When we interpret modal ◊ as the limit point operator of a topological space, the Gödel-Löb modal system GL defines the class Scat of scattered spaces. We give a partition of Scat into α-slices S α , where α ranges over all ordinals. This provides topological completeness and definability results for extensions of GL. In particular, we axiomatize the modal logic of each ordinal α, thus obtaining a simple proof of the Abashidze–Blass theorem. On the other hand, when we interpret (...) ◊ as closure in a topological space, the Grzegorczyk modal system Grz defines the class HI of hereditarily irresolvable spaces. We also give a partition of HI into α-slices H α , where α ranges over all ordinals. For a subset A of a hereditarily irresolvable space X and an ordinal α, we introduce the α-representation of A, give an axiomatization of the α-representation of A, and characterize H α in terms of α-representations. We prove that ${X \in {\bf H}_{1}}$ iff X is submaximal. For a positive integer n, we generalize the notion of a submaximal space to that of an n-submaximal space, and prove that ${X \in {\bf H}_{n}}$ iff X is n-submaximal. This provides topological completeness and definability results for extensions of Grz. We show that the two partitions are related to each other as follows. For a successor ordinal α = β + n, with β a limit ordinal and n a positive integer, we have ${{\bf H}_{\alpha} \cap {\bf Scat} = {\bf S}_{\beta+2n-1} \cup {\bf S}_{\beta+2n}}$ , and for a limit ordinal α, we have ${{\bf H}_{\alpha} \cap {\bf Scat} = {\bf S}_{\alpha}}$ . As a result, we obtain full and faithful translations of ordinal complete extensions of Grz into ordinal complete extensions of GL, thus generalizing the Kuznetsov–Goldblatt–Boolos theorem. (shrink)

It is a classic result in modal logic, often referred to as Jónsson-Tarski duality, that the category of modal algebras is dually equivalent to the category of descriptive frames. The latter are Kripke frames equipped with a Stone topology such that the binary relation is continuous. This duality generalizes the celebrated Stone duality for boolean algebras. Our goal is to generalize descriptive frames so that the topology is an arbitrary compact Hausdorff topology. For this, instead of working with the boolean (...) algebra of clopen subsets of a Stone space, we work with the ring of continuous real-valued functions on a compact Hausdorff space. The main novelty is to define a modal operator on such a ring utilizing a continuous relation on a compact Hausdorff space.Our starting point is the well-known Gelfand duality between the category ${\sf KHaus}$ of compact Hausdorff spaces and the category $\boldsymbol {\mathit {uba}\ell }$ of uniformly complete bounded archimedean $\ell $ -algebras. We endow a bounded archimedean $\ell $ -algebra with a modal operator, which results in the category $\boldsymbol {\mathit {mba}\ell }$ of modal bounded archimedean $\ell $ -algebras. Our main result establishes a dual adjunction between $\boldsymbol {\mathit {mba}\ell }$ and the category ${\sf KHF}$ of what we call compact Hausdorff frames; that is, Kripke frames equipped with a compact Hausdorff topology such that the binary relation is continuous. This dual adjunction restricts to a dual equivalence between ${\sf KHF}$ and the reflective subcategory $\boldsymbol {\mathit {muba}\ell }$ of $\boldsymbol {\mathit {mba}\ell }$ consisting of uniformly complete objects of $\boldsymbol {\mathit {mba}\ell }$. This generalizes both Gelfand duality and Jónsson-Tarski duality. (shrink)

Tens of thousands of students have learned to be more discerning at constructing and evaluating arguments with the help of Patrick J. Hurley. Hurley’s lucid, friendly, yet thorough presentation has made A CONCISE INTRODUCTION TO LOGIC the most widely used logic text in North America. In addition, the book’s accompanying technological resources, such as CengageNOW and Learning Logic, include interactive exercises as well as video and audio clips to reinforce what you read in the book and hear in class. (...) In short, you’ll have all the assistance you need to become a more logical thinker and communicator. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. (shrink)

An e-mail discussion can be rendered into print in several ways. Rather than trying to imitate a genuine conversation, this is a personal essay containing comments and replies by the other contributors. Most of the substantial points made in the e-mail discussion are contained here, although not always in the order they happened.

