We prove that if p ≠ q are distinct primes, then the classification problems for p-local and q-local torsion-free abelian groups of rank two are incomparable with respect to Borel reducibility.

Safe stair negotiation is an everyday task that children with developmental coordination disorder are commonly thought to struggle with. Yet, there is currently a paucity of research supporting these claims. We investigated the visuomotor control strategies underpinning stair negotiation in children with and without DCD by measuring kinematics, gaze behavior and state anxiety as they ascended and descended a staircase. A questionnaire was administered to determine parents' confidence in their child's ability to safely navigate stairs and their child's fall history. (...) Kinematics were measured using three-dimensional motion capture, whilst gaze was measured using mobile eye-tracking equipment. The parents of DCD children reported significantly lower confidence in their child's ability to maintain balance on the stairs and significantly more stair-related falls in the previous year compared to the parents of typically developing children. During both stair ascent and stair descent, the children with DCD took longer to ascend/descend the staircase and displayed greater handrail use, reflecting a more cautious stair negotiation strategy. No differences were observed between groups in their margin of stability, but the DCD children exhibited significantly greater variability in their foot-clearances over the step edge, which may increase the risk of a fall. For stair descent only, the DCD children reported significantly higher levels of state anxiety than the TD children and looked significantly further along the staircase during the initial entry phase, suggesting an anxiety-related response that may bias gaze toward the planning of future stepping actions over the accurate execution of an ongoing step. Taken together, our findings provide the first quantifiable evidence that safe stair negotiation is a significant challenge for children with DCD, and that this challenge is reflected by marked differences in their visuomotor control strategies and state anxiety levels. Whilst it is currently unclear whether these differences are contributing to the frequency of stair-related falls in children with DCD, our findings pave the way for future research to answer these important questions. (shrink)

Nowadays references to the afterlife-angels strumming harps, demons brandishing pitchforks, God enthroned on heavenly clouds-are more often encountered in New Yorker cartoons than in serious Christian theological reflection. Speculation about death and its sequel seems to embarrass many theologians; however, as Greg Garrett shows in Entertaining Judgment, popular culture in the U.S. has found rich ground for creative expression in the search for answers to the question: What lies in store for us after we die? The lyrics of Madonna, (...) Los Lonely Boys, and Sean Combs; the plotlines of TV's Lost, South Park, and The Walking Dead; the implied theology in films such as The Dark Knight, Ghost, and Field of Dreams; the heavenly half-light of Thomas Kinkade's popular paintings; the ghosts, shades, and after-life way-stations in Harry Potter; and the characters, situations, and locations in the Hunger Games saga all speak to our hopes and fears about what comes next. In a rich survey of literature and popular media, Garrett compares cultural accounts of death and the afterlife with those found in scripture. Denizens of the imagined afterlife, whether in heaven, hell, on earth, or in purgatory, speak to what awaits us, at once shaping and reflecting our deeply held-if often somewhat nebulous-beliefs. They show us what rewards and punishments we might expect, offer us divine assistance, and even diabolically attack us. Ultimately, we are drawn to these stories of heaven, hell, and purgatory--and to stories about death and the undead--not only because they entertain us, but because they help us to create meaning and to learn about ourselves, our world, and, perhaps, the next world. Garrett's deft analysis sheds new light on what popular culture can tell us about the startlingly sharp divide between what modern people profess to believe and what they truly hope and expect to find after death--and how they use those stories to help them understand this life. (shrink)

This essay is an examination of Dante Alighieri as a spiritual theologian of grace. Using Cantos 9 and 29–30 of the Purgatorio the essay shows that Dante constructs his other-worldly journey as one that is grace-filled and dependent on the grace bestowed through the church's sacraments, in concert with Thomas Aquinas’ theology of grace. Further, in light of the creation of the Feast of Corpus Christi in the thirteenth century, the essay offers a unique interpretation of the figure of (...) Beatrice, showing that she, at least within the context of Purgatorio 29–30, is divine grace. (shrink)

