The connections between mathematical logic and combinatorics have a rich history. This paper focuses on one aspect of this relationship: understanding the strength, measured using the tools of computability theory and reverse mathematics, of various partition theorems. To set the stage, recall two of the most fundamental combinatorial principles, König's Lemma and Ramsey's Theorem. We denote the set of natural numbers by ω and the set of finite sequences of natural numbers by ω<ω. We also identify each n ∈ ω (...) with its set of predecessors, so n = {0, 1, 2, …, n − 1}. (shrink)

We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. Connected choice is the operation that finds a point in a non-empty connected closed set given by negative information. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the Euclidean unit cube of the same dimension. Another main result is that connected choice is complete for dimension greater than (...) or equal to two in the sense that it is computably equivalent to Weak Kőnig’s Lemma. While we can present two independent proofs for dimension three and upward that are either based on a simple geometric construction or a combinatorial argument, the proof for dimension two is based on a more involved inverse limit construction. The connected choice operation in dimension one is known to be equivalent to the Intermediate Value Theorem; we prove that this problem is not idempotent in contrast to the case of dimension two and upward. We also prove that Lipschitz continuity with Lipschitz constants strictly larger than one does not simplify finding fixed points. Finally, we prove that finding a connectedness component of a closed subset of the Euclidean unit cube of any dimension greater than or equal to one is equivalent to Weak Kőnig’s Lemma. In order to describe these results, we introduce a representation of closed subsets of the unit cube by trees of rational complexes. (shrink)

In his recent paper ‘Knowing What Things Look Like’, Matthew McGrath offers a challenge to the idea that knowing an object by seeing it, ‘visual objectual knowledge’ is an instance of immediate knowledge. I offer supporters of the notion of immediate visual objectual knowledge two potential strategies for blocking McGrath’s argument: either by questioning McGrath’s claim about the role that knowing what an object looks like plays in visual objectual knowledge or by denying that any explanation of how knowing what (...) an object looks like plays that role must proceed through an appeal to factual knowledge involving that object’s looks. (shrink)

The debate concerning the role of intuitions in philosophy has been characterized by a fundamental disagreement between two main camps. The first, the autonomists, hold that, due to the use in philosophical investigation of appeals to intuition, most of the central questions of philosophy can in principle be answered by philosophical investigation and argument without relying on the sciences. The second, the naturalists, deny the possibility of a priori knowledge and are skeptical of the role of intuition in providing evidence (...) in philosophical inquiry. In spite of the seemingly stark and deep disagreement between the autonomist and the naturalist, in this paper I will attempt to suggest that there is a way to mount a partial defense of intuition-based philosophical practice on naturalist grounds. As will be seen, doing so will require a number of concessions that will satisfy few autonomists while simultaneously disappointing those naturalists who might have thought that all notions of the a priori had been successfully laid to rest. However, I will argue that the account proposed here will preserve those features of traditional philosophical practice that matter most and better explain the history of successes and failures of that practice, thus answering the worries of the autonomist, and that the rejection of the No A Priori Thesis attendant with the account presented here is indeed demanded by the current theories of our best scientific understanding of the mind, thus pacifying the rabid naturalistic critic of any version of apriorism. (shrink)

