The purpose of the study is to consider the concept of "philosopheme", which allows analyzing such basic categories of philosophical and legal reflections of the writer and thinker F.M. Dostoevsky as crime and punishment and correlating their interpretation with his personal life experience. The scientific novelty of the work lies in the fact that through the disclosure of the content of the philosophems "crime" and "punishment", the existential aspects of F.M. Dostoevsky's anthropological and philosophical-legal reflections are revealed. As a result (...) of the analysis of Dostoevsky's novel "Crime and Punishment", his other works, the writer's letters, autobiographical testimonies, it becomes clear that the core of these philosophies for Dostoevsky is a moral code that allows a person to overcome the" disconnection "and" disconnection " of modern man's being both with himself and with society. (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.

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)

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)

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)

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.

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 char- acteristics (particularly stereotypical ones) can create normative conflicts between the requirements of epistemic rationality and our moral obligations to each other. In a recent paper, Johnson-King and Babic argue that such conflicts can usually be avoided: what ordinary morality requires, they argue, epistemic rationality permits. In this paper, we show that as data gets 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)

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.

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)

The metaphysics of a social reality assumes definition ontology various plans of its realization as sorts of attitude to kinds. The last ones represent phenomena of a social reality - as classical and nonclassical. The economy, morals, religion, the right concern to classical kinds of a social reality. Attributes of a sociality of the given kinds: activity, attitudes, forms of social consciousness. A nonclassical kinds given attributes yet "do not possess" to the full. Their metaphysics is defined through parity with (...) classical kinds of society. The structure of a social reality is mobile that is why "updating" of the list of classical kinds of a social reality is not soproblematic that is why the urgency of an explication ontology and metaphysics of a sort of a reality social and numerous kinds is undoubtedly rather productive and duly. (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.

This brief article, appearing in Issue #2 of The Cambridge Journal of Law, Politics and Art, published online on 22 November 2022), explores Nietzsche's perspective on the perils of mass psychosis in modern society and the threat it entails in accommodating increasingly repressive systems of social control against the background of the COVID pandemic, and drawing on the example of Novak Djokovic's deportation from Australia in January 2022.

In this paper, I make a contribution to a naturalistically-minded theory of truthmakers by proposing a solution to the nasty problem of truthmakers for negative truths. After formulating the difficulty, I consider and reject a number of solutions to the problem, including Armstrong's states of affairs of totality, incompatibility accounts, and JC Beall 's polarity view. I then defend the position that absences of truthmakers are real and are responsible for making negative truths true. According to the positive account of (...) absences I offer, absences of contingent states of affairs are causally relevant mind-independent features of the physical world, located within space and time, and capable of being discovered by scientific inquiry. Recognition of the reality of absences strengthens truthmaker theory as a naturalistic metaphysics, as truth and falsity of each and every contingent proposition finds an ontological grounding in some region of the physical universe. (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)

Guided to the notion of the eternal return by the philosophical intuitions of the Greek antiquity, Nietzsche turned to the physical sciences of his day in order to further his inquiry. This extensive intellectual engagement represented a genuine attempt to investigate the possible continuity of meaning between the mythical tradition, on the one hand, and the rational-empirical (i.e. scientific), on the other. In particular, Nietzsche was intrigued by the manner in which the relationship between myth and science played out in (...) the wide-ranging debates on the eternal recurrence and entropy. Obscuring the view, however, lay the debris of metaphysical imports into the discourse of secular modern science. In the course of his ambitious undertaking to disentangle physics from metaphysics, Nietzsche discerned a possibility for synthesising the scientific explanation for his ‘fundamental conception’ (EH: Z, §1) with the mythical wisdom of the ages. His inferences proved nothing short of explosive. The doctrine of the eternal return of the same, instead of the docile cosmic torpor, urged the radical revaluation of all values. The measure of the eternal return’s power was to dissolve its impersonation – the Übermensch – into a form of well-being. Nietzsche was convinced that his ‘mightiest idea’ (NF-1881:11[148]) illuminated the path we must follow lest we wish to incur the full force of the ‘frightening wisdom of Silenus’ (BT: §4). (shrink)

Nietzsche is absent from today’s growing debate on slavery past and present. In this article I argue that his views on the subject add a pertinent, if challenging, dimension to this wide-ranging discussion. Nietzsche’s analysis is capable of contributing to our understanding of this multifaceted phenomenon in a number of respects. I look at Nietzsche’s use of the controversial notions of slavery, understood both historically and in the context of modern society, to explore such central concerns of political anthropology as (...) the nature and role of leadership, and the questions of development and inequality. The key focus of Nietzsche’s examination concerns slavery as an enduring facet of human existence. He sees it becoming an important hallmark of the industrial culture as a barometer of modern society’s physiological well-being, as well as acting as the repository for its externalities. Nietzsche’s genealogical inquiry leads him to explore the psychological content of slavery and to conceptualise it in terms of human vulnerability, which increases susceptibility to exploitation. In these respects, Nietzsche’s views resonate with pertinence today and deserve closer critical attention and scrutiny – something Nietzsche would undoubtedly welcome. (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 chapter argues that the distinction between ambitious and modest transcendental arguments, developed and deployed by various authors in the wake of Stroud’s influential critique of transcendental reasoning, may be pointless when applied to transcendental arguments from performative inconsistency that have moral statements as their conclusions. If moral truth is assertorically constrained, then any modest moral transcendental argument from performative inconsistency can be converted into an ambitious moral transcendental argument. The chapter provides an account of performative inconsistency and suggests an (...) alternative to the widespread reading of transcendental conditionals in terms of an ‘if-then’-sentences whose antecedents express a proposition to the effect that some x is possible and whose consequents express a statement to the effect that some y is actual. (shrink)