In this paper we argue that Prior and Reichenbach are best viewed as allies, not antagonists. We do so by combining the central insights of Prior and Reichenbach in the framework of hybrid tense logic. This overcomes a well-known defect of Reichenbach’s tense schema, namely that it gives multiple representations to sentences in the future perfect and the future-in-the-past. It also makes it easy to define an iterative schema for tense that allows for multiple points of reference, a possibility noted (...) by Prior and demanded by Comrie, and we sketch how this schema can be generalized to a shift-and-restrict pattern in which special propositional symbols act as restrictors on the range of tense operators. (shrink)

Gerrit Lindeboom’s biography, Herman Boerhaave: The Man and His Work, presents a heroic account of Herman Boerhaave’s life and his many contributions to medicine and medical education. He is portrayed as an outstanding eighteenth century educator who introduced into Leiden’s Medical School a novel method of clinical teaching that was to be widely adopted and today remains at the centre of medical student instruction. Lindeboom’s historiography induced a resurgence of interest in Boerhaave, a renewal of the myth concerning Boerhaave’s innovative (...) teaching and the publication of many acclamatory articles and false epithets, and several critical analyses. Such varying responses prompted this critical examination of the extant Boerhaavian literature, an appraisal of Lindeboom’s objectivity and an assessment of his representations of Boerhaave’s clinical teaching. In doing so, the moral nature of his historiography and that of those who were to sustain his assertions will be established, and the myth that surrounds the novelty and excellence of Boerhaave’s clinical teaching will be evident. (shrink)

This book examines the theory and practice of argument in primary, secondary and tertiary education. Several of its chapters offer theoretical discussion of the forms and functions of argument within social, philosophical, historical and rhetorical contexts.

Despite its philosophical interest, Susanna Newcome’s Enquiry Into the Evidence of the Christian Religion (1728, revised 1732) has received little attention from commentators. This paper seeks to redress this oversight by offering a reconstruction of Newcome’s innovative argument for God’s existence. Newcome employs a cosmological argument that differs from Thomist and kalām version of the argument. Specifically, Newcome challenges that idea that the causal chains observed in nature can exist independently. She does this through an appeal to findings from Newtonian (...) natural philosophy that suggest that the universe has entropic tendencies. This suggests that the continued operations of nature are dependent on a cause external to the universe. Newcome identifies this external cause with God. Various strengths and weaknesses of Newcome’s argument are discussed and an attempt is made to situate the argument within her broader epistemic framework and the larger context of Newtonian physico-theology. The paper also explores what is known of Newcome’s biography and intellectual milieu. (shrink)

On the 4th of December 1967, Hans Kamp sent his UCLA seminar notes on the logic of ‘now’ to Arthur N. Prior. Kamp’s two-dimensional analysis stimulated Prior to an intense burst of creativity in which he sought to integrate Kamp’s work into tense logic using a one-dimensional approach. Prior’s search led him through the work of Castañeda, and back to his own work on hybrid logic: the first made temporal reference philosophically respectable, the second made it technically feasible in a (...) modal framework. With the aid of hybrid logic, Prior built a bridge from a two-dimensional UT calculus to a one-dimensional tense logic containing the ‘now’ operator J. Drawing on material from the Prior archive, and the paper “‘Now”’ that detailed Prior’s findings, we retell this story. We focus on Prior’s completeness conjecture for the hybrid system and the role played by temporal reference. (shrink)

This anthology assembles original contributions by leadinganalytical philosophers to a broad range of topics on whichSuppes set out ideas which still point the way ahead. All the papersincluded were originally given at the 1st International LauenerSymposium on Analytical Philosophy, which accompanied the Presentationof the first Lauener Prize to Patrick Suppes. His detailedcommentaries on each of the revised articles as well as the addedinterview elicit a spirit of constructive academic conversation.The book joins together contributions by Patrick Suppes, DagfinnFllesdal, Nancy (...) Cartwright, Wilhelm K. Essler, Steven French,Stephan Hartmann, and Michael Frauchiger. The collection as awhole puts a different and stimulating perspective on a varietyof issues in the methodology of science and philosophy. (shrink)