The miniseries Frank Herbert’s Dune (2000) and Frank Herbert’s Children of Dune (2003) offer a stark warning that people must think for themselves rather than relying on authority. In particular, they warn against overreliance on leaders and on religious authorities. The series tell the story of how, in the far future, Paul Atreides becomes dictator and religious leader over the human race, bringing slaughter and oppression in his wake. The chapter will consider the views of philosophers like Plato, who believed (...) that power should be concentrated in the hands of leaders with absolute authority, along with the views of philosophers who advocated democracy, like John Locke, John Stuart Mill, and John Dewey. The chapter will also examine the views of philosophers on religion, especially philosophers critical of religion, such as Locke, Thomas Paine, and Bertrand Russell. It is argued that the series present a strong case against allowing others to think for us, because the story they tell matches the historical record of the real world. When leaders have been given the power to be arbiters of truth, they have too often exploited those beneath them, using their positions to accumulate wealth, power, and glory. When too much trust has been placed in religious authority, it has likewise too often led to exploitation and repression. What is worse, the power of religion is uncontrollable, easily leading to violence and destruction. Having said that, the series fail to reflect that religion does good in the world. This chapter argues that, as maintained by W. K. Clifford, whether people should accept religious views depends on whether they have good grounds to believe that these views are true. This implies that people must not accept religious views without thinking the views through for themselves. (shrink)

For much of the second half of the 20th Century, the primary role logical empiricism played was that of the argumentative foil. The 'received view' on a given topic (especially in philosophy of science, logic, or language) was frequently identified with some supposedly dogmatic tenet of logical empiricism. However, during the last twenty-five years, scholars have paid serious, sustained attention to what the logical positivists, individually and collectively, actually said. Early scholarship on logical empiricism had to engage in heavy-duty PR (...) work: why should anyone study the now-discarded mixture of blunders and implausibilities collected under the label 'logical empiricism'? However, thanks to the efforts of the pioneers, people studying the logical empiricists today need not articulate an extended apologia for their chosen subject of study -- rather, they can simply get on with their work. Many of the best fruits of these recent labors are on display in The Cambridge Companion to Logical Empiricism (CCLE), edited by Alan Richardson and Thomas Uebel. (shrink)

Putting the ‘empiricism’ in ‘logical empiricism’: the director’s cut Content Type Journal Article DOI 10.1007/s11016-010-9444-x Authors Greg Frost-Arnold, Department of Philosophy, Hobart and William Smith Colleges, Geneva, NY 14456, USA Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

Sport continues to be one of the primary means through which notions of Englishness and Britishness are constructed, contested, and resisted. The legacy of the role of sport in the colonial project of the British Empire, combined with more recent connections between sport and far right fascist/nationalist politics, has made the association between Britishness, Englishness, and ethnic identity(ies) particularly intriguing. In this paper, these intersections are explored through British media coverage of the Canadian‐born, British tennis player, Greg Rusedski. This (...) coverage is examined through the lens of ‘performativity,’ as articulated by Judith Butler. Through a critical application of Butler's ideas, the ways in which the media seek to recognise and normalise certain identities, while problematising and excluding others, can be more fully appreciated. Thus, it was within newspaper framings of Rusedski that hegemonic notions of White Englishness could be performed, maintained, and embedded. (shrink)

Bounds consequence provides an interpretation of a multiple-conclusion consequence relation in which the derivability of a sequent is understood as the claim that it is conversationally out-of-bounds to take a position in which each member of Γ is asserted while each member of Δ is denied. Two of the foremost champions of bounds consequence—Greg Restall and David Ripley—have independently indicated that the shape of the bounds in question is determined by conversational practice. In this paper, I suggest that the (...) standard treatments of bounds consequence have focused heavily on the matter of veridicality at the expense of ignoring other features by which conversational bounds are set, prime among them being the matter of content or subject-matter. Furthermore, I argue that the semantic behavior of propositions containing “monstrous” content—content whose introduction is inappropriate to a context independently of veridical considerations—leads to a weak Kleene account of bounds consequence. (shrink)

