En règle générale, l’office du juge est réduit aux possibilités techniques offertes au juge par les codes pour exercer sa fonction. Or, l’office du juge est bien plus que cela. Il est l’expression d’un pouvoir autonome d’une force considérable, distinct du pouvoir qui offre au juge sa légitimité. Qu’est-ce qui fonde alors ce pouvoir propre? Il apparaît que ce « mystère », ainsi que l’évoquait Pierre Ayrault au XVI e siècle, se niche au cœur de la dimension liturgique de la (...) forme de procéder. Or, cette théorie de l’office du juge prend un sens particulier aujourd’hui, dans un monde où l’autorité des normes se renverse. (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.

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)

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)

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)

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.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Becoming Human: Matter and Meaning in an Antiblack World by Zakiyyah Iman JacksonBernabé S. Mendoza (bio)Zakiyyah Iman Jackson, Becoming Human: Matter and Meaning in an Antiblack World New York: By New York University Press, 2020, 320 pp. ISBN 978-1-4798-9004-0the radical work of black feminism is to upend Western dualistic ways of thinking that structure our understanding of what it means to be human. In Becoming Human: Matter and (...) Meaning in an Antiblack World, Zakiyyah Iman Jackson troubles the dominant dualistic distinction of the human and the animal. Jackson argues that antiblackness undergirds Enlightenment discourses on the human-animal divide such that blackness cannot be extricated from the very concept of the animal because both “are not only interdependent representations but also entangled concepts” (28). Central to Jackson’s argument on the animalization of blackness is the notion of “ontologized plasticity,” which posits the being of black(ened) people as infinitely malleable and mutable matter and further points to the fluidification of form and “fleshly existence.” Far from seeing the human as a category that has “ontological integrity,” as scholars in the fields of animal studies, new materialisms, and posthumanism presuppose, Jackson instead seeks to redefine the concept of the human through the theorization of blackness (16). She points out that such theorization has been, for such scholars, a lacuna and the “space of the unthought,” which thus marks her intervention in these fields. [End Page 211]The author offers a sustained engagement with the knowledge claims of science and philosophy, reading them through and against the intellectual contributions of black feminist writers and artists. She draws from such luminaries as Toni Morrison, Nalo Hopkinson, Octavia Butler, Audre Lorde, and the artist Wangechi Mutu to show the ways in which they reject an enclosed notion of the human that is defined only by keeping the racialized other at bay and in a degraded animalized and liquified state. As such, she showcases how black feminist visual and literary culture “theorizes and philosophizes” and reveals the faulty, antiblack premises upon which science and philosophy establish their claims of knowledge on the human.Offering a materialist theory of black ontology and temporality, Jackson poses three main arguments on the racialization of the human-animal distinction. The first is the aforementioned notion of ontologized and black(ened) plasticity that speaks to the constant modulation and manipulation of black matter as it relates to gender, sexuality, and sexual reproduction. Reading US slavery as an experimental playground for testing the limits of the human, Jackson argues that “black female f lesh... functions as the limit case of ‘the human’ and is its matrix-figure” (4). She defines plasticity as a “praxis that seeks to define the essence of a black(ened) thing as infinitely mutable in antiblack, often paradoxical sexuating terms as a means of hierarchically delineating sex/gender, reproduction, and states of being more generally” (11). There is, in other words, an inversion that takes place in that it is only through opposition and the imposed instability and illegibility of blackness—of black matter and the black mater(nal) situated as “chaos by design”—that such categories as “woman,” “mother,” and “female body” can themselves take hold and become intelligible forms (11). Jackson engages with the work of Hortense Spillers and Sylvia Wynter in order to argue that “Man,” as the object of analysis within liberal humanism, “produces an untenable dichotomy—‘the human’ versus ‘the animal,’ whereby the black(ened) female is posited as the abyss dividing organic life into ‘human’ or ‘animal’ based on wholly unsound metaphysical premises” (12). This claim on the centrality of the black female in the plasticization of blackness is given support in chapter 2, which focuses on Nalo Hopkinson’s speculative novel Brown Girl in the Ring, where plasticity gives way to opacity.In this chapter, Jackson explores the ways in which the black female body, as that which is opaque and nonrepresentable within the “dominant grammar of representation,” shatters what she argues is Heidegger’s metaphysical and hierarchical ordering of human, animal, and world. In exploring “how our received conceptions of being hinges on our im/perception of black mater... (shrink)

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.

