The great mathematician, physicist, and philosopher, Hermann Weyl, once called mathematics the “science of the infinite.” This is a fitting title: contemporary mathematics—especially Cantorian set theory—provides us with marvelous ways of taming and clarifying the infinite. Nonetheless, I believe that the epistemic significance of mathematical infinity remains poorly understood. This dissertation investigates the role of the infinite in three diverse areas of study: number theory, cosmology, and probability theory. A discovery that emerges from my work is that the epistemic role (...) of the infinite varies, often in surprising ways, across different domains of knowledge. -/- My first chapter examines the role of mathematical infinity in number theory. It is reasonable to think that theorems concerning finite patterns and structures in the natural numbers are particularly “simple” or “elementary.” Indeed, such statements are comprehensible to a wide range of investigators, regardless of their mathematical training. One might then expect proofs of these theorems to be similarly comprehensible. However, many proofs, especially those that utilize only finitary methods, are exceedingly difficult to understand. Consequently, one finds that finitary theorems are often re-proved using infinitary techniques. My claim is that this is because infinitary proofs are often explanatory, while finitary proofs are not. This chapter analyzes why this is the case. Along the way, I investigate other questions of long-standing interest in the philosophy of mathematics, e.g., the role of purity/impurity ascriptions and the nature of the content of a theorem. In particular, I diagnose the explanatory potential of the infinite by articulating a new construal of content. This new construal both saves intuitive epistemic ascriptions made in mathematical practice and explains the unexpected role of the infinite in providing explanatory proofs of finitary statements. Thus, in number theory, my claim is that the infinite often plays an explanatory role. -/- My second chapter turns to the role of the infinite in cosmology. It investigates a question much discussed by philosophers and physicists alike: is the spatial extent of the universe finite or infinite? Contemporary cosmological research has indicated that one of the essential determinants of the extent of the universe is the topology we ascribe to space. Topology is a global property, which may suggest that it is not testable through local observation. Nonetheless, some cosmologists have indicated that it may be empirically detected, thereby providing an answer to the question of spatial extent. I argue that, in fact, the epistemic status of the topology of space is extremely subtle and not well captured by any of the categories commonly employed by philosophers of science. In particular, I argue that topological properties are neither empirical nor a priori (even in suitably weakened senses). Furthermore, I claim that we should prefer topological properties that generate finite universe models (consistent with our best data) in order to avoid extremely thorny issues concerning the physics of an infinite universe. I argue for such a preference on the grounds of the simplicity and explanatory power of finite universe models. Thus, in cosmology, my claim is that the finite often plays an explanatory and simplifying role. -/- My third chapter investigates several paradoxes that arise in the foundations of infinitary probability theory: the Label Invariance Paradox, God’s Lottery, and Bertrand’s Paradox. I argue that these have been poorly understood because they do not expressly concern probability theory, but rather our intuitions about—and formal techniques for dealing with— infinite sets. The paradoxes in question are, in fact, symptoms of our complete reliance upon Cantorian cardinality and its associated criterion of sameness of “size.” That is, two sets have the same cardinality if and only if the elements of the sets can be placed in 1-1 correspondence. When applied to infinite sets, this criterion produces counterintuitive verdicts. For instance, given a fair lottery on the natural numbers, we expect that the probability of drawing an even number is 1/2, and likewise for drawing an odd number. However, one can construct “relabellings” of the naturals such that the probability of drawing an even number remains 1/2, while the probability for drawing an odd number becomes 1/4. I argue that, ultimately, it is the coarseness of Cantorian cardinality that generates the probabilistic paradoxes. I then propose that finer-grained measures of infinite sets from mathematical logic and number theory can help to dissolve the paradoxes in question. Thus, in probability theory, we find that particular kinds of infinitary techniques effectively systematize our theory, while others lead to paradox. (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)

