The aim of this paper is to provide epistemic reasons for investigating the notions of informal rigour and informal provability. I argue that the standard view of mathematical proof and rigour yields an implausible account of mathematical knowledge, and falls short of explaining the success of mathematical practice. I conclude that careful consideration of mathematical practice urges us to pursue a theory of informal provability.

We analyse Kreisel’s notion of human-effective computability. Like Kreisel, we relate this notion to a concept of informal provability, but we disagree with Kreisel about the precise way in which this is best done. The resulting two different ways of analysing human-effective computability give rise to two different variants of Church’s thesis. These are both investigated by relating them to transfinite progressions of formal theories in the sense of Feferman.

This paper considers Maddy’s strategy for naturalising mathematics in the context of Quine’s scientific naturalism. The aim of this proposal is to account for the acceptability of mathematics on scientific grounds without committing to revisionism about mathematical practice entailed by the Quine-Putnam indispensability argument. It has been argued that Maddy’s mathematical naturalism makes inconsistent assumptions on the role of mathematics in scientific explanations to the effect that it cannot distinguish mathematics from pseudo-science. I shall clarify Maddy’s arguments and show that (...) the objection can be overcome. I shall then reformulate a novel version of the objection and consider a possible answer, and I shall conclude that mathematical naturalism does not ultimately provide a viable strategy for accommodating an anti-revisionary stance on mathematics within a Quinean naturalist framework. (shrink)

The History of Philosophical and Formal Logic introduces ideas and thinkers central to the development of philosophical and formal logic. From its Aristotelian origins to the present-day arguments, logic is broken down into four main time periods: Antiquity and the Middle Ages The early modern period High modern period Early 20th century Each new time frame begins with an introductory overview highlighting themes and points of importance. Chapters discuss the significance and reception of influential works and look at historical arguments (...) in the context of contemporary debates. To support independent study, comprehensive lists of primary and secondary reading are included at the end of chapters, along with exercises and discussion questions. By clearly presenting and explaining the changes to logic across the history of philosophy, The History of Philosophical and Formal Logic constructs an easy-to-follow narrative. This is an ideal starting point for students looking to understand the historical development of logic. (shrink)

Our ability to deal with abstract concepts is one of the most intriguing faculties of human cognition. Still, we know little about how such concepts are formed, processed, and represented in mind. Current views are presented in their most recent and advanced form in this special issue, and directly compared and discussed in a lively debate, reported at the end of each chapter. The main results are reported in the editors’ introduction.

Traditional medical practices and relationships are changing given the widespread adoption of AI-driven technologies across the various domains of health and healthcare. In many cases, these new technologies are not specific to the field of healthcare. Still, they are existent, ubiquitous, and commercially available systems upskilled to integrate these novel care practices. Given the widespread adoption, coupled with the dramatic changes in practices, new ethical and social issues emerge due to how these systems nudge users into making decisions and changing (...) behaviours. This article discusses how these AI-driven systems pose particular ethical challenges with regards to nudging. To confront these issues, the value sensitive design approach is adopted as a principled methodology that designers can adopt to design these systems to avoid harming and contribute to the social good. The AI for Social Good factors are adopted as the norms constraining maleficence. In contrast, higher-order values specific to AI, such as those from the EU High-Level Expert Group on AI and the United Nations Sustainable Development Goals, are adopted as the values to be promoted as much as possible in design. The use case of Amazon Alexa's Healthcare Skills is used to illustrate this design approach. It provides an exemplar of how designers and engineers can begin to orientate their design programs of these technologies towards the social good. (shrink)

In this paper, I will focus on a type of confabulation that emerges in relation to questions about mental attitudes whose causes we cannot introspectively access. I argue against two popular views that see confabulations as mainly offering a psychological story about ourselves. On these views, confabulations are the result of either a cause-tracking mechanism or a self-directed mindreading mechanism. In contrast, I propose the view that confabulations are mostly telling a normative story: they are arguments primarily offered to justify (...) one’s attitudes, and they are produced by our argumentative reasoning mechanism driven by the biological goal of presenting ourselves as good reasoners and as reliable sources of information. (shrink)

