Boris Hessen’s ‘The Social and Economic Roots of Newton’s Principia’ (see https://doi.org./10.1163/1569206X-00002041) is considered a pioneering work in the historiography of the natural sciences. For some, it marks the founding moment of the ‘externalist’ approach to this field of study. Previously, Hessen published another paper on Newton entitled ‘Preface to Articles by A. Einstein and J.J. Thomson’, which, some maintain, bears a stronger resemblance to works in the ‘internalist’ camp of the historiography of the natural sciences. For decades, (...) scholars have puzzled over why Hessen chose to argue for, seemingly, diametrically opposed positions. In this paper, however, I argue that Hessen does not advance two different historiographical methods, but a single, dialectical-materialist approach that accounts for the ‘unity in opposition’ of the external and internal dimensions of natural-scientific theory. I draw from Hessen’s two papers on Newton, his previously untranslated writings, as well as selections from the secondary literature. (shrink)

Im 2009 erschienenen Buch "Philosophie des Leidens" versucht Boris Wandruszka, jene immanente Lebensstruktur und Lebensdynamik aufzudecken, die zu den einfachsten und fundamentalen Strukturmomenten des Leidens vorstosst; diese erste "Wissenschaft vom Leiden" transzendierte daher nicht die Grenzen der Anschaubarkeit, sondern verblieb in der "Immanenz des 'inneren Lebens' bzw. des Erlebens". Im aktuellen Buch "Metaphysik des Leidens" werden die "realen Bedingungen der Moglichkeit von Leiden" ermittelt: Wie muss eine Welt beschaffen sein, damit darin ein leidendes Wesen erscheinen konne? Welche Rolle hat (...) das Leiden in Bezug zum fundamentalen Widerfahrnis-, Resonanz- und Responsivitatscharakter des Lebens? Es wird gezeigt, dass menschliches Leben, das einer plural-agonalen Welt ausgesetzt ist, nicht leidfrei moglich ist, dass aber andererseits das Leid nicht das letzte Wort sein kann, sondern notwendig auf Ganzheit, Reifung, Erlosung und Harmonie bezogen ist. Nur auf dem Hintergrund der Spannung zwischen absoluter Seins-, Sinn- und Lebensfulle und der stets problematischen und fragilen Teilhabe von Menschen am "absoluten und leiduberwindenden Urleben" kann Leiden entstehen, durchlitten, verstanden, aber auch uberwunden werden. Hier erreicht der "Opfergedanke", in dem das unvermeidliche Leid frei angenommen und dadurch transformiert wird, seine reinste und hochste Ausformung. Erst nach Klarung dieser Verhaltnisse wird die "Theodizeefrage" als "das Problem der Probleme" angegangen und am Leitfaden der Hiob-Erzahlung diskutiert. Letztlich erweist sich, dass trotz allem Schmerz, Mangel, Unrecht und Unsinn ein "Potential des Unendlichen" im Leiden verborgen liegt, das auf seine Uberwindung durch Sein-, Sinn- und Werterfullung, durch Tat, Erkenntnis und Liebe verweist und dass diese drei "Machte" der Leidensherausforderung bedurfen, um ihre Weite, Tiefe und Hohe auszuloten. (shrink)

In this handbook, I put into practice my philosophical views on children's mathematics. The handbook contains brief instructions and examples of mathematical activities. In the INSTRUCTIONS section, instructions are given on how, and in part why that way, to help preschool children in their mathematical development. In the ACTIVITIES section, there are examples of activities through which the child develops her mathematical abilities.

Boris Kment takes a new approach to the study of modality that emphasises the origin of modal notions in everyday thought. He argues that the concepts of necessity and possibility originate in counterfactual reasoning, which allows us to investigate explanatory connections. Contrary to accepted views, explanation is more fundamental than modality.

