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 responds to Colin Cheyne's new anti-platonist argument according to which knowledge of existential claims—claims of the form such-tmd-so exist—requires a caused connection with the given such-and-so. If his arguments succeed then nobody can know, or even justifiably believe, that acausal entities exist, in which case (standard) platonism is untenable. I argue that Cheyne's anti-platonist argument fails.

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)

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.

James L. Anderson analyzed the novelty of Einstein's theory of gravity as its lack of "absolute objects." Michael Friedman's related work has been criticized by Roger Jones and Robert Geroch for implausibly admitting as absolute the timelike 4-velocity field of dust in cosmological models in Einstein's theory. Using the Rosen-Sorkin Lagrange multiplier trick, I complete Anna Maidens's argument that the problem is not solved by prohibiting variation of absolute objects in an action principle. Recalling Anderson's proscription of "irrelevant" variables, I (...) generalize that proscription to locally irrelevant variables that do no work in some places in some models. This move vindicates Friedman's intuitions and removes the Jones-Geroch counterexample: some regions of some models of gravity with dust are dust-free and so naturally lack a timelike 4-velocity, so diffeomorphic equivalence to is spoiled. Torretti's example involving constant curvature spaces is shown to have an absolute object on Anderson's analysis, viz., the conformal spatial metric density. The previously neglected threat of an absolute object from an orthonormal tetrad used for coupling spinors to gravity appears resolvable by eliminating irrelevant fields. However, given Anderson's definition, GTR itself has an absolute object : a change of variables to a conformal metric density and a scalar density shows that the latter is absolute. (shrink)

It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors \emph{as such} cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed (...) spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is Ockhamized, with most of the fluff removed. As developed nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix $diag$, the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and \emph{values} of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, Ogievetsky-Polubarinov spinors form, with the metric, a nonlinear geometric object, for which important results on Lie and covariant differentiation are recalled. Such spinors avoid a spurious absolute object in the Anderson-Friedman analysis of substantive general covariance. They also permit the gauge-invariant localization of the infinite-component gravitational energy in General Relativity. Density-weighted spinors exploit the conformal invariance of the massless Dirac equation to show that the volume element is absent. Thus instead of an arbitrary nonsingular matrix with 16 components, 6 of which are gauged away by a new local $O$ gauge group and one of which is irrelevant due to conformal covariance, one can, and presumably should, use density-weighted Ogievetsky-Polubarinov spinors coupled to the 9-component symmetric square root of the part of the metric that fixes null cones. Thus $\frac{7}{16}$ of the orthonormal basis is eliminated as surplus structure. Greater unity between spinors and tensors and the like is achieved, such as regarding conservation laws. Regarding the conventionality of simultaneity, an unusually wide range of $\epsilon$ values is admissible, but some extreme values are inadmissible. Standard simultaneity uniquely makes the spinor transformation law linear and independent of the metric, because transformations among the standard Cartesian coordinate systems fall within the conformal group, for which the spinor transformation law is linear. The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited. (shrink)

This paper presents a new puzzle for certain positions in the theory of truth. The relevant positions can be stated in a language including a truth predicate T and an operation that takes sentences to names of those sentences; they are positions that take the T-schema A ↔ T to hold without restriction, for every sentence A in the language. As such, they must be based on a nonclassical logic, since paradoxes that cannot be handled classically will arise. The bestknown (...) of these paradoxes is probably the liar paradox – a sentence that says of itself that it is not true – but our concern here is not with the liar. Instead, our focus is a variant of Curry ’s paradox – a sentence that says of itself that if it is true, everything is [3, 5, 7, 11]. In §1, we present the standard version of Curry ’s paradox and the strain of response to it we wish to focus on. This strain of response crucially invokes non-normal worlds: worlds at which the laws of logic differ from the laws that actually hold. In §2, we go on to argue that, in light of temporal curry paradox, this strain of response ought also to accept non-normal times: times at which the laws of logic in the actual world differ from the laws that hold now. We then consider, in §3, what this would mean for the theorists in question. (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.

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.