The idea of God: absolute intellectuality.-- The creation: absolute emanation.-- Matter and force: the universe in its potentiality and actuality.-- The universal mechanism: motion and its transformations.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in (...) the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Most discussions of the epistemology of testimony include personalist requirements. These include either requirements that stipulate certain features that individual testifiers must have in order to count as transmitters of knowledge, or that stipulate certain features that individual recipients of testimony must have in order to count as acquiring knowledge on the basis of that testimony. For example, in the former case, many views require that testifiers be competent and honest, whereas, in the latter case, many views require that recipients (...) of testimony employ faculties for reliably assessing the competence and honesty of testifiers. After presenting and discussing problems for both of these personalist requirements, in this chapter we consider a social epistemology of testimony based on socially distributed cognitive systems, an epistemology of testimony that eschews both forms of personalist requirement. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Christianity and the Religions: From Confrontation to DialogueJohn BorelliChristianity and the Religions: From Confrontation to Dialogue. By Jacques Dupuis, SJ. Maryknoll, NY: Orbis Books, 2001. 276 pp.Why read Jacques Dupuis's Christianity and the Religions (2001) when his more comprehensive, ground-breaking Toward a Christian Theology of Religious Pluralism (Orbis, 1997) is still available? Father Dupuis reminds us in the introduction to Christianity that he has actually written three books (...) on the same subject—Jesus Christ at the Encounter of World Religions (Orbis, 1991) being the first—but he reaffirms the central importance of Religious Pluralism. After publication of this second work, his editors wanted another volume on the same topic, "less ponderous, more accessible, and aimed at an audience broader than the circle of specialists and the academy." That was the origin of Christianity and the Religions, a story Fr. Dupuis related to me when I visited him at Gregorian University in early February 2001. It was meant to be an easier-to-read version of Religious Pluralism, something for students who do not need abundant references to authors and historical developments. Circumstances, however, added another dimension to the need for yet another volume. [End Page 182]Christianity and the Religions was ready for publication in early 2001, but Fr. Dupuis was waiting for "official notification" from the Holy See's Congregation for the Doctrine of the Faith regarding its charges that Religious Pluralism contained "serious doctrinal error." By then, the case was in its thirty-second and final month, for later in February 2001 he received word from Cardinal Joseph Ratzinger, prefect of the Congregation, that the charge had been reduced to "ambiguities and difficulties on important points which could lead a reader to erroneous or harmful opinions." Dupuis last appeared before Cardinal Ratzinger and the Congregation's advisers on the day before Dominus Iesus was released in September 2000, accompanied by Fr. Peter-Hans Kolvenbach, superior general of the Jesuits, and Dupuis's advocate and colleague at the Gregorian University, Fr. Gerald O'Collins. Dupuis used the opportunity of a more accessible version of the book in question to address squarely the charges raised against him. He writes in the introduction to Christianity and the Religions: "Suffice it to say that in this new book I have scrupulously avoided all expressions that could raise any misunderstanding or create ambiguity over either the content of the faith or my thought." Dupuis dedicated the book to retired Cardinal Franz Kōnig. He chose to quote an earlier (1963) text by Cardinal Ratzinger on the page following the dedication: "What the Church needs today, as always, are not adulators to extol the status quo, but men whose humility and obedience are no less than their passion for truth: men who brave every misunderstanding and attack as they bear witness; men who in a word, love the Church more than ease and the unruffled course of their personal destiny." In 1999, Ratzinger and Kōnig had exchanged views, point and counterpoint, in the British Catholic weekly, The Tablet, over Dupuis's earlier Religious Pluralism.Fr. Jacques Dupuis died of an apparent stroke on 28 December 2004 at age 81. Although the investigation had brought him increased attention and invitations to speak, he was in Rome, his home since 1984, at the time of his death. When I visited him in 2001 and again heard him speak at the Catholic University of America just twenty-four days before his death, it was clear how much the case and accompanying suspicion had hurt him. Dupuis was principally a theologian who had considered it his good fortune to have lived and taught in India for thirty-six years. He also had taught theology for nearly fifteen years at Gregorian University, the premier university of his religious order. Many viewed the outcome of the investigation as a vindication of his work because he did not have to change a single sentence in Religious Pluralism for it to remain in publication, but the success of his defense came at a great price. The shadow of suspicion never left him. He had adopted a style of stopping, often amidst reflections on religious... (shrink)

In a number of recent articles, Hartry Field has attempted to reclaim the a priori for his own brand of non‐factualist epistemology by introducing a non‐epistemic notion of the a priori based purely upon the position of individual beliefs within belief systems. In this article we examine (i) whether a robust enough notion of aprioricity is available to Field, and, by extension, to the radical empiricist and (ii) whether it is possible to connect up the non‐epistemic notion of aprioricity with (...) questions about the epistemic status of those beliefs that happen to be a priori in the non‐epistemic sense. (shrink)