Although episodes of captive breeding for display and acclimatization purposes date back to the 19th century, systematic breeding for species conservation first became the central mission for European zoological gardens in the interwar period. While most scholars explain this shift as a result of a decline in the global trade of exotic animals, my analysis points to the simultaneous renewed interest in native endangered and extinct species as a catalyst for captive breeding experiments. This article considers the role of zoos (...) in one of the earliest de-extinction projects, namely the breeding back of the Eurasian wild horse. By investigating two breeding programs, those initiated by Tadeusz Vetulani in Poland and the Heck brothers in Germany, my analysis reveals not only the political stakes, but also the different methods employed in these attempts to resurrect the tarpan. More specifically, I explore how scientific ideas about heredity and hybridization, as well as understandings of the porous boundary between domestic and wild horses, paved the way for selective breeding to be mobilized as a means of bringing back the extinct species. This ambitious goal reinvigorated the scientific function of the zoo by making it an experimental ground for undoing extinction, and laid the groundwork for its future role in the emergent wildlife conservation movement. In addition to mapping out knowledge exchange between zoologists, geneticists, and paleontologists, this article traces the circulation of specimens between natural history museums, zoos, and wildlife reserves to underscore the material dimension of ex situ conservation practices. (shrink)

The Depression Anxiety Stress Scales is a set of psychometrically sound scales that is widely used to assess negative emotional states in adults. In this project, we developed the Depression Anxiety Stress Scales for Youth and tested its psychometric properties. Data were collected from 2,121 Australian children and adolescents aged 7–18. This sample was split randomly into a calibration group and a cross-validation group. First, we used Confirmatory Factor Analysis on the calibration group to test the 3-factor DASS model on (...) 40 items we had developed in previous exploratory studies. We then selected the best-performing 21 items based on both statistical and theoretical considerations, guided by the structure and item content of the adult DASS. We cross-validated this new 21-item model in the second half of the sample. Results indicated good fit for the final 21-item 3-factor DASS model in both groups of children and adolescents. Multiple regression analyses showed that when scores on the other DASS-Y scales were held constant, the DASS-Y Depression scale had a strong negative relationship with positive affect and life satisfaction, the DASS-Y Anxiety scale was strongly associated with physiological hyperarousal, and the DASS-Y Stress scale was associated with excessive worrying. However, the relationship between Stress and worrying was only evident from age 10 onwards. Our results show that the core symptoms that define depression, anxiety and stress in children and adolescents are similar to those previously found in adults. The DASS-Y is a public domain instrument that we hope will prove useful in both research and clinical contexts. (shrink)

Words are not just labels for conceptual categories. Words construct conceptual categories, frame situations and influence behavior. Where do they get their meaning? This book describes how words acquire their meaning. The author argues that mechanisms based on associations, pattern detection, and feature matching processes explain how words acquire their meaning from experience and from language alike. Such mechanisms are summarized by the distributional hypothesis, a computational theory of meaning originally applied to word occurrences only, and hereby extended to extra-linguistic (...) contexts. By arguing in favor of the cognitive foundations of the distributional hypothesis, which suggests that words that appear in similar contexts have similar meaning, this book offers a theoretical account for word meaning construction and extension in first and second language that bridges empirical findings from cognitive and computer sciences. Plain language and illustrations accompany the text, making this book accessible to a multidisciplinary academic audience. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in (...) the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The logic of Conditional Beliefs has been introduced by Board, Baltag, and Smets to reason about knowledge and revisable beliefs in a multi-agent setting. In this article both the semantics and the proof theory for this logic are studied. First, a natural semantics forCDLis defined in terms of neighbourhood models, a multi-agent generalisation of Lewis’ spheres models, and it is shown that the axiomatization ofCDLis sound and complete with respect to this semantics. Second, it is shown that the neighbourhood semantics (...) is equivalent to the original one defined in terms of plausibility models, by means of a direct correspondence between the two types of models. On the basis of neighbourhood semantics, a labelled sequent calculus forCDLis obtained. The calculus has strong proof-theoretic properties, in particular admissibility of contraction and cut, and it provides a decision procedure for the logic. Furthermore, its semantic completeness is used to obtain a constructive proof of the finite model property of the logic. Finally, it is shown that other doxastic operators can be easily captured within neighbourhood semantics. This fact provides further evidence of the naturalness of neighbourhood semantics for the analysis of epistemic/doxastic notions. (shrink)