In view of scholarly work that has explored the socio-psycho significance of national performativity, the body and the “other,” this article critically analyses newspaper representations of the Canadian-born British tennis player Greg Rusedski. Drawing on Lacanian interpretations of the body, it illustrates how Rusedski’s media framing centered on a particular feature of his body—his “smile.” In doing so, we detail how Rusedski’s “post-imperial” Otherness—conceived as a form of “extimacy” (extimité)—complicated any clear delineation between “us” and “them,” positing instead a (...) dialectical understanding of the splits, voids and contradictions that underscore the national “us.”. (shrink)

A.P. Martinich's interpretation that in Leviathan Thomas Hobbes believed that the laws of nature are the commands of God and that he did not rely on the Bible to prove this has been criticized by Greg Forster in this journal (2003). Forster uses these criticisms to develop his own view that Hobbes was insincere when he professed religious beliefs. We argue that Forster misrepresents Martinich's view, is mistaken about what evidence is relevant to interpreting whether Hobbes was sincere (...) or not, and is mistaken about some of Hobbes's central doctrines. Forster's criticisms are worth discussing at length for at least three reasons. He takes the debate about Hobbes's sincerity to a new level of sophistication; his misinterpretations of Hobbes may become accepted as correct; and his criticisms raise issues about the proper method of interpreting historical texts. (shrink)

Greg Hjorth and Simon Thomas proved that the classification problem for torsion-free abelian groups of finite rank strictly increases in complexity with the rank. Subsequently, Thomas proved that the complexities of the classification problems for p-local torsion-free abelian groups of fixed rank n are pairwise incomparable as p varies. We prove that if 3≤m (...) that for q-local torsion-free abelian groups of rank n. (shrink)

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both (...) students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading. (shrink)

Our topic is the notion of logical consequence: the link between premises and conclusions, the glue that holds together deductively valid argument. How can we understand this relation between premises and conclusions? It seems that any account begs questions. Painting with very broad brushtrokes, we can sketch the landscape of disagreement like this: “Realists” prefer an analysis of logical consequence in terms of the preservation of truth [29]. “Anti-realists” take this to be unhelpful and o:er alternative analyses. Some, like Dummett, (...) look to preservation of warrant to assert [9, 36]. Others, like Brandom [5], take inference as primitive, and analyse other notions in terms of it. There is plenty of disagreement on the “realist” side of the fence too. It is one thing to argue that logical consequence involves preservation of truth. It is another to explain how far truth must be preserved. Is the preservation essentially modal (in all circumstances [25]) or analytic (vouchsafed by.. (shrink)

In this paper I urge friends of truth-value gaps and truth-value gluts – proponents of paracomplete and paraconsistent logics – to consider theories not merely as sets of sentences, but as pairs of sets of sentences, or what I call ‘bitheories,’ which keep track not only of what holds according to the theory, but also what fails to hold according to the theory. I explain the connection between bitheories, sequents, and the speech acts of assertion and denial. I illustrate the (...) usefulness of bitheories by showing how they make available a technique for characterising different theories while abstracting away from logical vocabulary such as connectives or quanti- fiers, thereby making theoretical commitments independent of the choice of this or that particular non-classical logic. (shrink)

Paraconsistent logics are often semantically motivated by considering "impossible worlds." Lewis, in "Logic for equivocators," has shown how we can understand paraconsistent logics by attributing equivocation of meanings to inconsistent believers. In this paper I show that we can understand paraconsistent logics without attributing such equivocation. Impossible worlds are simply sets of possible worlds, and inconsistent believers (inconsistently) believe that things are like each of the worlds in the set. I show that this account gives a sound and complete semantics (...) for Priest's paraconsistent logic LP, which uses materials any modal logician has at hand. (shrink)

In this paper, I distinguish different kinds of pluralism about logical consequence. In particular, I distinguish the pluralism about logic arising from Carnap’s Principle of Tolerance from a pluralism which maintains that there are different, equally “good” logical consequence relations on the one language. I will argue that this second form of pluralism does more justice to the contemporary state of logical theory and practice than does Carnap’s more moderate pluralism.