Longlisted for the PEN/E.O. Wilson Literary Science Writing Award A leading neuroscientist offers a history of the evolution of the brain from unicellular organisms to the complexity of animals and human beings today Renowned neuroscientist Joseph LeDoux digs into the natural history of life on earth to provide a new perspective on the similarities between us and our ancestors in deep time. This page-turning survey of the whole of terrestrial evolution sheds new light on how nervous systems evolved in (...) animals, how the brain developed, and what it means to be human. In The Deep History of Ourselves, LeDoux argues that the key to understanding human behavior lies in viewing evolution through the prism of the first living organisms. By tracking the chain of the evolutionary timeline he shows how even the earliest single-cell organisms had to solve the same problems we and our cells have to solve each day. Along the way, LeDoux explores our place in nature, how the evolution of nervous systems enhanced the ability of organisms to survive and thrive, and how the emergence of what we humans understand as consciousness made our greatest and most horrendous achievements as a species possible. (shrink)

A defining characteristic of Alzheimer’s disease is difficulty in retrieving semantic memories, or memories encoding facts and knowledge. While it has been suggested that this impairment is caused by a degradation of the semantic store, the precise ways in which the semantic store is degraded are not well understood. Using a longitudinal corpus of semantic fluency data, we derive semantic network representations of patients with Alzheimer’s disease and of healthy controls. We contrast our network-based approach with analyzing fluency data with (...) the standard method of counting the total number of items and perseverations in fluency data. We find that the networks of Alzheimer’s patients are more connected and that those connections are more randomly distributed than the connections in networks of healthy individuals. These results suggest that the semantic memory impairment of Alzheimer’s patients can be modeled through the inclusion of spurious associations between unrelated concepts in the semantic store. We also find that information from our network analysis of fluency data improves prediction of patient diagnosis compared to traditional measures of the semantic fluency task. (shrink)

Joseph Owens presents an introduction to metaphysics designed to develop in the reader a habitus of thinking. Using original Thomistic texts and Etienne Gilson's interpretation of St. Thomas Aquinas, Owens examines the application of metaphysical principles to the issues that arise in a specifically Christian environment. An Elementary Christian Metaphysics focuses on questions of existence and the nature of revealed truths. Following his historical introduction to metaphysics, Owens provides a general investigation of the first principles and causes of being (...) and also a study of knowledge and of the divine nature and attributes in light of natural reason. "Irrespective of one's intellectual genotype, an exposure to the sustained, developmental elucidation of Aquinas' insights executed by an author such as Owens can only enhance any metaphysical approach to reality." --The New Scholastic "An Elementary Christian Metaphysics is intended primarily for undergraduate students as an introduction to metaphysics. . . . The scope of the metaphysical study pursued by Owens includes not only a general investigation of beings but also an analysis of knowledge (epistemology) and of the divine nature, all in light of natural reason." --Studies in Religion Joseph Owens (1908-2005) taught philosophy at the Pontifical Institute of Mediaeval Studies and the University of Toronto for forty years. He is the author of a number of books, including An Interpretation of Existence, also published by the University of Notre Dame Press. (shrink)

The Specter of Capital provides a searching historical analysis and critique of the role of classical and neoclassical economic theory in creating the economic conditions which produced the global financial crisis.