While the subjective experience of insight during problem solving is a common occurrence, an understanding of the processes leading to solution remains relatively uncertain. The goal of this study was to investigate the restructuring patterns underlying solution of a creative problem, and how providing cues to solution may alter the process. Results show that both providing cues to solution and analyzing problem solving performance on an aggregate level may result in restructuring patterns that appear incremental. Analysis of performance on an (...) individual level provides evidence for insight-like solution patterns. However, no evidence is found for a relationship between an individual’s restructuring pattern and their subjective experience of insight during problem solving. (shrink)

?Objectivity?; has been a traditional ideal for American journalism despite recent characterizations of the principle as ?biased toward the status quo, against independent thinking, and against countenancing questions of morality and responsibility.?; This article explores the role of traditional objectivity in newspaper coverage of the nomination in Alaska of a socialist commissioner of environmental conservation and the subsequent ?framing?; of public discussion. The human qualities of sensitivity to history, to civil liberties, and to questions of morality appeared in editorials, but (...) professional norms of objectivity denied reporters the right to exercise their creativity and public responsibility. Reportorial sensitivity to diverse sources is necessary, supplemented by a fundamental and far?reaching examination of how reportorial language encodes public and private questions in ways that further established positions of power and privilege. (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)

_"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)

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)

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)

Both Holmes and Langdell believed that science was the model for all human inquiry and the source of all human progress. Langdell was influenced by an unsophisticated scientism, which led him to attempt to identify the true meaning of legal doctrines. Holmes was influenced by the sophisticated positivism of John Stuart Mill, which led him to attempt to reduce legal rules and doctrines to scientific laws of antecedence and consequence, justified only by their social consequences. Both Holmes and Langdell concluded (...) that judges ought to decide a case by applying the rules established by precedent, without appeal to any special claims of justice and without appeal to any higher‐order normative principle. (shrink)

ABSTRACT Social‐scientific data, such as those found in Philip E. Converse's 1964 essay, “The Nature of Belief Systems in Mass Publics,” have led some to question whether basic assumptions about democratic legitimacy are unfounded. However, by another set of criteria, we have the “democracy” that was intended by the Framers—namely, a liberal representative system that avoids strong civic engagement by the citizenry. At its deepest level, the American system has been designed to ensure elite influence over the main ambitions of (...) American policy: the expansion of public and private power. When social scientists accumulate findings of civic disengagement and ignorance, it is wrongly supposed to be an indictment of the citizenry; rather, those findings should be understood as the expected result of a certain set of commitments throughout American political history, of which civic apathy and ignorance are the desired outcomes. (shrink)

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 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)

This paper explores the metaphysical system developed in Richard Bentley’s 1692 Boyle Lectures. The lectures are notable for their attempt to argue that developments in natural philosophy, including Newton’s Principia, could bolster natural theology. The paper explores Bentley’s matter theory focusing on his commitment to a particular form of mechanism and his rejection of occult qualities. It then examines his views on the nature of divine omnipotence. Finally, it turns to his understanding of gravitational attraction. While some recent commentators have (...) argued for a “superaddition” interpretation of gravitation in Bentley, this paper argues for an “occasionalist” interpretation. The argument proceeds on the basis of both textual considerations and considerations stemming from the systematic interpretation of Bentley’s metaphysics developed earlier in the paper. (shrink)

ABSTRACTThe Chief Ethics and Compliance Officer is an essential and important function in organizations. The CECO position is, however, a relatively new position and, as such, is not yet institutionalized as a separate function within those organizations. This article addresses what the author believes are the reasons the CECO should be independent from the General Counsel and that the position should report to the highest levels within that organization, including the Board of Directors. The questions addressed will have a lasting (...) impact on the strength and lasting viability of the CECO in organizations in future years. The author outlines seven conditions that, if met, will enhance and fortify the CECO position for the future. (shrink)

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)

The central claim of this book is that the dichotomy between economic dependence and economic independence is completely inadequate for describing the political challenges faced by contemporary capitalist welfare states. The simplistic contrast between markets and states as sources of income renders invisible the relations of dependence established in our basic economic institutions such as the family, property, and money. This book is a work of political theory that attacks narrow conceptions of dependence and identifies distinct senses of dependence that (...) might allow political communities to make clearer decisions about the justice of our economic institutions and practices. Inheritance, for example, is as much a form of dependence as support by a welfare state, but these are never compared in debates about economic justice. This book begins the work of comparing forms of economic dependence, and argues that economic dependence is always an issue of both vulnerability and parasitism. It builds bridges between political theory and social science, and is of relevance to those concerned with social and economic justice in and beyond contemporary capitalist welfare states. (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)

