In the Aristotelian tradition, the psychological difference between virtue and continence is commonly understood in terms of inner harmony versus inner conflict. Virtuous agents experience inner harmony between feeling and action because they do not care to do other than what their circumstances call for, whereas continent agents feel conflicted about doing what is called for because of competing concerns. Critics of this view argue, however, that when the circumstances require sacrificing something of genuine value, virtuous agents can indeed feel (...) conflicted about acting well. But if this is so, what differentiates virtuous from merely continent agency? This essay argues that the traditional distinction conflates two aspects of virtue as well as two species of continence. And distinguishing between them provides resources for making sense of the complex relationship between inner conflict and good moral agency. (shrink)

John Stuart Mill, whose relevance for Nietzsche’s late work has been documented by recent research, is not directly mentioned in On the Genealogy or Morality (1887). This article argues that Mill’s On Liberty (1859) nevertheless played a crucial role in the development of the Genealogy. Following a source-based methodology, three major references demonstrate how Nietzsche used On Liberty as a resource as he initiated and developed his own exploration into the origin of morality. After tracing Nietzsche’s reading of Mill through (...) pencil marks in his copy of On Liberty, I discuss the reappearance of Mill’s motives and terminology as well as the explanatory power of Mill as a source for the respective sections in the Genealogy. It becomes clear to what extent Nietzsche adapts Mill and how he turns Mill’s own weapons against him through skillful transformations. The article concludes that instead of delivering the “better” Mill, Nietzsche builds up a fruitful tension between a then-common take on morality and its transgression. (shrink)

We investigate how nonstandard reals can be established constructively as arbitrary infinite sequences of rationals, following the classical approach due to Schmieden and Laugwitz. In particular, a total standard part map into Richman's generalised Dedekind reals is constructed without countable choice.

ABSTRACTThis article examines the professional boundaries and obstacles encountered by Eritrean graduates of a medical interpreter course in Israel. Through a series of personal interviews held about a year after their graduation, we identified professional and personal boundaries as a recurring theme. Drawing on the inspiring work of Erving Goffman, we discuss the tension between their “normative roles” and “typical roles.” By deploying two heuristic two-way typologies—in reference to the service provider or the patient, and in reference to formal or (...) informal interpreting settings—we propose that the tension between the normative and the typical manifests most clearly within formal interpreting settings and vis-à-vis the service providers, and is least present outside formal settings and vis-à-vis the patients. Recognizing that the role of the interpreter tends to extend well beyond its formal setting, we conclude by reflecting on how the circumstances of marginalization and lack of support—incurred by t... (shrink)

The most comprehensive collection of essays on Descartes' scientific writings ever published, this volume offers a detailed reassessment of Descartes' scientific work and its bearing on his philosophy. The 35 essays, written by some of the world's leading scholars, cover topics as diverse as optics, cosmology and medicine, and will be of vital interest to all historians of philosophy or science.

Uniform sequential continuity, a property classically equivalent to sequential continuity on compact sets, is shown, constructively, to be a consequence of strong continuity on a metric space. It is then shown that in the case of a separable metric space, uniform sequential continuity implies strong continuity if and only if one adopts a certain boundedness principle that, although valid in the classical, recursive and intuitionistic setting, is independent of Heyting arithmetic.

This volume describes the main theoretical aspects of this practice based on an open-ended dialogue between a philosophical practitioner and a client or a group ...

In the early decades of the seventeenth century, various attempts were made to develop a dynamical vocabulary on the basis of work in the practical mathematical disciplines, particularly statics and hydrostatics. The paper contrasts the Mechanica and Archimedean approaches, and within the latter compares conceptions of statics and hydrostatics and their possible extensions in the work of Stevin, Beeckman and Descartes. Descartes’ approach to hydrostatics, a discussion of which forms the core of the paper, is shown to be quite different (...) from that of his contemporaries, above all in its attempt to provide a natural-philosophical grounding for hydrostatics while at the same time using it to develop a range of concepts, approaches and ways of thinking through problems that would shape Descartes’ mature work in optics and cosmology.Author Keywords: Scientific revolution; René Descartes; Isaac Beeckman; Simon Stevin; History of mechanics; History of statics; History of optics. (shrink)