The pervasiveness of AI-empowered technologies across multiple sectors has led to drastic changes concerning traditional social practices and how we relate to one another. Moreover, market-driven Big Tech corporations are now entering public domains, and concerns have been raised that they may even influence public agenda and research. Therefore, this chapter focuses on assessing and evaluating what kind of business model is desirable to incentivise the AI for Social Good (AI4SG) factors. In particular, the chapter explores the implications of this (...) discourse for SDG #17 (global partnership) and how this goal may encourage Big Tech corporations to strengthen multi-stakeholder partnerships that promote effective public-private and civil society partnerships and the meaningful co-presence of non-market and market values. In doing so, the chapter proposes an analysis of the sociological notion of "social license to operate" (SLO) elaborated in the mining and extractive industry literature and introduces it into the discourse on sustainable digital business models and responsible management of risks in the digital age. This serves to explore how such a social license can be adopted as a practice by digital business models to foster trust, collaboration and coordination among different actors - AI researchers and initiatives, institutions and civil society at large - for the support of SDGs interrelated targets and goals. (shrink)

Although still highly controversial, the idea that we can use technology to radically alter our environment in order to mitigate the climate challenges we now face is becoming an ever more discussed approach. This chapter takes up a specific climate engineering technology, carbon capture, usage, and storage (CCUS), and highlights how this technology works and how its governance still needs further work to ensure that it is aligned to the ideal of sustainable development. Given that climate engineering technologies like CCUS (...) have the potential to ameliorate many of the climate issues and support the SDGs, there remains a lacuna of inserting these globally impactful technologies within a normative political framework to respect that proper responsibility is attributed. The aim of the chapter is to examine the concept of accountability, how it has been traditionally understood in the literature, and why a polysemic and multidimensional account of accountability is required if climate engineering technologies like CCUS are actually to support sustainable development. This may serve as a first theoretically informed basis for reflection on how to create a synergy between the responsible deployment of climate engineering innovation and the achievement of the SDGs targets, one that can shed light on how justifications and decisions about sustainable strategies and constraints are managed, taken and communicated. (shrink)

Healthcare is becoming increasingly automated with the development and deployment of care robots. There are many benefits to care robots but they also pose many challenging ethical issues. This paper takes care robots for the elderly as the subject of analysis, building on previous literature in the domain of the ethics and design of care robots. Using the value sensitive design approach to technology design, this paper extends its application to care robots by integrating the values of care, values that (...) are specific to AI, and higher-scale values such as the United Nations Sustainable Development Goals. The ethical issues specific to care robots for the elderly are discussed at length alongside examples of specific design requirements that work to ameliorate these ethical concerns. (shrink)

Analytic Philosophy, Volume 62, Issue 3, Page 295-311, September 2021.

Artistic practices of postmodern art do not only express the principles of the conceptions of the world of modern culture but on the whole they prepare the anthropological "project" of a cosmopolit. But the danger of leveling and even ruining the system of the Ukrainian world outlook traditions exists in the framework of this project. In this article the author investigates the peculiarities of Yu. Andrukhovych' creative work in the context of the Ukrainian postmodern art. Thanks to the ironic form (...) and extreme spontaneity in the choice of dedication and epigraph, postulates the model in which the contextual neo-mythological features are traced and the features reveal the essential peculiarities of the anthropological project of a "post-totalitarian" person. The author's tragic world-outlook and apocalyptical mood are hidden behind the humor and eclectic glare. It doesn't look like "banquet during the plague", but like the comprehension of the problem of one's existence under the totally new historic-cultural conditions. The neo-mythological axis is grounded on the Christian-mythological model-antithesis. The neo-mythological peculiarities analyzed by the author interact with each other in the dialectical unity and make the organic entirety of the artistic work, they are actual for a contemporary person finding himself under the conditions of a transitional period when culture is looking for stable landmarks in its development. It is proved that the neomyth by Yu. Andrukhovych was being built on the synthesis of Christianity and folk culture, ascertaining the European character of the Ukrainian culture and surge for its legitimacy, uniting together the Dianetical and Apologian features. It gave the author the chance to model the modern culture in the coordinates "Bu - bo - bu" and build the anthropological project in the direction of a Cosmopolitan pole. (shrink)