The two-dimensional modal logic of Davies and Humberstone [3] is an important aid to our understanding the relationship between actuality, necessity and a priori knowability. I show how a cut-free hypersequent calculus for 2D modal logic not only captures the logic precisely, but may be used to address issues in the epistemology and metaphysics of our modal concepts. I will explain how the use of our concepts motivates the inference rules of the sequent calculus, and then show that the completeness (...) of the calculus for Davies–Humberstone models explains why those concepts have the structure described by those models. The result is yet another application of the completeness theorem. (shrink)

An advanced-level logic textbook that presents proof construction on equal footing with model building. Potentially relevant to students of mathematics and computer science as well.

In this paper I introduce a sequent system for the propositional modal logic S5. Derivations of valid sequents in the system are shown to correspond to proofs in a novel natural deduction system of circuit proofs (reminiscient of proofnets in linear logic, or multiple-conclusion calculi for classical logic). -/- The sequent derivations and proofnets are both simple extensions of sequents and proofnets for classical propositional logic, in which the new machinery—to take account of the modal vocabulary—is directly motivated in terms (...) of the simple, universal Kripke semantics for S5. The sequent system is cut-free and the circuit proofs are normalising. (shrink)

I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.

In his classic 1936 essay "On the Concept of Logical Consequence", Alfred Tarski used the notion of satisfaction to give a semantic characterization of the logical properties. Tarski is generally credited with introducing the model-theoretic characterization of the logical properties familiar to us today. However, in his book, The Concept of Logical Consequence, Etchemendy argues that Tarski's account is inadequate for quite a number of reasons, and is actually incompatible with the standard model-theoretic account. Many of his criticisms are meant (...) to apply to the model-theoretic account as well. In this paper, I discuss the following four critical charges that Etchemendy makes against Tarski and his account of the logical properties: (1) (a) Tarski's account of logical consequence diverges from the standard model-theoretic account at points where the latter account gets it right. (b) Tarski's account cannot be brought into line with the model-theoretic account, because the two are fundamentally incompatible. (2) There are simple counterexamples (enumerated by Etchemendy) which show that Tarski's account is wrong. (3) Tarski committed a modal fallacy when arguing that his account captures our pre-theoretical concept of logical consequence, and so obscured an essential weakness of the account. (4) Tarski's account depends on there being a distinction between the "logical terms" and the "non-logical terms" of a language, but (according to Etchemendy) there are very simple (even first-order) languages for which no such distinction can be made. Etchemendy's critique raises historical and philosophical questions about important foundational work. However, Etchemendy is mistaken about each of these central criticisms. In the course of justifying that claim, I give a sustained explication and defense of Tarski's account. Moreover, since I will argue that Tarski's account and the model theoretic account really do come to the same thing, my subsequent defense of Tarski's account against Etchemendy's other attacks doubles as a defense against criticisms that would apply equally to the familiar model-theoretic account of the logical properties. (shrink)

This essay is structured around the bifurcation between proofs and models: The first section discusses Proof Theory of relevant and substructural logics, and the second covers the Model Theory of these logics. This order is a natural one for a history of relevant and substructural logics, because much of the initial work — especially in the Anderson–Belnap tradition of relevant logics — started by developing proof theory. The model theory of relevant logic came some time later. As we will see, (...) Dunn’s algebraic models [76, 77] Urquhart’s operational semantics [267, 268] and Routley and Meyer’s relational semantics [239, 240, 241] arrived decades after the initial burst of activity from Alan Anderson and Nuel Belnap. The same goes for work on the Lambek calculus: although inspired by a very particular application in linguistic typing, it was developed first proof-theoretically, and only later did model theory come to the fore. Girard’s linear logic is a different story: it was discovered though considerations of the categorical models of coherence.. (shrink)