In this 6-year, multi-study paper we summarize a new and effective framework of single-session problem-solving developed in an elite sport context at a world leading national institute of sport science and medicine. In Study 1, we used ethnography to observe how single-session problem-solving methods were being considered, explored, introduced and developed within the EIS. In Study 2, we used case-study methods split into two parts. A multiple case-study design was employed in Part one to evaluate how the approach was refined (...) into an effective framework of practice. An individual case-study is then illustrated to detail the framework in-action. Collectively, findings realized a framework of single-session problem-solving for use both inside and outside of elite sport that focused on ways to reframe clients’ problems into more ‘solvable’ descriptions. Guidance for psychologists wishing to integrate these problem-solving techniques into their practice are offered. (shrink)

O tema deste artigo é o insucesso da produção teatral do poeta suábio Friedrich Holderlin na confecção de “A morte de Empédocles”_. _O objetivo é apontar a crescente ausência de indicações cênicas e elementos de representação entre as três versões inacabadas da obra. Para tal comentaremos diversos instantes do objeto analisado nos quais transparecem ora caracteres filosóficos, ora caracteres poéticos e também teatrais, com indicações do abandono da teatralidade e do ambiente cênico em favorecimento da poesia e de uma visão (...) mítica da personagem principal. Nosso fundamento teórico será composto por alguns autores que consideram o desenvolvimento histórico da obra de Holderlin enquanto poeta do século XVIII. Os resultados alcançados indicam que a constante revisão da peça teatral deveu-se às mudanças de concepção sobre o sentido da tragédia como conceito, não tendo o autor conseguido transpor para o texto cênico a quintessência de sua ideia criadora. A conclusão a que chegamos indica que Holderlin não atende ao escopo da tragédia como expressão teatral no sentido aristotélico porque seu personagem principal supera a dicotomia que está na base de toda obra trágica: o conflito entre o indivíduo livre e seu tempo obscuro, sua cultura decaída, seu destino fatídico. Empédocles vira um mito. (shrink)

In a framework describing manifestly covariant relativistic evolution using a scalar time τ, consistency demands that τ-dependent fields be used. In recent work by the authors, general features of a classical parametrized theory of gravitation, paralleling general relativity where possible, were outlined. The existence of a preferred “time” coordinate τ changes the theory significantly. In particular, the Hamiltonian constraint for τ is removed From the Euler-Lagrange equations. Instead of the 5-dimensional stress-energy tensor, a tensor comprised of 4-momentum density mid flux (...) density only serves as the source. Building on that foundation, in this paper we develop a linear approximate theory of parametrized gravitation in the spirit of the flat spacetime approach to general relativity. Using a modified form of Kraichnan's flat spacetime derivation of general relativity, we extend the linear theory to a family of nonlinear theories in which the flat metric and the gravitational field coalesce into a single effective curved metric. (shrink)

It is now more than ten years since the EU FET project ALFEBIITE finished, during which its researchers made original and distinctive contributions to (inter alia) formal models of trust, model-checking, and action logics. ALFEBIITE was also a highly inter-disciplinary project, with partners from computer science, philosophy, cognitive science and law. In this paper, we reflect on the interaction between computer scientists and information and IT lawyers on the idea of the ‘open agent society’. This inspired a programme of research (...) whose investigation into conceptual challenges has carried it from the logical specification of agent societies and dynamic norm-governed systems to self-organising electronic institutions, while developing several technologies for agent-based modelling and complex event recognition. The outcomes of this inter-disciplinary collaboration have also influenced current research into using the open agent society as a platform for socio-technical systems, and other collective adaptive systems. We present a number of research challenges, including the ideas of computational justice and polycentric governance, and explore a number of ethical, legal and social implications. We contend that, in order to address these issues and challenges, the continued inter-disciplinary collaboration between computer science and IT lawyers is critical. (shrink)

This volume brings together many prominent philosophical voices today focusing on issues of U. S. Latinx and Latin American identities and feminist theory. As such, the essays collected here highlight the varied and multidimensional aspects of gender, racial, cultural, and sexual questions impacting U.S. Latinx and Latin American communities today. The collection also highlights a number of important threads of analysis from fields as diverse as disability studies,aesthetics, literary theory, and pop culture studies.

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.

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)