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)

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)

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.

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)

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)

Evidential decision theory (EDT) says that the choiceworthiness of an option depends on its evidential connections to possible outcomes. Causal decision theory (CDT) holds that it depends on your beliefs about its causal connections. While Newcomb cases support CDT, Arif Ahmed has described examples that support EDT. A new account is needed to get all cases right. I argue that an option A's choiceworthiness is determined by the probability that a good outcome ensues at possible A‐worlds that match actuality in (...) the facts causally unaffected by your decision (the “unaffected facts”). Moreover, you should evaluate A on the assumption that A is compossible with the unaffected facts. This view entails that you should use EDT when evaluating A on the assumption that the unaffected facts determine your action, but use CDT when assessing A on the opposite assumption. A's choiceworthiness equals a weighted average of these conditional assessments. The weights are determined by your beliefs about whether the unaffected fact determine your action. This account gets both Newcomb and Ahmed cases right. According to an influential view, whether you take the unaffected facts to determine your action can make a difference to whether you can regard yourself as free and the action as being under your control. While my account is neutral on this issue, it entails that whether you take the unaffected facts to determine your action is important in a different way: it matters to whether you should follow EDT or CDT. (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)

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.

El grado de Relaciones Internacionales de la Universidad Complutense de Madrid aplica en la parte práctica de algunas asignaturas el uso de herramientas innovadoras para lograr acercar algunos espacios laborales al alumnado.Este artículo analiza las herramientas que se articularon a través de dos proyectos de innovación docente aprobados en convocatorias competitivas: la realización de campañas de sensibilización a través de redes sociales y páginas web, la participación en el diseño y la ejecución de proyectos de cooperación para el desarrollo reales, (...) y la redacción de un libro publicado por una prestigiosa universidad. (shrink)

Name der Zeitschrift: Philologus Jahrgang: 159 Heft: 2 Seiten: 327-364.

If definitive evidence concerning treatment effectiveness becomes available from an ongoing randomized clinical trial, then the trial could be stopped early, with the public release of results benefiting current and future patients. However, stopping an ongoing trial based on accruing outcome data requires methodological rigor to preserve validity of the trial conclusions. This has led to the use of formal interim monitoring procedures, which include inefficacy monitoring that will stop a trial early when the experimental treatment appears not to be (...) working. For participants, inefficacy monitoring is especially important as it ensures that they are not being treated worse than if they had not enrolled on the trial. We discuss the importance of reporting with trial results the formal interim inefficacy monitoring guidelines that were utilized, and, if none were used, the reasons for their absence. A survey of two leading medical journals suggests that this is not current practice. (shrink)

Drawing from cognitive learning theories we hypothesize that exposure to nationalistic appeals that suggest consumers should shun foreign brands for moral reasons increases the general belief in consumers that buying foreign brands is morally wrong. In parallel, drawing from the theory of psychological reactance we posit that such appeals may, against their communication goal, increase the reputation of foreign luxury brands. We term the juxtaposition of these apparently contradictory effects the “Ambivalence Hypothesis.” Further, drawing from prior research on source-similarity effects (...) we posit that foreign luxury brands that communicate cultural proximity to target consumers (i.e., a local brand positioning) reinforce psychological reactance (“Clean Conscience Hypothesis”). We test these hypotheses experimentally in the context of luxury car brand advertising in China, a market that is heavily dominated by foreign brands, and therefore provides a breeding ground for ambivalent consumer reactions. Results show that exposure to nationalistic appeals enhances consumers’ national identity dispositions (patriotism, local identity), which results in higher levels of consumer ethnocentrism. Further, nationalistic appeals enhance the social responsibility associations that consumers hold for foreign luxury brands and their countries of origin, which results in a higher brand reputation. Finally, effects of nationalistic appeals on foreign luxury brand reputation are positively stronger for brands using a local vs. a foreign or a global positioning. These findings suggest that nationalistic appeals are a double-edged sword with important implications for ethics in political communication and luxury brand marketing. (shrink)