A generation ago, we adopted a national system for the protection of human subjects in research. Today, that system is facing new challenges. Many argue that the system has failed to evolve in concert with dramatic changes in the research environment. Accordingly, efforts are underway to reform the existing process to make it both more efficient and more effective. At the same time, many are also reexamining the system in more fundamental ways — going well beyond considerations of policies and (...) compliance and raising questions that go to the very foundations of what constitutes an ethical conduct of human research.Experimentation involving human subjects is a necessary step in the process of translating scientific discovery and technological advancement into procedures and products that offer the prospect of better lives for all of us. It helps us to better understand why we do the things we do and believe what we believe. (shrink)

A generation ago, we adopted a national system for the protection of human subjects in research. Today, that system is facing new challenges. Many argue that the system has failed to evolve in concert with dramatic changes in the research environment. Accordingly, efforts are underway to reform the existing process to make it both more efficient and more effective. At the same time, many are also reexamining the system in more fundamental ways — going well beyond considerations of policies and (...) compliance and raising questions that go to the very foundations of what constitutes an ethical conduct of human research.Experimentation involving human subjects is a necessary step in the process of translating scientific discovery and technological advancement into procedures and products that offer the prospect of better lives for all of us. It helps us to better understand why we do the things we do and believe what we believe. (shrink)

Are demands for equality motivated by envy? Nietzsche, Freud, Hayek, and Nozick all thought so. Call this the Envy Objection. For egalitarians, the Envy Objection is meant to sting. Many egalitarians have tried to evade the Envy Objection.. But should egalitarians be worried about envy? In this paper, I argue that egalitarians should stop worrying and learn to love envy. I argue that the persistent unwillingness to embrace the Envy Objection is rooted in a common misunderstanding of the nature of (...) the charge, what it reveals, and what can be said in response to it. I develop what Bernard Williams might call a vindicatory genealogy of envy, thereby allowing us to see that envy, rather than undermining egalitarian intuitions, can in fact play a distinct justificatory role (when it is fitting), which undermines the Envy Objection. (shrink)

This Element is an introduction to recent work proofs and models in philosophical logic, with a focus on the semantic paradoxes the sorites paradox. It introduces and motivates different proof systems and different kinds of models for a range of logics, including classical logic, intuitionistic logic, a range of three-valued and four-valued logics, and substructural logics. It also compares and contrasts the different approaches to substructural treatments of the paradox, showing how the structural rules of contraction, cut and identity feature (...) in paradoxical derivations. It then introduces model theoretic treatments of the paradoxes, including a simple fixed-point model construction which generates three-valued models for theories of truth, which can provide models for a range of different non-classical logics. The Element closes with a discussion of the relationship between proofs and models, arguing that both have their place in the philosophers' and logicians' toolkits. (shrink)

It appears that in the 30 years that business ethics has been a discipline in its own right a model of business ethics has not been proffered. No one appears to have tried to explain the phenomenon known as 'business ethics' and the ways that we as a society interact with the concept, therefore, the authors have addressed this gap in the literature by proposing a model of business ethics that the authors hope will stimulate debate. The business ethics model (...) consists of three principal components that are interconnected by five sub-components. The introduced model makes a contribution to the creation of a conceptual framework for business ethics. A few tentative conclusions may be drawn from the introduced model of business ethics. The model aspires to be highly dynamic. The ultimate outcome is dependent upon the evolution of time and contexts. It is also dependent upon and provides reference to the behaviours and perceptions of people. The model proposes business ethics to be a continuous and an iterative process. There is no actual end of the process, but a constant reconnection to the initiation of successive process iterations of the business ethics model. The principals and sub-components of the model construct the dynamics of this continuous process. They provide guidance on what and how to explore our common efforts to understand the phenomenon known as business ethics. The model provides opportunities for further research in the field of business ethics. (shrink)