According to agent-centered virtue ethics, acting well is not a matter of conforming to agent-independent moral standards, like acting so as to respect humanity or maximize utility. Instead, virtuous agents determine what is called for in their circumstances through good practical reason. This is an attractive view, but it requires a plausible account of how good practical reason works. To that end, some theorists invoke the skill model of virtue, according to which virtue involves essentially the same kind of practical (...) reason as ordinary skills. I contend, however, that ordinary skills provide a plausible and informative model of good practical reason only insofar as they are assessed by agent-independent standards. And so virtue, likewise, must be assessed primarily by agent-independent moral standards, if the skill model is to serve its purpose. I consider how agent-centered virtue ethics might avert this dilemma. But I ultimately suggest proceeding a different way. (shrink)

Self-referential sentences have troubled our understanding of language for centuries. The most famous self-referential sentence is probably the Liar, a sentence that says of itself that it is false. The Liar Paradox has encouraged many philosophers to establish theories of truth that manage to give a proper account of the truth predicate in a formal language. Kripke’s Fixed Point Theory from 1975 is one famous example of such a formal theory of truth that aims at giving a plausible notion of (...) truth by allowing truth value gaps. However, not only the concept of truth gives rise to paradoxes. A syntactical treatment of epistemic notions like belief and knowledge leads to contradictions that very much resemble the Liar Paradox. Therefore, it seems to be fruitful to apply the established theories of truth to epistemic concepts. In this paper, I will present one such attempt of solving the epistemic paradoxes: I adapt Kripke’s Fixed Point Theory and interpret truth, knowledge and belief within the framework of a partial logic. Thereby I find not only the fixed point of truth but also the fixed points of knowledge and belief. In this fixed point, the predicates of truth, belief and knowledge find their definite interpretation and the paradoxes are avoided. (shrink)

The theory of apartness spaces, and their relation to topological spaces (in the point–set case) and uniform spaces (in the set–set case), is sketched. New notions of local decomposability and regularity are investigated, and the latter is used to produce an example of a classically metrisable apartness on R that cannot be induced constructively by a uniform structure.

Justified belief is a core concept in epistemology and there has been an increasing interest in its logic over the last years. While many logical investigations consider justified belief as an operator, in this paper, we propose a logic for justified belief in which the relevant notion is treated as a predicate instead. Although this gives rise to the possibility of liar-like paradoxes, a predicate treatment allows for a rich and highly expressive framework, which lives up to the universal ambitions (...) of investigating epistemological concepts. We start with a base theory for justified belief, and then systematically present putative additional axioms for justified belief. We provide an overview of consistency results when the additional principles are added to the base theory, and discuss their philosophical plausibility. (shrink)

The existence and uniqueness of a maximum point for a continuous real—valued function on a metric space are investigated constructively. In particular, it is shown, in the spirit of reverse mathematics, that a natural unique existence theorem is equivalent to the fan theorem.

The seventeenth century marked a critical phase in the emergence of modern science. But we misunderstand this process, if we assume that seventeenth-century modes of natural inquiry were identical to the highly specialised, professionalised and ever proliferating family of modern sciences practised today.

Methods and equations for analysing the kinetics of enzyme-catalysed reactions were developed at the beginning of the 20th century in two centres in particular; in Paris, by Victor Henri, and, in Berlin, by Leonor Michaelis and Maud Menten. Henri made a detailed analysis of the work in this area that had preceded him, and arrived at a correct equation for the initial rate of reaction. However, his approach was open to the important objection that he took no account of the (...) hydrogen-ion concentration (a subject largely undeveloped in his time). In addition, although he wrote down an expression for the initial rate of reaction and described the hyperbolic form of its dependence on the substrate concentration, he did not appreciate the great advantages that would come from analysis in terms of initial rates rather than time courses. Michaelis and Menten not only placed Henri's analysis on a firm experimental foundation, but also defined the experimental protocol that remains standard today. Here, we review this development, and discuss other scientific contributions of these individuals. The three parts have different authors, as indicated, and do not necessarily agree on all details, in particular about the relative importance of the contributions of Michaelis and Menten on the one hand and of Henri on the other. Rather than force the review into an unrealistic consensus, we consider it appropriate to leave the disagreements visible. (shrink)

Recommender systems are artificial intelligence technologies, deployed by online platforms, that model our individual preferences and direct our attention to content we’re likely to engage with. As the digital world has become increasingly saturated with information, we’ve become ever more reliant on these tools to efficiently allocate our attention. And our reliance on algorithmic recommendation may, in turn, reshape us as moral agents. While recommender systems could in principle enhance our moral agency by enabling us to cut through the information (...) saturation of the internet and focus on things that matter, as they’re currently designed and implemented they’re apt to interfere with our ability to attend appropriately to morally relevant factors. In order to analyze the distinctive moral problems algorithmic recommendation poses, we develop a framework for the ethics of attention and an account of judicious attention allocation as a moral skill. We then discuss empirical evidence suggesting that attentional moral skill can be thwarted and undermined in various ways by algorithmic recommendation and related affordances of online platforms, as well as economic and technical considerations that support this concern. Finally, we consider how emerging technologies might overcome the problems we identify. (shrink)