This monograph is set forth in three sections. The first presents Whitehead's "La théorie Relationniste De L'Espace" in the original French. With the exception of page numerals, this reproduction is an exact duplicate of the original printing. (See the Commentary, p.65, for references.) The second section consists of an English translation of this essay. Here the aim has been the faithful rendering of Whitehead's ideas—sometimes, perhaps, at the expense of rhetorical polish. The third section, the commentary, attempts to shed some (...) light on some of the philosophical and mathematical difficulties of the essay.My thanks are extended to Librairie Armand Colin for granting me permission to reproduce the French original. (shrink)

In this paper I argue for an association between impurity and explanatory power in contemporary mathematics. This proposal is defended against the ancient and influential idea that purity and explanation go hand-in-hand (Aristotle, Bolzano) and recent suggestions that purity/impurity ascriptions and explanatory power are more or less distinct (Section 1). This is done by analyzing a central and deep result of additive number theory, Szemerédi’s theorem, and various of its proofs (Section 2). In particular, I focus upon the radically impure (...) (ergodic) proof due to Furstenberg (Section 3). Furstenberg’s ergodic proof is striking because it utilizes intuitively foreign and infinitary resources to prove a finitary combinatorial result and does so in a perspicuous fashion. I claim that Furstenberg’s proof is explanatory in light of its clear expression of a crucial structural result, which provides the “reason why” Szemerédi’s theorem is true. This is, however, rather surprising: how can such intuitively different conceptual resources “get a grip on” the theorem to be proved? I account for this phenomenon by articulating a new construal of the content of a mathematical statement, which I call structural content (Section 4). I argue that the availability of structural content saves intuitive epistemic distinctions made in mathematical practice and simultaneously explicates the intervention of surprising and explanatorily rich conceptual resources. Structural content also disarms general arguments for thinking that impurity and explanatory power might come apart. Finally, I sketch a proposal that, once structural content is in hand, impure resources lead to explanatory proofs via suitably understood varieties of simplification and unification (Section 5). (shrink)

This debate, principally between myself (Nigel Thomas) and Patrick Hayes, the well known computer scientist and Artificial Intelligence researcher, took place through the internet mailing list for the discussion of the scientific study of consciousness, PSYCHE-D (moderated by Patrick Wilken), which is associated with the on-line journal PSYCHE. The discussion touches on the various different senses in which the expression "mental image" may be used, the underlying cognitive mechanisms of imagery, and the relevance of an understanding of imagery (...) to the understanding of conscious thought, and thought in general. As the debate became rather 'unthreaded' on the list, following it through this page may help the reader to better understand what was going on. (shrink)

_"One of the most important political books of 2018."—Rod Dreher, ___American Conservative__ Of the three dominant ideologies of the twentieth century—fascism, communism, and liberalism—only the last remains. This has created a peculiar situation in which liberalism’s proponents tend to forget that it _is _an ideology and not the natural end-state of human political evolution. As Patrick Deneen argues in this provocative book, liberalism is built on a foundation of contradictions: it trumpets equal rights while fostering incomparable material inequality; its (...) legitimacy rests on consent, yet it discourages civic commitments in favor of privatism; and in its pursuit of individual autonomy, it has given rise to the most far-reaching, comprehensive state system in human history. Here, Deneen offers an astringent warning that the centripetal forces now at work on our political culture are not superficial flaws but inherent features of a system whose success is generating its own failure. (shrink)

This paper provides a response to Hanna Pickard and Stephen Pearce’s paper ‘Balancing costs and benefits: a clinical perspective does not support a harm minimisation approach for self-injury outside of community settings.’ This paper responded to my article ‘Should healthcare professionals sometimes allow harm? The case of self-injury.’ There is much in the paper that I would agree with, but I feel it is important to respond to a number of the criticisms of my paper in order to clarify my (...) position and to facilitate ongoing debate in relation to this important issue. (shrink)

Rendall and Whitehead overstate the weak evidence for social learning in cetaceans as a group, including the current evidence for vocal learning in killer whales. Ethnographic techniques exist to test genetic explanations of killer whale calling behavior, and additional captive experiments are feasible. Without such tests, descriptions of learning could be considered pseudo-scientific, ad hoc auxiliary assumptions of an untested theory.