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 paper explores Locke’s thinking specifically about syllogisms and more generally about logic and proper logical method. Locke’s texts display a mixed attitude toward syllogisms. On the one hand, he was highly critical of syllogisms and their central role in Scholastic disputation. On the other hand, he sometimes allowed that syllogisms could effectively capture valid forms of inference and could be useful in certain contexts. This paper seeks to explain Locke’s mixed attitude by showing that he believed syllogisms were useful (...) in the context of explanation but not in the context of discovery. Syllogisms could help to formalize and evaluate arguments already constructed using informal psychologistic methods, but they would not help to generate new arguments or to make new discoveries. The second part of the paper examines substantial changes to the fourth edition of the Essay in which Locke expands his critical remarks on syllogisms and related topics. Evidence is presented that strongly suggests Locke made these changes to the Essay in response to works published by John Sergeant. This discovery is important because it indicates Locke’s willingness to consider the views of his adversaries and reformulate his own views accordingly. (shrink)

Social entrepreneurship activity continues to surge tremendously in market and economic systems around the world. Yet, social entrepreneurship theory and understanding lag far behind its practice. For instance, the nature of the entrepreneurial discovery phenomenon, a critical area of inquiry in general entrepreneurship theory, receives no attention in the specific context of social entrepreneurship. To address the gap, we conceptualize social entrepreneurial discovery based on an extension of corporate social responsibility into social entrepreneurship contexts. We develop a model that emphasizes (...) mobilization and timing as underpinnings of social entrepreneurial discovery and offer distinct conceptual aspects and theoretic propositions instrumental to future social entrepreneurship research. (shrink)

Locke famously claimed that morality was capable of demonstration. But he also refused to provide a system of demonstrative morality. This paper addresses the mismatch between Locke’s stated views and his actual philosophical practice. While Locke’s claims about demonstrative morality have received a lot of attention it is rare to see them discussed in the context of his general theory of demonstration and his specific discussions of particular demonstrations. This paper explores Locke’s general remarks about demonstration as well as his (...) claims about demonstration in natural philosophy, mathematics, and morality. Careful attention to these detailed discussions motivates a reevaluation of Locke’s views on demonstrative knowledge of morality. Specifically, while Locke did believe that some demonstrative moral knowledge might be in-principle available to us he also believed that facts about the difficulty of demonstration meant that this knowledge would in-practice be largely unattainable. (shrink)

This article explores a previously neglected manuscript essay in which Thomas White offers an account of the metaphysics underpinning transubstantiation. White’s views are of particular interest because his explanation employs a broadly mechanist framework, rather than the hylomorphism traditionally associated with Roman Catholic discussions of the Eucharist. The manuscript helps to shed light on a number of topics of importance to early modern philosophy including the reception of Descartes’ views, the relationship between theology and natural philosophy, and mechanist accounts of (...) identity and individuation. (shrink)

This essay addresses a stream of thought manifested in some forms of social justice activism – namely, that members of marginalized groups have privileged insight into the nature of social reality which others cannot understand, much less critique. This position, which I call “epistemic isolationism,” seems to rest on the claim that the knowledge that is embedded in lived experience is incommunicable. The essay proceeds in three parts: first, there is a brief overview of standpoint epistemology, including a recent version (...) which seems to support epistemic isolationism. Second, there is an explication of the concept of “lived experience” as developed by Wilhelm Dilthey. Third, there is an argument against the claim that lived experience is incommunicable, drawing from the work of Dilthey, Hans-Georg Gadamer, and Paul Ricoeur. The payoff of the argument is that sharing lived experience through expressions like literature and narrative inspires mutual recognition and respect which can, in turn, support a robust form of solidarity and serve as a foundation for more effective social justice advocacy. (shrink)