Dini's theorem says that compactness of the domain, a metric space, ensures the uniform convergence of every simply convergent monotone sequence of real-valued continuous functions whose limit is continuous. By showing that Dini's theorem is equivalent to Brouwer's fan theorem for detachable bars, we provide Dini's theorem with a classification in the recently established constructive reverse mathematics propagated by Ishihara. As a complement, Dini's theorem is proved to be equivalent to the analogue of the fan theorem, weak König's lemma, in (...) the original classical setting of reverse mathematics started by Friedman and Simpson. (shrink)

We try to recast in modern terms a choice principle conceived by Beppo Levi. who called it the Approximation Principle (AP). Up to now. there was almost no discussion about Levi's contribution. due to the quite obscure formulation of AP the author has chosen. After briefly reviewing the historical and philosophical surroundings of Levi's proposal. we undertake our own attempt at interpreting AP. The idea underlying the principle. as well as the supposed faithfulness of our version to Levi's original intention. (...) are then discussed. Finally. an application of AP to a property of metric spaces is presented. with the aim of showing how AP may work in contexts where other forms of choice are commonly at use. (shrink)

This edited collection bridges the foundations and practice of constructive mathematics and focuses on the contrast between the theoretical developments, which have been most useful for computer science (ie: constructive set and type theories), and more specific efforts on constructive analysis, algebra and topology. Aimed at academic logician, mathematicians, philosophers and computer scientists with contributions from leading researchers, it is up to date, highly topical and broad in scope.

LET ME BEGIN this inquiry with the simple but fundamental fact that the flow of time, or passage, as it is also known, is given in experience, that it is as indubitable an aspect of our perception of the world as the sights and sounds that come in upon us, even though it is not the peculiar property of a special sense. Consider, by way of illustration, that I am now sitting at the desk in my study. This particular event (...) was not present at any earlier time, nor will it be present shortly as I become involved in other activities. The present, as I experience it, is regularly associated with later and later events. It does not hop about capriciously from here to a later time, to a previous time, and then to a much later time, or trace out some other such indiscriminate pattern; instead I find it always in association with the next moment, and as I look backward and inward, so to speak, I find that the prior moment was present and that this next-later moment is present. Quite often this condition is expressed by means of imagery. We are asked to envision either a moving present racing along a fixed track of moments or events from earlier to later, or alternatively a fixed present through which stream a series of moments or events, first the earlier and then the later ones. One is in truth hard-pressed to find references to passage which do not employ quasi-poetical tropes and metaphors, and while these do help in some sense to say what we mean, great caution is required when handling them because of their ready tendency to draw us away from the actual phenomenon requiring explanation. (shrink)

This book argues that we can only understand transformations of nature studies in the Scientific Revolution if we take seriously the interaction between practitioners and scholars. These are not in opposition, however. Theory and practice are end points on a continuum, with some participants interested only in the practical, others only in the theoretical, and most in the murky intellectual and material world in between. It is this borderland where influence, appropriation, and collaboration have the potential to lead to new (...) methods, new subjects of enquiry, and new social structures of natural philosophy and science. The case for connection between theory and practice can be most persuasively drawn in the area of mathematics, which is the focus of this book. Practical mathematics was a growing field in early modern Europe and these essays are organised into three parts which contribute to the debate about the role of mathematical practice in the Scientific Revolution. First, they demonstrate the variability of the identity of practical mathematicians, and of the practices involved in their activities in early modern Europe. Second, readers are invited to consider what practical mathematics looked like and that although practical mathematical knowledge was transmitted and circulated in a wide variety of ways, participants were able to recognize them all as practical mathematics. Third, the authors show how differences and nuances in practical mathematics typically depended on the different contexts in which it was practiced: social, cultural, political, and economic particularities matter. Historians of science, especially those interested in the Scientific Revolution period and the history of mathematics will find this book and its ground-breaking approach of particular interest. (shrink)

The Dedekind cuts in an ordered set form a set in the sense of constructive Zermelo—Fraenkel set theory. We deduce this statement from the principle of refinement, which we distill before from the axiom of fullness. Together with exponentiation, refinement is equivalent to fullness. None of the defining properties of an ordering is needed, and only refinement for two—element coverings is used. In particular, the Dedekind reals form a set; whence we have also refined an earlier result by Aczel and (...) Rathjen, who invoked the full form of fullness. To further generalise this, we look at Richman's method to complete an arbitrary metric space without sequences, which he designed to avoid countable choice. The completion of a separable metric space turns out to be a set even if the original space is a proper class; in particular, every complete separable metric space automatically is a set. (shrink)