I propose a general alethic theory of epistemic risk according to which the riskiness of an agent’s credence function encodes her relative sensitivity to different types of graded error. After motivating and mathematically developing this approach, I show that the epistemic risk function is a scaled reflection of expected inaccuracy. This duality between risk and information enables us to explore the relationship between attitudes to epistemic risk, the choice of scoring rules in epistemic utility theory, and the selection of priors (...) in Bayesian epistemology more generally. (shrink)

I begin by distinguishing two notions of model, the notion of a truth-making structure and the notion of a mathematical model (in one specific sense). I then argue that although the models of the semantic view have often been taken to be both truth-making structures and mathematical models, this is in part due to a failure to distinguish between two ways of truth-making; in fact, the talk of truth-making is best excised from the view altogether. The result is a version (...) of the semantic view which is better supported by the direct evidence offered for it, better equipped to achieve its avowed aims, and, I think, closer to the intentions of the original proponents of the view in many ways, despite some of their own declarations to the contrary. (shrink)

Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial interpretation of the corresponding language. It follows from the analysis that (i) mathematical objects do not exist in the external world: they are our internally imagined objects, some of which, at least approximately, we can realize or represent; (ii) mathematical truths are not (...) truths about the external world but specifications (formulations) of mathematical conceptions; (iii) mathematics is first and foremost our imagined tool by which, with certain assumptions about its applicability, we explore nature and synthesize our rational cognition of it. (shrink)

While there are satisfactory answers to the question “How should we teach children mathematics?”, there are no satisfactory answers to the question “What mathematics should we teach children?”. This paper provides an answer to the last question for preschool children (early childhood), although the answer is also applicable to older children. This answer, together with an appropriate methodology on how to teach mathematics, gives a clear conception of the place of mathematics in the children’s world and our role in helping (...) children develop their mathematical abilities. Briefly, children’s mathematics consists of the world of children’s internal activities that they eventually purposefully organize in order to understand and control the outside world and organize their overall activities in it. We need to support a child in mathematical activities that she does spontaneously and in which she shows interest, and we need to teach her mathematics that she is interested in developing through these activities. In doing so, we must be fully aware that the child’s mathematics is part of the child’s world of internal activities and is not outside of it. We help the child develop mathematical abilities by developing them in the context of her world and not outside of it. From the point of view of this conception, the standards established today are limiting and too focused on numbers and geometric figures: these topics are too prominent and elaborated, and other mathematical contents are subordinated to them. Adhering to the standards, we drastically limit the mathematics of the child’s world, hamper the correct mathematical development of a child, and we can turn her away from mathematics. (shrink)

In this paper we develop a general theory of algorithmic fairness. Drawing on Johnson King and Babic’s work on moral encroachment, on Gary Becker’s work on labor market discrimination, and on Strawson’s idea of resentment and indignation as responses to violations of the demand for goodwill toward oneself and others, we locate attitudes to fairness in an agent’s utility function. In particular, we first argue that fairness is a matter of a decision-maker’s relative concern for the plight of people from (...) different groups, rather than of the outcomes produced for different groups. We then show how an agent’s preferences, including in particular their attitudes to error, give rise to their decision thresholds. Tying these points together, we argue that the agent’s relative degrees of concern for different groups manifest in a difference in decision thresholds applied to these groups. (shrink)

According to the aspect theory of instantiation, a particular A instantiates a universal B if and only if an aspect of A is cross-count identical with an aspect of B. This involves the assumption that both particulars and universals have aspects, and that aspects can mediate between different ways of counting things. I will ask what is new about this account of instantiation and, more importantly, whether it is an improvement on its older relatives. It will turn out that the (...) part of it that is new is the notion of cross-count identity among aspects. As I will show, this notion is both dubious and unnecessary. I will end by presenting a simplified aspect theory of instantiation that does not involve cross-count identity. (shrink)

We further investigate a divisibility relation on the set of BN ultrafilters on the set of natural numbers. We single out prime ultrafilters (divisible only by 1 and themselves) and establish a hierarchy in which a position of every ultrafilter depends on the set of prime ultrafilters it is divisible by. We also construct ultrafilters with many immediate successors in this hierarchy and find positions of products of ultrafilters.

The essential role of language in rational cognition is analysed. The approach is functional: only the results of the connection between language, reality, and thinking are considered. Scientific language is analysed as an extension and improvement of everyday language. The analysis gives a uniform view of language and rational cognition. The consequences for the nature of ontology, truth, logic, thinking, scientific theories, and mathematics are derived.