Entre 1150 et 1280, le monde latin herite de la totalite de l'oeuvre d'Aristote par la biais d'une vaste entreprise de traductions du grec et de l'arabe, accompagnee d'interpretations arabes et neoplatoniciennes, et se trouve ainsi confronte a de nouvelles theories face auxquelles il s'agit de mettre en place des strategies d'assimiltation. Par l'etude des textes, ce livre restaure le temoignage de ces entreprises relativement aux lectures arabes de la Metaphysique et a la notion de matiere. Ou l'on voit qu'a (...) Paris, des disputes se mettent en place pour debattre sur les notions d'etre et d'essence, de temporalite et d'historicite du monde, de possibilite des choses et du statut des relations. Sont egalement abordees les difficultes theoriques que rencontrent les lecteurs latins face aux textes aristoteliciens, de Thomas d'Aquin a Guillaume d'Ockham, pour en mettre les principes au service de leur cosmogonie et de leur anthropologie. (shrink)

We document outcome bias in situations where an agent makes risky financial decisions for a principal. In three experiments, we show that the principal’s evaluations and financial rewards for the agent are strongly affected by the random outcome of the risky investment. This happens despite her exact knowledge of the investment strategy, which can, therefore, be assessed independently of the outcome. The principal thus judges the same decision by the agent differently, depending on factors that the agent has no influence (...) on. The effect of outcomes persists in a setting where principals communicate a preferred investment level. Principals are more satisfied with the agent after a random success when the agent did not follow the requested investment level, than after a failed investment that followed their explicit request. (shrink)

Joseph Priestley (1733-1804) was arguably the most important English theorist to focus on the issue of political liberty during the English Enlightenment. His concept of freedom is of crucial importance to two of the major issues of his day: the right of dissenters to religious toleration, and the right of the American colonists to self-government. Priestley's writings lack a modern edition and this new collection will be the first to render accessible his Essay on First Principles, The Present State (...) of Liberty and the Letter of Advice. An introduction and notes, and guides to further reading and key figures in the text provide the student with all the material necessary for approaching Priestley. (shrink)

In computer-mediated communication, users cannot ensure that responsive postings are placed in a directly adjacent position. Yet, paired actions are discernible in which a first pair part makes a second pair part conditionally relevant. While previous studies of short messaging service communication show that users usually send clusters of FPPs and that SPPs are ordered in the same chronology, little is known about sequential practices of dealing with multiple FPPs in text-based WhatsApp communication. This article shows that in German WhatsApp (...) dialogues, users apply a chronological as well as a reversed ordering of SPPs. It is argued that this result can only be partly attributed to the affordances of the mobile messenger. Rather, users arrange SPPs in order to foreground particular topics in extended, chat-like dialogues. (shrink)

We argue that brains generate predictions only within the constraints of the action repertoire. This makes the computational complexity tractable and fosters a step-by-step parallel development of sensory and motor systems. Hence, it is more of a benefit than a literal constraint and may serve as a universal normative principle to understand sensorimotor coupling and interactions with the world.

ABSTRACTMichelle Amazeen's rebuttal of Uscinski and Butler 2013 is unsuccessful. Amazeen's attempt to infer the accuracy of fact checks from their agreement with each other fails on its own terms and, in any event, could as easily be explained by fact checkers’ political biases as their common access to the objective truth. She also ignores the distinction between verifiable facts and unverifiable claims about the future, as well as contestable claims about the causes of political, social, and economic phenomena. The (...) social benefits that she claims for the fact-checking enterprise must, at the very least, be weighed against the strong possibility that what passes for fact checking is actually just a veiled continuation of politics by means of journalism rather than being an independent, objective counterweight to political untruths. (shrink)

JOSEPH AGASSI 1. Sir Karl Popper has offered two different theories of scientific progress, his theory of conjectures and refutations and corroboration, as well as his theory of verisimilitude increase. The former was attacked by some old-fashioned inductivists, yet is triumphant; the latter has been refuted by Tichy and by Miller to Popper’s own satisfaction. Oddly, however, the theory of verisimilitude was developed because of some deficiency in the theory of corroboration, and though in its present precise formulation it (...) was refuted, Popper still holds it in general terms, and I think he still hopes to find a better precise formulation of it. My aims in the present note are to pin-point the deficiency of Popper’s theory of corroboration and to use this for a precise formulation of verisimilitude increase acceptable to him. For my part, however, I see the situation in a different way, as will be indicated at the end of this note. (shrink)

Joseph Boyle discusses deontology, which derives precepts from moral principles, particularly making a case with reference to Alan Donagan's The Theory of Morality, which appeared the same year as Just and Unjust Wars.