This paper argues that a new genre of therapy has appeared in the arena of contemporary spiritual alternative healing, which expresses an outlook never-before-seen in the history of medicine: postmodern therapy. Postmodern therapeutic methods express a popularization of postmodernist philosophy in regards to language’s role in the therapeutic process, expressing a novel cosmology. These methods are illustrated in the paper, and then analyzed in comparison to two other groups of methods: traditional/occult magic, and modern medicine. Finally, PTMs are characterized as (...) neo-magic, bearing features similar to modernistic outlook on the one hand, and features similar to pre-modern magic outlook on the other hand. Thus, these new outlook demonstrate a double appropriation and rejection of perceptions viewed as contradictory – traditional magic and secular science. (shrink)

In the article the key terms including “coach”, “coaching”, “coaching technology” used in the area of educational leadership are investigated. The purpose, tasks and types of coaching in the educational management are determined. The coaching algorithm as a technology targeted at unlocking the potential of university faculty and staff is explained. The emphasis is placed on the use of coaching principles that ensure effective leadership. The immense potential that coaching technology provides for the educational leadership is considered. The role of (...) master programs that offer specialized training for future leaders in different educational environments is outlined. In order to stimulate professional education, leader’s ability to make ethical managerial decisions, develop responsibility, confidence in their own capabilities, the ways of implementing coaching technology in higher education are substantiated. The key competencies and masteries that educational leaders have to acquire are outlined. Today’s schools lack experienced leader that can ensure stability and growth. To understand the problems and challenges that schools in Ukraine are facing, principals in two regions of Ukraine have been served regarding their awareness of the term “coaching” and its practical importance for the effective educational management. It is argued that coaching as a strategy to ensure effective leadership is considered to be a powerful resource for any educational setting. The framework of coaching treats each and every employee as a unique, creative personality, able to independently solve a number of tasks, take initiative, make choices, and realize goals. (shrink)

While the notion of risk remains under-theorised in moral philosophy, risk aversion and moralist self-protection appear as dominant cultural tendencies saturating educational orientation and practice. Philosophy of education has responded to the educational emphasis on risk management by exposing the unavoidable and positive presence of risk in any endeavour to learn and teach. Taking such responses into account, I discuss how the theoretical connection of risk and education could be radicalised through an ethical approach combined with epistemological and existential concerns. (...) My aim is to propose an ethics that is sensitive to the difference between risks taken and risks imposed and to the cultural variations of what counts as danger. Finally, I explain how the educational relevance of such an ethics requires a prior questioning of the western understanding of self and world that has functioned as a subtext of the dominant view of risk. (shrink)

In search for the “missing links” of queer posthumanist discourses, some nonhuman animals play a crucial role in setting up new possible ontologies of sexual diversity. However, the desire to trace “natural” evidence for sexual diversity and a non-binary gender system that goes beyond the simplistic “social constructionism” vs. “biological essentialism” dichotomy in the nonhuman world should be critically examined. In this article I analyze both the scientific and popular representations of “wild and weird” nonhuman animals that became rich semiotic-material (...) referents to human sexuality and gender diversity in order to propose “transpecies intimacies” as a strategy for overcoming the deadlock present in naturalizing and essentializing discourses. This essay focuses on the case of the spotted hyena, because this nonhuman animal functions as an important signifier and material resource for sexual differences on multiple levels of power relations – institutional, scientific, educational, somatic, discursive, and even affective. I consider how biomedical narratives on sexualized nonhuman animals employ hegemonic economies of sexual difference to build stories of a naturalized sexuality and an embodied gender difference wherein some chemical substances, like hormones, and some body parts, like genitals, serve as primary actors in this semiotic-material system. (shrink)