This article offers the critical concept misfit in an effort to further think through the lived identity and experience of disability as it is situated in place and time. The idea of a misfit and the situation of misfitting that I offer here elaborate a materialist feminist understanding of disability by extending a consideration of how the particularities of embodiment interact with the environment in its broadest sense, to include both its spatial and temporal aspects. The interrelated dynamics of fitting (...) and misfitting constitute a particular aspect of world-making involved in material-discursive becoming. The essay makes three arguments: the concept of misfit emphasizes the particularity of varying lived embodiments and avoids a theoretical generic disabled body; the concept of misfit clarifies the current feminist critical conversation about universal vulnerability and dependence; the concept of misfitting as a shifting spatial and perpetually temporal relationship confers agency and value on disabled subjects. (shrink)

It is commonly believed that disability disqualifies people from full participation in or recognition by society. This view is rooted in eugenic logic, which tells us that our world would be a better place if disability could be eliminated. In opposition to this position, I argue that that disability is inherent in the human condition and consider the bioethical question of why we might want to conserve rather than eliminate disability from our shared world. To do so, I draw together (...) an eclectic, rather than systematic, configuration of counter-eugenic arguments for conserving disability. The idea of preserving intact, keeping alive, and even encouraging to flourish denoted by conserve suggests that disabilities would be better understood as benefits rather than deficits. I present, then, a reading of disability as a potentially generative resource rather than unequivocally restrictive liability. In other words, what I consider here is the cultural and material contributions disability offers to the world. (shrink)

Many philosophers have argued that statistical evidence regarding group characteristics (particularly stereotypical ones) can create normative conflicts between the requirements of epistemic rationality and our moral obligations to each other. In a recent article, Johnson-King and Babic argue that such conflicts can usually be avoided: what ordinary morality requires, they argue, epistemic rationality permits. In this article, we show that as data get large, Johnson-King and Babic’s approach becomes less plausible. More constructively, we build on their project and develop a (...) generalized model of reasoning about stereotypes under which one can indeed avoid normative conflicts, even in a big data world, when data contain some noise. In doing so, we also articulate a general approach to rational belief updating for noisy data. (shrink)

In this paper, we reflect on the connection between the notions of organism and organisation, with a specific interest in how this bears upon the issue of the reality of the organism. We do this by presenting the case of Buffon, who developed complex views about the relation between the notions of “organised” and “organic” matter. We argue that, contrary to what some interpreters have suggested, these notions are not orthogonal in his thought. Also, we argue that Buffon has a (...) view in which organisation is not just ubiquitous, but basic and fundamental in nature, and hence also fully natural. We suggest that he can hold this view because of his anti-mathematicism. Buffon’s case is interesting, in our view, because he can regard organisation, and organisms, as perfectly natural, and can admit their reality without invoking problematic supernaturalist views, and because he allows organisation and the organismal to come in kinds and degrees. Thus, his view tries to do justice to two cautionary notes for the debate on the reality of the organism: the need for a commitment to a broadly naturalist perspective, and the need to acknowledge the interesting features of organisms through which we make sense of them. (shrink)

We continue the research of an extension of the divisibility relation to the Stone‐Čech compactification. First we prove that ultrafilters we call prime actually possess the algebraic property of primality. Several questions concerning the connection between divisibilities in and nonstandard extensions of are answered, providing a few more equivalent conditions for divisibility in. Results on uncountable chains in are proved and used in a construction of a well‐ordered chain of maximal cardinality. Probably the most interesting result is the existence of (...) a chain of type in. Finally, we consider ultrafilters without divisors in and among them find the greatest class. (shrink)

Approximate coherentism suggests that imperfectly rational agents should hold approximately coherent credences. This norm is intended as a generalization of ordinary coherence. I argue that it may be unable to play this role by considering its application under learning experiences. While it is unclear how imperfect agents should revise their beliefs, I suggest a plausible route is through Bayesian updating. However, Bayesian updating can take an incoherent agent from relatively more coherent credences to relatively less coherent credences, depending on the (...) data observed. Thus, comparative rationality judgments among incoherent agents are unduly sensitive to luck. (shrink)

This book examines public policy in physical education and sport and provides insights into practices of school curriculum and after-school sport programs from a global context. The authors reflect on the continuously shifting understanding of the field of physical education and suggest a new direction for the profession.

This book examines public policy in physical education and sport and provides insights into practices of school curriculum and after-school sport programs from a global context. The authors reflect on the continuously shifting understanding of the field of physical education and suggest a new direction for the profession.