Summary Descartes' two treatises of corpuscular-mechanical natural philosophy—Le Monde (1633) and the Principia philosophiae (1644/1647)—differ in many respects. Some historians of science have studied their significantly different theories of matter and elements. Others have routinely noted that the Principia cites much evidence regarding magnetism, sunspots, novae and variable stars which is absent from Le Monde. We argue that far from being unrelated or even opposed intellectual practices inside the Principles, Descartes' moves in matter and element theory and his adoption of (...) wide swathes of novel matters of fact, were two sides of the same coin—that coin being his strategies for improving the systematic power, scope and consistency of the natural philosophy presented in the Principia. We find that Descartes' systematising strategy centred upon weaving ranges of novel matters of fact into explanatory and descriptive narratives with cosmic sweep and radical realist Copernican intent. Gambits of this type have recently been labelled as ‘cosmographical’ (the natural philosophical relating of heavens and earth in contemporary usage). Realist Copernican natural philosophers, from Copernicus himself, through Bruno, Gilbert and Galileo did this to varying degrees; but, we suggest, Descartes presented in Books III and IV of the Principia the most elaborate and strategically planned version of it, underneath the ostensible textbook style of the work. (shrink)

It is folklore that if a continuous function on a complete metric space has approximate roots and in a uniform manner at most one root, then it actually has a root, which of course is uniquely determined. Also in Bishop's constructive mathematics with countable choice, the general setting of the present note, there is a simple method to validate this heuristic principle. The unique solution even becomes a continuous function in the parameters by a mild modification of the uniqueness hypothesis. (...) Moreover, Brouwer's fan theorem for decidable bars turns out to be equivalent to the statement that, for uniformly continuous functions on a compact metric space, the crucial uniform “at most one” condition follows from its non-uniform counterpart. This classification in the spirit of the constructive reverse mathematics, as propagated by Ishihara and others, sharpens an earlier result obtained jointly with Berger and Bridges. (shrink)

Proceedings of the NATO Advanced Study Institute on Proof and Computation, held in Marktoberdorf, Germany, July 20 - August 1, 1993.

How are the various classically equivalent definitions of compactness for metric spaces constructively interrelated? This question is addressed with Bishop-style constructive mathematics as the basic system – that is, the underlying logic is the intuitionistic one enriched with the principle of dependent choices. Besides surveying today's knowledge, the consequences and equivalents of several sequential notions of compactness are investigated. For instance, we establish the perhaps unexpected constructive implication that every sequentially compact separable metric space is totally bounded. As a by-product, (...) the fan theorem for detachable bars of the complete binary fan proves to be necessary for the unit interval possessing the Heine-Borel property for coverings by countably many possibly empty open balls. (shrink)

We extend the concept of apartness spaces to the concept of quasi-apartness spaces. We show that there is an adjunction between the category of quasi-apartness spaces and the category of neighbourhood spaces, which indicates that quasi-apartness is a more natural concept than apartness. We also show that there is an adjoint equivalence between the category of apartness spaces and the category of Grayson’s separated spaces.

ABSTRACT A new phenomenon in the philosophical discipline, philosophical practice—or counselling—is introduced to the reader through the description of three different approaches to philosophical practice. What is common to these approaches is that an academically trained philosopher philosophises together with a ‘sane’person—the visitor—on questions and problems relevant to the visitor. The essential difference between this and psychological counselling is that philosophers do not use therapeutic methods or make diagnoses. The philosophical practitioner triggers in his dialogue partner a didactic philosophical process, (...) which enables the visitor to become an authentic thinker and eventually to arrive at philosophical answers by her/himself. The effectiveness of the language used in philosophical practice is not so much in applying philosophical ideas or theories as in the philosophical knowledge, skills and attitudes attained by the visitor. (shrink)

At the close of this psychotherapeutic century, an alternative to psychotherapy has begun to emerge: the use of philosophy as guidance in order to ameliorate everyday life situations. This new approach to so?called psychological problems, consisting of various forms of open?ended dialogue and reflection on life, may prevent or resolve many of the ?illnesses? for which people seek psychiatric or psychological treatment. If successful, philosophical counseling would mark not only a radical shift in the direction of psychological care, but a (...) radical return to the original, practical purposes of philosophy. (shrink)