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 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.

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)

_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)

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)

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)

In his travels, and in his accompanying readings, he had come to the conclusion that the essential secret of life was harmony. . . . And he proceeded to put his philosophy into practice by forcing order into the established world, translating the mystic word harmony into the practical word organisation.1 Harmony becomes organization. And Gerald dedicates himself to work, to feverish, totally absorbing work, inspired with an almost religious exaltation in his fight with matter. The world is split in (...) two: on one side matter , on the other side his own isolated will. He wants to create on earth a perfect machine, "an activity of pure order, pure mechanical repetition"; a man of the twentieth century with no nostalgia for the superannuated ideals of Christianity or democracy, he wishes to found his eternity, his infinity, in the machine. So inchoate and mysterious is the imaginative world Lawrence creates for Women in Love that we find no difficulty in reading Gerald Crich as an allegorical figure in certain chapters and as a quite human, even fluid personality in others. As Gudrun's frenzied lover, as Birkin's elusive beloved, he seems a substantially different person from the Gerald Crich who is a ruthless god of the machine; yet as his cultural role demands extinction , so does his private emotional life, his confusion of the individual will with that of the cosmos, demand death—death by perfect cold. He is Lawrence's only tragic figure, a remarkable creation on a remarkable novel, and though it is a commonplace thing to say that Birkin represents Lawrence, it seems equally likely that Gerald Crich represents Lawrence—in his deepest, most aggrieved, most nihilist soul. · 1. All quotations from Women in Love are taken from the Modern Library edition. Joyce Carol Oates' works include the novels Childhood, Son of the Morning, and a collection of short stories, Night-Side. “Lawrence’s Götterdämmerung” is part of a larger work exploring tragedy and comedy. Her contributions to Critical Inquiry include "Jocoserious Joyce" , and "The Picture of Dorian Gray: Wilde's Parable about the Fall". (shrink)

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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)

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+.

One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley-Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing (...) a general conception of conditionality that may unify the three given conceptions. (shrink)

Beyond the defiance of the young iconoclast—Wilde himself, of course—and the rather perfunctory curve of Dorian Gray to that gothic final sight , there is another, possibly less strident, but more central theme. That one is damned for selling one's soul to the devil is a commonplace in legends; what arrests our attention more, perhaps, is Wilde's claim or boast or worry or warning that one might indeed be poisoned by a book . . . and that the artist, even (...) the presumably "good" Basil Hallward, is the diabolical agent. Wilde's novel must be seen as a highly serious meditation upon the moral role of the artist—an interior challenge, in fact, to the insouciance of the famous pronouncements that would assure us that there is no such thing as a moral or an immoral book or that all art is "quite useless." Wilde's genius was disfigured by his talent: he always sounds much more flippant, far more superficial, than he really is. So one always say about Dorian Gray, with an air of surprise, that the novel is exceptionally good after all—and anyone who has read it recently replies, with the same air of faint incredulity, yes, it is exceptionally good—in fact, one of the strongest and most haunting of English novels. Yet its reputation remains questionable. Gerald Weales virtually dismisses it as "terribly fin de siècle " in a rather flippant introduction to the novel, and it would be difficult to find a critic who would choose to discuss it in terms other than the familiar ones of decadence, art for art's sake, art as "the telling of beautiful untrue things." Joyce Carol Oates has written, among others, Bellefleur, Childhood, a collection of short stories, Nightside, and Son of the Morning. Her contributions to Critical Inquiry, include "Jocoserious Joyce" and "Lawrence's Gotterdammerung". (shrink)

Emily Dickinson is the most paradoxical of poets: the very poet of paradox. By way of voluminous biographical material, not to mention the extraordinary intimacy of her poetry, it would seem that we know everything about her; yet the common experience of reading her work, particularly if the poems are read sequentially, is that we come away seeming to know nothing. We could recognize her inimitable voice anywhere—in the “prose” of her letters no less than in her poetry—yet it is (...) a voice of the most deliberate, the most teasing anonymity. “I’m Nobody!” is a proclamation to be interpreted in the most literal of ways. Like no other poet before her and like very few after her—Rilke comes most readily to mind, and, perhaps, Yeats and Lawrence—Dickinson exposes her heart’s most subtle secrets; she confesses the very sentiments that, in society, would have embarrassed her dog . Yet who is this “I” at the center of experience? In her astonishing body of 1,775 poems Dickinson records what is surely one of the most meticulous examinations of the phenomenon of human “consciousness” ever undertaken. The poet’s persona—the tantalizing “I”—seems, in nearly every poem, to be addressing us directly with perceptions that are ours as well as hers. The poems’ refusal to be rhetorical, their daunting intimacy, suggests the self-evident in the way that certain Zen koans and riddles do while being indecipherable. But what is challenged is, perhaps, “meaning” itself: Wonder—is not precisely KnowingAnd not precisely Knowing not—A beautiful but bleak conditionHe has not lived who has not felt—Suspense—is his maturer Sister—Whether Adult Delight is PainOr of itself a new misgiving—This is the Gnat that mangles men— [1331, ca. 1874]1 1. The Complete Poems of Emily Dickinson, ed. Thomas H. Johnson ; subsequent references in the text to the poems will cite the Johnson number and the date assigned by Johnson to each poem. Joyce Carol Oates is the Roger S. Berlind Distinguished Lecturer at Princeton University and the author most recently of the booklength essay On Boxing. “Soul at the White Heat” will be included in her book of essays, Writer: Occasions and Opportunities, to be published in the spring of 1988. (shrink)

We shed light on an old problem by showing that the logic LP cannot define a binary connective $\odot$ obeying detachment in the sense that every valuation satisfying $\varphi$ and $(\varphi\odot\psi)$ also satisfies $\psi$ , except trivially. We derive this as a corollary of a more general result concerning variable sharing.

A longstanding problem confronting Christian theology and its doctrine of incarnation is the apparent contradiction that it faces. For example, to be divine, in the relevant sense, is to have the limitlessness of God. To be human, in the relevant sense, is to have the limitations of humans. The incarnation (in the person of Jesus per Christian doctrine) is to be both divine and human. Many theologians and sympathetic philosophers have attempted to ‘consistentize’ (i.e., make consistent) incarnation. Timothy Pawl has (...) been one of the latest to do so. In this paper, I concisely note a dilemma for Pawl’s approach. (shrink)

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.

Weber, Colyvan, and Priest have advanced glutty approaches to the sorites, on which the truth about the penumbral region of a soritical series is inconsistent. The major benefit of a glut-based approach is maintaining the truth of all sorites premisses while none the less avoiding, in a principled fashion, the absurdity of the sorites conclusion. I agree that this is a major virtue of the target glutty approach; however, I think that it can be had without gluts. If correct, this (...) result weighs heavily against the proposed glutty approach, at least given the default-consistency principle that all target glutty philosophers accept: posit gluts only if there is no consistent theory that enjoys the same virtues as the would-be glutty solution. (shrink)

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)