SummaryChristian theologians can explain the Trinitarian faith today in dialogue with Islamic thinkers as “deepened monotheism”. Therefore it is important to widen the systematic-theological discourse in an ecumenical and transcultural perspective and to retrieve resources from Western and non-Western traditions of Trinitarian thought (I).In this paper I will first work out historically that the Trinitarian creed of Nicea and Constantinople was originally an ecumenical but non-Western creed (II). Afterwards, I investigate the philosophical-theological reflection on the Trinity by Anselm of Canterbury (...) (1033–1109) in the context of early interreligious encounters in the Latin West. Based on biblical, augustinian and Greek sources, he developed an approach to understand the mystery of the Trinity by rational arguments as “deepened monotheism” (III). Then I will proceed to explore the philosophical-theological dialogues on the Trinity from the Arabic philosopher and Syrian-orthodox theologian Yaḥyā ibn ‘Adī (893–974). Much earlier he developed rational arguments for the Triunity of God with reference to Aristotle. Thereby he answers to anti-trinitarian arguments from Islamic thinkers like al-Kindī and al-Warrāq. He intends that the Trinitarian faith of Christian minorities can thereby be understood and tolerated by Islamic thinkers as rationally founded “deepened monotheism” (IV).In the end I will evaluate what these classics from the Western and non-western traditions of Trinitarian thought contribute to explicate the doctrine of the Trinity today in a pluralistic religious context as “deepened monotheism” (V). (shrink)

Symptôme psychosomatique de la condition pécheresse de l’âme humaine, processus d’usure naturel et progressif de la machinerie psychique ou corporelle, propriété exclusive du monde des corps ou lieu de la ligature obligée de l’intellect au corps, la fatigue traverse la littérature philosophique et théologique médiévale. Les divers traitements de la fatigue peuvent à leur tour valoir comme symptômes pour différencier les approches anthropologiques médiévales. Cet article en présente quatre figures: l’anthropologie du danger élaborée par Augustin, le diagnostic médical grec et (...) arabe dont Constantin l’Africain est le passeur au xi e siècle, et les lectures de la psychologie d’Aristote par Albert le Grand et Thomas d’Aquin au xiii e siècle. (shrink)

Specifying accurate informative prior distributions is a question of carefully selecting studies that comprise the body of comparable background knowledge. Psychological research, however, consists of studies that are being conducted under different circumstances, with different samples and varying instruments. Thus, results of previous studies are heterogeneous, and not all available results can and should contribute equally to an informative prior distribution. This implies a necessary weighting of background information based on the similarity of the previous studies to the focal study (...) at hand. Current approaches to account for heterogeneity by weighting informative prior distributions, such as the power prior and the meta-analytic predictive prior are either not easily accessible or incomplete. To complicate matters further, in the context of Bayesian multiple regression models there are no methods available for quantifying the similarity of a given body of background knowledge to the focal study at hand. Consequently, the purpose of this study is threefold. We first present a novel method to combine the aforementioned sources of heterogeneity in the similarity measure ω. This method is based on a combination of a propensity-score approach to assess the similarity of samples with random- and mixed-effects meta-analytic models to quantify the heterogeneity in outcomes and study characteristics. Second, we show how to use the similarity measure ωas a weight for informative prior distributions for the substantial parameters in Bayesian multiple regression models. Third, we investigate the performance and the behavior of the similarity-weighted informative prior distribution in a comprehensive simulation study, where it is compared to the normalized power prior and the meta-analytic predictive prior. The similarity measure ω and the similarity-weighted informative prior distribution as the primary results of this study provide applied researchers with means to specify accurate informative prior distributions. (shrink)