During the last few years many writers have pointed out that notions like ‘family resemblance’, ‘open texture’ and ‘systematic ambiguity’ which play a considerable role in contemporary philosophy are akin to Aquinas' concept of analogy. Yet no one has made a thorough comparison between modern linguistic philosophy and the Thomistic doctrine of analogy. In this article I want to explore their relationship and to assess the value of the latter. Just how much has Aquinas to contribute to modern discussions about (...) the nature of language and about God's attributes? And does modern philosophy of language destroy Aquinas' case, or can it rather be used to supplement it? (shrink)

Herein are presented excerpts of papers read at the Philosophical Academy at Spokane this year. Should you wish to read more of any of these papers, it is suggested that you write to either Mr. Holloran, or to the author of the paper.

This paper offers a new approach to an old debate about superaddition in Locke. Did Locke claim that some objects have powers that are unrelated to their natures or real essences? The question has split commentators. Some (Wilson, Stuart, Langton) claim the answer is yes and others (Ayers, Downing, Ott) claim the answer is no. This paper argues that both of these positions may be mistaken. I show that Locke embraced a robust epistemic humility. This epistemic humility includes ignorance of (...) the real essences of bodies, of the causal processes underlying the production of natural phenomena, and of God’s method of creation. I show how this epistemic humility offers strong support for an agnostic response to the question of superaddition. Locke did not intend to claim that bodies either do or do not have properties unrelated to their real essences. Instead, his primary goal in discussing the topic was to emphasize the strict limits to human knowledge. (shrink)

This chapter examines a little-known movement to make the Our Lady of Perpetual Help icon the patroness of the proceedings of the Second Vatican Council. Begun by American Redemptorists, it sought to integrate a Marian piety into the conciliar ethos, but one that was decidedly cross-cultural and ecumenical. Explicit in its mission for unity between Roman Catholics and the separated churches of the East, the movement promoted the icon as the key to repairing centuries-old wounds. Insofar as 2015 begins the (...) sesquicentennial year of the icon’s association with Redemptorists, as well as its value as an ecumenical tool, the author explores whether OLPH can lend new impetus for unity between Orthodox and Catholics ahead of the proposed joint synod in 2025. (shrink)

Wilfrid Sellars, Idealism, and Realism is the first study of its kind to address a range of realist and idealist views inspired by psychological nominalism. Bringing together premier analytic realists and distinguished defenders of German idealism, it reveals why psychological nominalism is one of the most important theories of the mind to come out the 20th century. The theory, first put forward by Wilfrid Sellars, argues that language is the only means by which humans can learn the types of socially (...) shared practices that permit rationality. Although wedded to important aspects of German idealism, Sellars' theory is couched in bold realist terms of the analytic tradition. Those who are sympathetic to German idealism find this realist's appropriation of German idealism problematic. Wilfrid Sellars, Idealism and Realism thus creates a rare venue for realists and idealists to debate the epistemic outcome of the mental processes they both claim are essential to experience. Their resulting discussion bridges the gap between analytic and continental philosophy. In providing original and accessible chapters on psychological nominalism, this volume raises themes that intersect with numerous disciplines: the philosophy of mind, philosophy of language, epistemology, and metaphysics. It also provides clarity on arguably the best available account of why humans can reason, be self-aware, know, and act as agents. (shrink)

Despite any shortcomings of Kant's transcendental philosophy, the spirit of Kant's approach is correct. In particular, Kant is correct to believe an accurate account of the types of “access” humans possess to internal and empirical content should form the groundwork for epistemic and ethical investigation and epistemic and ethical investigations cannot successfully circumvent this groundwork. In this context, the term “access” concerns the mental processes that render internal and external experience possible. In supporting the above claims, this article outlines and (...) defends what can be considered a weak version of Kant's transcendental approach. This weaker approach does not require the achievement of synthetic a priori judgments, which permit deductive conclusions concerning possible experience. (shrink)

