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)

This essay argues for a more methodologically diverse search for extraterrestrial intelligence (SETI) and study of habitable exoplanets that might contribute to the emergent field of critical habitability studies across the sciences and humanities. Whether or not contact is made with extraterrestrials, this effort is implicated in changing concepts of otherness at home and the ongoing work to decolonize Earth and make it more inhabitable. I examine historical efforts to think aliens philosophically in the work of Kant, to conclude with (...) a reflection on the trope of contact between humans, nonhuman animals, and aliens in Ted Chiang’s short story “The Great Silence.”. (shrink)

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)

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)

Even after yet another grand conjecture has been proved or refuted, any omniscience principle that had trivially settled this question is just as little acceptable as before. The significance of the constructive enterprise is therefore not affected by any gain of knowledge. In particular, there is no need to adapt weak counterexamples to mathematical progress.

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.

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 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)

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)

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.

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)

A form of Kripke's schema turns out to be equivalent to each of the following two statements from metric topology: every open subspace of a separable metric space is separable; every open subset of a separable metric space is a countable union of open balls. Thus Kripke's schema serves as a point of reference for classifying theorems of classical mathematics within Bishop-style constructive reverse mathematics.

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.

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.

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)

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.

In this conceptual paper, we propose that both skill set development and mindset development would be desirable dimensions of negotiation training. The second dimension has received little attention thus far, but negotiation mindsets, i.e., the psychological orientations by which people approach negotiations, are likely to have a considerable influence on the outcome of negotiations. Referring to empirical and conceptual mindset studies from outside the negotiation field, we argue that developing mindsets can leverage the effectiveness of skills and knowledge, increase learning (...) transfer, and lead to long-term behavioral changes. We introduce an integrative negotiation mindset that comprises three inclinations which complement each other: a collaborative, a curious, and a creative one. We also discuss activities that help people to develop and enhance this mindset both in and out of the classroom. Our general claim is that by moving beyond the activities of conventional negotiation training, which focuses on skills and knowledge, mindset-oriented negotiation training can increase training effectiveness and enable participants to more often reach what we define as sustainable integrative agreements. (shrink)

Alongside the analogy between maximal ideals and complete theories, the Jacobson radical carries over from ideals of commutative rings to theories of propositional calculi. This prompts a variant of Lindenbaum’s Lemma that relates classical validity and intuitionistic provability, and the syntactical counterpart of which is Glivenko’s Theorem. The Jacobson radical in fact turns out to coincide with the classical deductive closure. As a by-product we obtain a possible interpretation in logic of the axioms-as-rules conservation criterion for a multi-conclusion Scott-style entailment (...) relation over a single-conclusion one. (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.

There is growing interest in clinical ethics. However, we still have sparse knowledge about what is actually going on in the everyday practice of clinical ethics consultations. This paper introduces a descriptive evaluation tool to present, discuss and compare how clinical ethics case consultations are actually carried out. The tool does not aim to define ‘best practice’. Rather, it facilitates concrete comparisons and evaluative discussions of the role, function, procedures and ideals inherent in clinical ethics case consultation practices. The tool (...) was developed during meetings of the European Clinical Ethics Network. Based on written reports and participation in the network meetings, the development and the content of the tool and the results of its application in presenting and discussing 10 case consultations are summarized. The tool facilitated understanding of the details of clinical ethics case consultations across individuals and institutions with various experiences and cultures, and comparison between various practices. (shrink)

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)

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)

In the present note, we study a generalization of Dedekind cuts in the context of constructive Zermelo–Fraenkel set theory CZF. For this purpose, we single out an equivalent of CZF's axiom of fullness and show that it is sufficient to derive that the Dedekind cuts in this generalized sense form a set. We also discuss the instance of this equivalent of fullness that is tantamount to the assertion that the class of Dedekind cuts in the rational numbers, in the customary (...) constructive sense including locatedness, is a set. This is to be compared with the situation for the partial reals, a generalization in a different direction: if one drops locatedness from the notion of a Dedekind real, then it becomes inherently impredicative. We make this precise, and further present the curiosity that the irrational Dedekind reals form a set already with exponentiation. (shrink)

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

The notions of linear and metric independence are investigated in relation to the property: if U is a set of n+1 independent vectors, and X is a set of n independent vectors, then adjoining some vector in U to X results in a set of n+1 independent vectors. It is shown that this property holds in any normed linear space. A related property – that finite-dimensional subspaces are proximinal – is established for strictly convex normed spaces over the real or (...) complex numbers. It follows that metric independence and linear independence are equivalent in such spaces. Proofs are carried out in the context of intuitionistic logic without the axiom of countable choice. (shrink)

We try to recast in modern terms a choice principle conceived by Beppo Levi, who called it the Approximation Principle. 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)

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)

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 ...

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)

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)