While there is a widespread acceptance of the link between religiosity and ethics, there is less certainty how this influence occurs exactly, necessitating further research into these issues. A main roadblock to our understanding of this influence from an Islamic perspective is the absence of a validated measurement tool. The purpose of this study therefore is to develop a Scale of Muslims’ Views of Allah. This article discusses how the SMVA was developed through the following five steps: establishment of content (...) and face validity; application of a cognitive interviewing technique to pretest the SMVA with sixteen participants; pilot testing of the SMVA with twelve participants; administration of the SMVA online to marketing and management professionals via a multi-stage cluster sampling process to verify the scale’s reliability and validity; and testing criterion-related validity. The results showed that the newly constructed 13-item scale had adequate psychometric properties. Finally, the implications for organisations, limitations and future research are discussed. (shrink)

The aim of this article is to investigate possibilities for conceptions of critical thinking beyond the established educational framework that emphasizes skills. Distancing ourselves from the older rationalist framework, we explain that what we think wrong with the skills perspective is, amongst other things, its absolutization of performativity and outcomes. In reviewing the relevant discourse, we accept that it is possible for the skills paradigm to be change‐friendly and context‐sensitive but we argue that it is oblivious to other, non‐purposive kinds (...) of rationality that are indispensable to critical thought. Our suggestion is that there is an aporetic element in critical thought that is missing from contemporary educational positions. We consider some other efforts to redeem the surplus of criticality that performativity fails to take into account and conclude that the aporetic element that we highlight accommodates better than other theories do the significance of thematizing the taken‐for‐granted instead of focusing on problem solving. (shrink)

What form does power take in situations of retaliation against whistleblowers? In this article, we move away from dominant perspectives that see power as a resource. In place, we propose a theory of normative power and violence in whistleblower retaliation, drawing on an in-depth empirical study. This enables a deeper understanding of power as it circulates in complex processes of whistleblowing. We offer the following contributions. First, supported by empirical findings we propose a novel theoretical framing of whistleblower retaliation and (...) the role of mental health, which draws upon poststructuralist psychoanalytic thinking. Specifically, we highlight how intra- and inter-psychic affective and ambivalent attachments to organizations influence the use of normative violence in cases of whistleblower retaliation. The second contribution is empirical and builds upon the existing literature on whistleblower retaliation by highlighting how organizations position whistleblower subjects as mentally unstable and unreliable individuals, to undermine their claims. We conclude by highlighting the implications of normative power for the outcomes of whistleblower struggles. (shrink)

Whistleblowers are a vital means of protecting society because they provide information about serious wrongdoing. And yet, people who speak up can suffer. Even so, debates on whistleblowing focus on compelling employees to come forward, often overlooking the risk involved. Theoretical understanding of whistleblowers’ post-disclosure experience is weak because tangible and material impacts are poorly understood due partly to a lack of empirical detail on the financial costs of speaking out. To address this, we present findings from a novel empirical (...) study surveying whistleblowers. We demonstrate how whistleblowers who leave their role as a result of speaking out can lose both the financial and temporal resources necessary to redevelop their livelihoods post-disclosure. We also show how associated costs involving significant legal and health expenditure can rise. Based on these insights, our first contribution is to present a new conceptual framing of post-disclosure experiences, drawing on feminist theory, that emphasizes the bodily vulnerability of whistleblowers and their families. Our second contribution repositions whistleblowing as a form of labour defending against precarity, which involves new expenses, takes significant time, and often must be carried out with depleted income. Bringing forth the intersubjective aspect of the whistleblowing experience, our study shows how both the post-disclosure survival of whistleblowers, and their capacity to speak, depend on institutional supports or, in their absence, on personal networks. By reconceptualizing post-disclosure experiences in this way—as material, embodied and intersubjective—practical implications for whistleblower advocacy and policy emerge, alongside contributions to theoretical debates. Reversing typical formulations in business ethics, we turn extant debates on the ethical duty of employees to speak up against wrongdoing on their heads. We argue instead for a responsibility to protect whistleblowers exposed to vulnerability, a duty owed by those upon whose behalf they speak. (shrink)

