth century - the desire to enjoy the trappings of a modern enlightened culture made itself felt. The Austrians were not of course in a position to summon forth the means to create reputable institutions and traditions of science in the narrow sense, and this created a vacuum which the theory of a practice so attractively pursued elsewhere could then fill. (shrink)

In his “Deep Inconsistency?” Eklund attacks arguments to the effect that some contradictions are true, and especially those based on the liar paradox, to be found in Priest’ In Contradiction. The point of this paper is to evaluate his case.

A series of papers on different aspects of practical knowledge by Roderick Chisholm, Rudolf Haller, J. C. Nyiri, Eva Picardi, Joachim Schulte Roger Scruton, Barry Smith and Johan Wrede.

This paper is a sequel to Beall (2011), in which I both give and discuss the philosophical import of a result for the propositional (multiple-conclusion) logic LP+. Feedback on such ideas prompted a spelling out of the first-order case. My aim in this paper is to do just that: namely, explicitly record the first-order result(s), including the collapse results for K3+ and FDE+.

Mark Balaguer argues for full blooded platonism (FBP), and argues that FBP alone can solve Benacerraf's familiar epistemic challenge. I note that if FBP really can solve Benacerraf's epistemic challenge, then FBP is not alone in its capacity so to solve; RFBP—really full blooded platonism—can do the trick just as well, where RFBP differs from FBP by allowing entities from inconsistent mathematics. I also argue briefly that there is positive reason for endorsing RFBP.

Wolność to idea, w imię której toczy się dzisiaj proces wyzwalania się Europy Wschodniej. Jest to potężna idea, która jednak w obecnych warunkach kryje w sobie również pewne niebezpieczeństwo, ponieważ podczas wyzwalania się spod dyktatury, uniezależniania się od wpływów Rosji i przebijania się ku klasycznym wartościom wolnosci obywatelskiej, można łatwo osiągnąć pozorne zwycięstwo; bezużyteczne zwycięstwo na peryferiach historii. Trzeba sobie obecnie zdac sprawę z tego, że Europa Wschodnia nie jest wcale widownią wydarzeń, mających zasadnicze znaczenie dla świata jako całości. Trzeba (...) uświadomić sobie, że dzisiaj inna, nowa rewolucja odciska swe piętno na historii swiata. Jest to rewolucja technologiczna, która rozgrywa się na calkiem innej płaszczyźnie; rewolucja, która przemienia nowoczesne przemysłowe społeczeństwo w post-nowoczesne społeczenstwo informacji. Przekształca się ono w społeczenstwo, w którym źródłem bogactwa nie jest już surowiec i kapitał, lecz wiedza - dostęp do informacji i umiejętność obchodzenia się z nią. „Nowa cywilizacja wkracza w nasze życie" - tak brzmią znane słowa Alvina Tofflera. (shrink)

The emergence and development of the humanities were initially bound up with the spread of alphabetic writing, and subsequently with the development of printing; the original task of the nascent humanities disciplines was a thoroughly practical one: that of building up our knowledge about the characteristics of the new media with the aim of exploiting this knowledge in everyday life—for the sake of economic, educational, or political benefits. In particular, the beginnings of philosophy lead us back to the times of (...) the first emergence of alphabetic writing. There is no philosophy in a purely oral culture; Western philosophy is in the first instance, and remains down to the twentieth century, reflection on conceptual relations generated by written language. Today, the printed word is losing its position as the dominant vehicle of communication. Philosophy faces a new educational challenge: that of articulating the logic of multimedia information storage and exchange. (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.

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.

There is the tension between, on the one hand, Wittgenstein’s not giving theoretical weight to metaphor, and on the other, his exuberant use of it. On a more fundamental level, there is a straightforward contradiction between Wittgenstein’s claim of the primordial literalness of everyday language, and his stress on the multiplicity and flexibility of language-games. Wittgenstein’s problem was that he did not succeed in making his ideas on metaphor, and indeed his ideas on metaphor and images, converge with the main (...) drift of TS 227 (the so-called ‘Part I’ of the so-called ‘Philosophical Investigations’). It was this divergence, I believe, that prevented him from rounding out his later philosophy. (shrink)

In the service of paraconsistent (indeed, ‘dialetheic’) theories, Graham Priest has long advanced a non-monotonic logic (viz., MiLP) as our ‘universal logic’ (at least for standard connectives), one that enjoys the familiar logic LP (for ‘logic of paradox’) as its monotonic core (Priest, G. In Contradiction , 2nd edn. Oxford: Oxford University Press. First printed by Martinus Nijhoff in 1987: Chs. 16 and 19). In this article, I show that MiLP faces a dilemma: either it is (plainly) unsuitable as a (...) universal logic or its role as a ‘universal logic’ (indeed, its role full stop) is a mystery. While familiarity with the basic ideas of dialetheism is assumed, formal details of the target logics are relegated to an appendix; the basic problem is evident without them. (shrink)