My goal in this dissertation is to start a conversation about the role of risk in the decision-theoretic assessment of partial beliefs or credences in formal epistemology. I propose a general theory of epistemic risk in terms of relative sensitivity to different types of graded error. The approach I develop is broadly inspired by the pragmatism of the American philosopher Charles Sanders Peirce and his notion of the ``economy of research.'' I express this framework in information-theoretic terms and show that (...) epistemic risk, so understood, is dual to information entropy. As a result, every unit increase in risk comes with a corresponding unit decrease in information entropy and epistemic risk may be expressed in terms of entropic change. I explain the significance of this for the selection of priors and the Laplacian principle of indifference. I also extend this notion of epistemic risk to the assessment of updating rules, where a similar duality between risk and information holds. In the dynamic context, epistemic risk is given by cross-entropic change. Here I explore the relationship between risk, the Value of Knowledge Theorem, dynamic coherence, and the role of expected accuracy in the selection of update rules. Finally, I apply these considerations to a social institution where attitudes to error are especially salient -- namely, legal decision-making -- and argue that considerations regarding the relative severity of different types of error are central to understanding evidentiary burdens of proof and the probative value of statistical evidence. (shrink)

Safronov’s Nietzsche’s Political Economy is a pioneering appraisal of Nietzsche’s critique of industrial culture and its unfolding crisis. The author contends that Nietzsche remains unique in conceptualizing the upheavals of modern political economy in terms of the crisis of its governing values. Nietzsche scrutinises the norms which, not only preside over the unfathomable build-up in debt, the proliferation of meaningless, impersonal slavery and the rise of increasingly repressive social control systems, but inevitably set these precarious tendencies of modern political (...) economy on a collision course liable to culminate in an unprecedented human and environmental catastrophe. Safronov explores the core themes of Nietzsche’s political economy—debt, slavery, and the division of labour—with reference to the influential views of Adam Smith and Karl Marx, as well as against the backdrop of the Long Depression (1873–1896), the first truly international crisis of industrial capitalism, during which most of Nietzsche’s work was completed. -/- In Nietzsche’s assessment, modern political economy is predicated on the valuations that diminish humankind’s prospects and harm the planet’s future by consistently enfeebling the present, as long as there is profit to be made from it. Nietzsche’s critical insight, which challenges the most fundamental tenet of modern economics and finance, is that in order to build a stronger and intrinsically more valuable future in lieu of simply speculating on it, as though the liberal Promised Land could descend upon us like the manna from heaven at the wave of an invisible hand [of the market], it is necessary to walk from the future we dare to envisage resolutely back to the present we inhabit to determine what demands achieving such a vision would impose upon us, instead of embellishing the ‘here and now’ by cynically discounting the future to the [net] value of the present while disparaging, disowning and rewriting the past to unburden ourselves of its troubling legacy, as we continue to frivolously squander its capital to the alluring tunes of the ‘sirens who in the marketplace sing to us of the future’. The enabling mechanism for changing our valuing perspectives, Nietzsche tells us, lies dormant in us and it must be unlocked before it is too late. (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.

Nietzsche is a silent interlocutor in Francis Fukuyama’s polemic The End of History and the Last Man (1992). But Fukuyama, I argue, ignores the rationale behind Nietzsche’s critique of the liberal worldview and misinterprets his call for the revaluation of all values. By exploring the relations between the end of history, the last man and the need for revaluation, this chapter aims to reconstruct the relevant aspects of Nietzsche’s critique of liberalism, which challenges the political vision of The End of (...) History. I contend that Nietzsche’s exposure of the conceptual and value inversions as central yet perilous sources of legitimacy in modern ‘industrial civilization’ continues to resonate today and deserves critical attention. (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)

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)

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)

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)

We investigate two questions, the relevance of memory for evaluative conditioning effects based on smell-taste pairings, and the potential preparedness of smell-taste combinations for...

In recent decades, memory has become one of the major concepts and a dominant topic in philosophy, sociology, politics, history, science, cultural studies, literary theory, and the discussions of trauma and the Holocaust. In contemporary debates, the concept of memory is often used rather broadly and thus not always unambiguously. For this reason, the clarification of the range of the historical meaning of the concept of memory is a very important and urgent task. This volume shows how the concept of (...) memory has been used and appropriated in different historical circumstances and how it has changed throughout the history of philosophy. In ancient philosophy, memory was considered a repository of sensible and mental impressions and was complemented by recollection-the process of recovering the content of past thoughts and perceptions. Such an understanding of memory led to the development both of mnemotechnics and the attempts to locate memory within the structure of cognitive faculties. In contemporary philosophical and historical debates, memory frequently substitutes for reason by becoming a predominant capacity to which one refers when one wants to explain not only the personal identity but also a historical, political, or social phenomenon. In contemporary interpretation, it is memory, and not reason, that acts in and through human actions and history, which is a critical reaction to the overly rationalized and simplified concept of reason in the Enlightenment. Moreover, in modernity memory has taken on one of the most distinctive features of reason: it is thought of as capable not only of recollecting past events and meanings, but also itself. In this respect, the volume can be also taken as a reflective philosophical attempt by memory to recall itself, its functioning and transformations throughout its own history. (shrink)