We continue the exploration of various aspects of divisibility of ultrafilters, adding one more relation to the picture: multiplicative finite embeddability. We show that it lies between divisibility relations \ and \. The set of its minimal elements proves to be very rich, and the \-hierarchy is used to get a better intuition of this richness. We find the place of the set of \-maximal ultrafilters among some known families of ultrafilters. Finally, we introduce new notions of largeness of subsets (...) of \, and compare it to other such notions, important for infinite combinatorics and topological dynamics. (shrink)

Mit dem Erscheinen der ersten Untersuchung der Autorin zu diesem Thema im Jahre 1984 (Φ.Εὐαγγελάτου-Νοταϱᾶ, Συλλογὴ χϱονολογημένων „σημειωμάτων“ ἑλληνιϰως ϰωδίϰων. 13ος αἰ. Athen) wurde seinerzeit ein Nachschlagewerk geschaffen, das für die Erforschung der spätbyzantinischen Handschriftenkunde unentbehrliche Dienste leistet. In dem vorliegenden Buch sind nunmehr erneut die Notizen und Einträge spätbyzantinischer Handschriften zum Gegenstand gewählt. Dabei wurde der chronologische Rahmen der Arbeit erheblich erweitert, doch bleibt die Auswahl der erörterten und edierten Texte auf jene eingeschränkt, die eben von den Auftraggebern, Besitzern (...) und Schenkern der Handschriften handeln. (shrink)

The discovery of a small collection of Darwin manuscripts at the Whipple Museum of the History of Science has allowed a reconsideration of Darwin’s interest in and knowledge of microscopy. Concentrating on the years between his return from the Beagle voyage and the publication of the major taxonomic work on barnacles, this paper recovers a number of important aspects of Darwin’s intellectual and practical development: on returning from the Beagle voyage he acquainted himself with the work of C. G. Ehrenberg, (...) and this informed both his private and public work; then through the 1840s Darwin transformed himself from a fascinated observer and consumer of others’ work into an expert on microscopy. I characterise this move as a piece of clever manoeuvring, and discuss more generally the kind of scientist—gentlemanly and expert—that Darwin was attempting to become.Keywords: Charles Darwin; Microscopy; Beagle voyage; Classification; Accuracy. (shrink)

As illiberal and authoritarian trends are on the rise--both in fragile and seemingly robust democracies--there is growing concern about the longevity of liberalism and democracy. The purpose of this volume is to draw on the analytical resources of various disciplines and public policy approaches to reflect on the current standing of liberal democracy. Leading social scientists from different disciplinary backgrounds aim to examine the ideological and structural roots of the current crisis of liberal democracies, in the West and beyond, conceptually (...) and empirically. The volume is divided into two main parts: Part I explores tensions between liberalism and democracy in a longer-term, historical perspective to explain immanent vulnerabilities of liberal democracy. Authors examine the conceptual foundations of Western liberal democracy that have shaped its standing in the contemporary world. What lies at the core of illiberal tendencies? Part II explores case studies from the North Atlantic, Eastern Europe, Turkey, India, Japan, and Brazil, raising questions whether democratic crises, manifested in the rise of populist movements in and beyond the Western context, differ in kind or only in degree. How can we explain the current popular appeal of authoritarian governments and illiberal ideas? The Emergence of Illiberalism will be of great interest to teachers and students of politics, sociology, political theory and comparative government. (shrink)

Commentary on Rob Sparrow’s (2022) target article, “Human Germline Genome Editing: On the Nature of Our Reasons to Genome Edit,” should consider the collection of articles Sparrow has authored on g...

We construct and study structures imitating the field of complex numbers with exponentiation. We give a natural, albeit non first-order, axiomatisation for the corresponding class of structures and prove that the class has a unique model in every uncountable cardinality. This gives grounds to conjecture that the unique model of cardinality continuum is isomorphic to the field of complex numbers with exponentiation.

This paper analyzes the historical context and systematic importance of Kant's hypothetical use of reason. It does so by investigating the role of hypotheses in Kant's philosophy of science. We first situate Kant’s account of hypotheses in the context of eighteenth-century German philosophy of science, focusing on the works of Wolff, Meier, and Crusius. We contrast different conceptions of hypotheses of these authors and elucidate the different theories of probability informing them. We then adopt a more systematic perspective to discuss (...) Kant's idea that scientific hypotheses must articulate real possibilities. We argue that Kant's views on the intelligibility of scientific hypotheses constitute a valuable perspective on scientific understanding and the constraints it imposes on scientific rationality. (shrink)