How are we to make sense of madness and psychosis? For most of us the words conjure up images from television and newspapers of seemingly random, meaningless violence. It is something to be feared, something to be left to the experts. But is madness best thought of as a medical condition? Psychiatrists and the drug industry maintain that psychoses are brain disorders amenable to treatment with drugs, but is this actually so? There is no convincing evidence that the brain is (...) disordered in psychosis, yet governments across the world are investing huge sums of money on mental health services that take for granted the idea that psychosis is an illness to be treated with medication. Although some people who use mental health services find medication helpful, many do not, and resist the idea that their experiences are symptoms of illnesses like schizophrenia. Consequently they are forced into having treatment against their wishes. So, how do we make sense of this situation? Postpsychiatry addresses these questions. It involves an attempt to rethink some of the fundamental assumptions of mental health work, showing how recent developments in philosophy and ethics can help us to clarify some of the dilemmas and conflicts around different understandings of madness. Throughout, the authors examine the conflicting ways in which politicians, academics, and mental health professionals appear to understand madness, and contrast this with voices and experiences that are usually excluded - those of the people who use mental health services. They then examine the power of psychiatry to shape how we understand ourselves and our emotions, before considering some of the basic limitations of psychiatry as science to make madness meaningful. In the final section of the book they draw on evidence from service users and survivors, the humanities and anthropology, to point out a new direction for mental health practice. This new direction emphasises the importance of cultural contexts in understanding madness, placing ethics before technology in responding to madness, and minimising 'therapeutic' coercion. (shrink)

This essay examines the cometary theory of Johannes Kepler and his claim that an “ethereal spirit” could lead a comet to appear at a providential place and time. In his account of the comet of 1607, Kepler suggested that a spirit served as a navigational principle that steered the comet on a particular course. I argue that this principle was an extension of Kepler’s celestial physics and part of his larger conception of causes at work in the heavens. I also (...) explore the critical response Kepler received from the theological faculty at the University of Leipzig, where he planned to publish his account. I explain why Kepler turned to natural philosophy to resolve the opposition of his religious authorities and how this was received as a foreign incursion on Sacred Scripture. In my final analysis, I discuss whether Kepler ultimately abandoned spiritual principles in his cometary theory and arrived at a system of celestial physics that was fully free of animistic ideas. (shrink)

This article explores the tension between the antithetical philosophies of empiricism and innatism underlying Chomskyan linguistics. It first follows the trail of empiricism in North American linguistics, starting from the work of Leonard Bloomfield at the beginning of the Twentieth century, and its influence on the Chomskyan paradigm, after which the Kantian trail of innatism initiated by Chomsky himself is reconnoitered. It is argued that the Chomskyan approach to natural language represents a paradigmatic example of the unsavory consequences of the (...) divorce between mind and matter instituted by Kant, in particular because human language involves an intimate relation between both types of reality. In Chomsky’s Generative Grammar, on the other hand, the material side of language is treated as completely autonomous from its mental correlate and analyzed in terms of a priori conceptual structures and computational operations; for its part, the mental side of language is treated as innate; the relation between the two is thus made utterly obscure and incomprehensible. The conclusion of the article argues in favour of a more balanced approach inspired by Aristotelianism and Paul Ricoeur’s hermeneutics. (shrink)

Do children derive different benefits from group collaboration at different ages? In the present study, 183 children from two age groups took part in a class quiz as members of a group, or individually. In some groups, cohesiveness was made salient by awarding prizes to the top performing groups. In other groups, prizes were awarded to the best performing individuals. Findings, both in terms of social outcomes and performance in the quiz, indicated that the 8-year olds viewed the benefits of (...) group membership in terms of the opportunities to receive information from other members. The 13-year olds, in contrast, viewed group collaboration as a constructive process where success was connected with group cohesiveness. (shrink)

This paper analyzes the metaphysical system developed in Cheyne’s Philosophical Principles of Religion. Cheyne was an early proponent of Newtonianism and tackled several philosophical questions raised by Newton’s work. The most pressing of these concerned the causal origin of gravitational attraction. Cheyne rejected the occasionalist explanations offered by several of his contemporaries in favor of a model on which God delegated special causal powers to bodies. Additionally, he developed an innovative approach to divine conservation. This allowed him to argue that (...) Newton’s findings provided evidence for God’s existence and providence without the need for continuous divine intervention in the universe. (shrink)