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)

This paper discusses a novel problem at the intersection of ethics and epistemology: there can be cases in which moral considerations seem to "encroach'' upon belief from multiple directions at once, and possibly to varying degrees, thereby leaving their overall effect on belief unclear. We introduce these cases -- cases of moral encroachment under moral uncertainty -- and show that they pose a problem for all predominant accounts of moral encroachment. We then address the problem, by developing a modular Bayesian (...) framework that, we argue, is sufficiently flexible and scaleable to accommodate the multifaceted uncertainty we describe while still generating clear recommendations for an agent's beliefs. Our framework has several practical upshots, and we close by articulating them: we derive insights about the relationship between moral character and doxastic behavior and make suggestions for how to encourage people to revise their doxastic states in morally laudable ways, without deviating from core Bayesian norms. (shrink)

On the received view, counterfactuals are analysed using the concept of closeness between possible worlds: the counterfactual 'If it had been the case that p, then it would have been the case that q' is true at a world w just in case q is true at all the possible p-worlds closest to w. The degree of closeness between two worlds is usually thought to be determined by weighting different respects of similarity between them. The question I consider in the (...) paper is which weights attach to different respects of similarity. I start by considering Lewis's answer to the question and argue against it by presenting several counterexamples. I use the same examples to motivate a general principle about closeness: if a fact obtains in both of two worlds, then this similarity is relevant to the closeness between them if and only if the fact has the same explanation in the two worlds. I use this principle and some ideas of Lewis's to formulate a general account of counterfactuals, and I argue that this account can explain the asymmetry of counterfactual dependence. The paper concludes with a discussion of some examples that cannot be accommodated by the present version of the account and therefore necessitate further work on the details. (shrink)

In the article, an argument is given that Euclidean geometry is a priori in the same way that numbers are a priori, the result of modelling, not the world, but our activities in the world.

The concept of truth has many aims but only one source. The article describes the primary concept of truth, here called the synthetic concept of truth, according to which truth is the objective result of the synthesis of us and nature in the process of rational cognition. It is shown how various aspects of the concept of truth -- logical, scientific, and mathematical aspect -- arise from the synthetic concept of truth. Also, it is shown how the paradoxes of truth (...) arise. (shrink)

During the last quarter of a century, a number of philosophers have become attracted to the idea that necessity can be analyzed in terms of a hyperintensional notion of essence. One challenge for proponents of this view is to give a plausible explanation of our modal knowledge. The goal of this paper is to develop a strategy for meeting this challenge. My approach rests on an account of modality that I developed in previous work, and which analyzes modal properties in (...) terms of the notion of a metaphysical law. I discuss what information about the metaphysical laws is required for modal knowledge. Moreover, I describe two ways in which we might be able to acquire this information. The first way employs inference to the best explanation. The metaphysical laws, including the essential truths, play a crucial role in causal and grounding explanations and we can gain knowledge of these laws by abductive inferences from facts of which we have perceptual or a priori knowledge. The second way of gaining information about the metaphysical laws rests on knowledge that is partly constitutive of competence with the concepts that are needed to express the relevant information. Finally, I consider how knowledge of the metaphysical laws can be used to establish modal claims, paying special attention to the much-discussed connection between conceiving and possibility. (shrink)