According to the “knowability thesis,” every truth is knowable. Fitch’s paradox refutes the knowability thesis by showing that if we are not omniscient, then not only are some truths not known, but there are some truths that are not knowable. In this paper, I propose a weakening of the knowability thesis (which I call the “conjunctive knowability thesis”) to the e:ect that for every truth p there is a collection of truths such that (i) each of them is knowable and (...) (ii) their conjunction is equivalent to p. I show that the conjunctive knowability thesis avoids triviality arguments against it, and that it fares very di:erently depending on another thesis connecting knowledge and possibility. If there are two propositions, inconsistent with one another, but both knowable, then the conjunctive knowability thesis is trivially true. On the other hand, if knowability entails truth, the conjunctive knowability thesis is coherent, but only if the logic of possibility is weak. (shrink)

This paper concerns a key point of decision in Donald Davidson's early work in philosophy of language — a fateful decision that set him and the discourse in the area on the path of truth-theoretic semantics. The decision of moment is the one Davidson makes when, in the face of a certain barrier, he gives up on the idea of constructing an explicit meaning theory that would parallel Tarski's recursive way with truth theory. For Davidson there was little choice: he (...) tells us he does not see how to deal with the difficulty except in the radical way he proposes. But there is a way to give such a meaning theory — a meaning theory proper which, using classical logic only, meets a meaning-theoretic analogue of Convention T, satisfies Davidson’s three key desiderata for a theory of meaning, reflects linguistic competence, and avoids quantifying over meanings. The meaning theory sketched here uses Tarskian strategies, as Davidson proposed, but differs from Davidson's approach in not going by way of a truth theory for the target language. (shrink)

In this paper we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness, and we show how normalisation in this system corresponds to cut elimination in the sequent calculus for lattice logic. This natural deduction system is inspired both by Shoesmith and Smiley's multiple conclusion systems (...) for classical logic and Girard's proofnets for linear logic. (shrink)

Formal systems seem to come in two general kinds: useful and useless. This is painting things starkly, but the point is important. Formal structures can either be used in interesting and important ways, or they can languish unused and irrelevant. Lewis' modal logics are good examples. The systems S4 and S5 are useful in many different ways. They map out structures that are relevant to a number of different applications. S1, S2 and S3 however, are not so lucky. They are (...) little studied, and used even less. It has become dear that the structures described by S4 and S5 are important in different ways, while the structures described by S1 to S3 are not so important. In this paper, we will see another formal system with a number of different uses. We will examine a substructural logic which is important in a number of different ways. The logic of Peirce monoids, inspired by the logic of relations, is useful in the independent areas of linguistic types and information flow.In what follows I will describe the logic of Peirce monoids in its various guises, sketch out its main properties, and indicate why it is important. As proofs of theorems are readily available elsewhere in the literature, I simply sketch the relevant proofs here, and point the interested reader to where complete proofs can be found. (shrink)

In this note I respond to Hartley Slater's argument 12 to the e ect that there is no such thing as paraconsistent logic. Slater's argument trades on the notion of contradictoriness in the attempt to show that the negation of paraconsistent logics is merely a subcontrary forming operator and not one which forms contradictories. I will show that Slater's argument fails, for two distinct reasons. Firstly, the argument does not consider the position of non-dialethic paraconsistency which rejects the possible truth (...) of any contradictions. Against this position Slater's argument has no bite at all. Secondly, while the argument does show that for dialethic paraconsistency according to which contradictions can be true, certain other contradictions must be true, I show that this need not deter the dialethic paraconsistentist from their position. (shrink)