Many utopian visions operate by scapegoating an Otherness. They blame an ‘enemy’ for an unbearable, dystopian current reality, holding the ‘enemy’ responsible for it or for obstructing the passage to a desired, new reality. Then they exclude (or even promise the elimination of) this ‘enemy’. Despite the renewed interest in utopias, such utopian frames remain theoretically neglected or, worse, they are considered typical of the logical structure of utopianism. This paper aims to show that this issue merits a different political-philosophical (...) attention. We begin with operations of utopian predicates in the relevant scholarship and distinguish them from the operations of the term ‘incriminatory’ that we are introducing. We term incriminatory the kind of utopian frame whose future-oriented, idealized and desired image is constructed in and through an incriminated ‘Other’. We indicate the re-conceptualizing merits of this new term and then we discuss the affirmative utopianism that does not incriminate a specific Other. Our main argument, which we deploy contra Yannis Stavrakakis’s position, is that utopias are not unavoidably or inherently incriminatory. (shrink)

Departing from the intention to explore Frank Gehry’s drawings serving to their own designer to grasp ideas during the process of their genesis, the article examines Frank Gehry’s concern about the revelation of the first gestural drawings and all the sketches and working models concerning the evolution of his projects, and his intention to capture the successive transformation and progressive concretisation of architectural concepts. The article also compares Gehry’s design process with that of Enric Miralles, Alvar Aalto, Bernard Tschumi, and (...) Le Corbusier. It sheds light on Miralles, Aalto, Le Corbusier and Gehry’s interest in a holistic understanding of all the parts of an architectural project, which is expressed through their tendency to draw the different sketches concerning the same project on the same sheet of paper. At the core of Gehry’s design approach is the osmosis of function and morphology. This aspect of his design vision could be compared to Alvar Aalto’s design process. At the core of the article are the distinction between communication drawings and conceptual drawings, and Gehry’s concern about achieving an osmosis between function and morphology. The article also investigates Gehry’s use of uninterrupted self-twisting line in his sketches, exploring his intention to enhance a straightforward relationship between the gesture and the decision-making regarding the form of the building. (shrink)

New technologies are the source of uncertainties about the applicability of moral and morally connotated concepts. These uncertainties sometimes call for conceptual engineering, but it is not often recognized when this is the case. We take this to be a missed opportunity, as a recognition that different researchers are working on the same kind of project can help solve methodological questions that one is likely to encounter. In this paper, we present three case studies where philosophers of technology implicitly engage (...) in conceptual engineering (without naming it as such). We subsequently reflect on the case studies to find out how these illustrate conceptual engineering as an appropriate method to deal with pressing concerns in the philosophy of technology. We have two main goals. We first want to contribute to the literature on conceptual engineering by presenting concrete examples of conceptual engineering in the philosophy of technology. This is especially relevant, because the technologies that are designed based on the conceptual work done by philosophers of technology potentially have crucial moral and social implications. Secondly, we want to make explicit what choices are made when doing this conceptual work. Making explicit that some of the implicit assumptions are, in fact, debated in the literature allows for reflection on these questions. Ultimately, our hope is that conscious reflection leads to an improvement of the conceptual work done. (shrink)

Local seed systems remain the fundamental source of seeds for many crops in developing countries. Climate resilience for small holder farmers continues to depend largely on locally available seeds of traditional crop varieties. High rainfall events can have as significant an impact on crop production as increased temperatures and drought. This article analyzes the dynamics of maize diversity over 3 years in a farming community of Yucatán state, Mexico, where elevated levels of precipitation forced farmers in 2012 to reduce maize (...) diversity in their plots. We study how farmers maintained their agroecosystem resilience through seed networks, examining the drivers influencing maize diversity and seed provisioning in the year preceding and following the 2012 climatic disturbance. We found that, under these challenging circumstances, farmers focused their efforts on their most reliable landraces, disregarding hybrids. We show that farmers were able to recover and restore the diversity usually cultivated in the community in the year following the critical climate event. The maize dynamic assessed in this study demonstrates the importance of community level conservation of crop diversity. Understanding farmer management strategies of agrobiodiversity, especially during a challenging climatic period, is necessary to promote a more tailored response to climate change in traditional farming systems. (shrink)

The first half of the twentieth century was marked by the simultaneous development of logic and mathematics. Logic offered the necessary means to justify the foundations of mathematics and to solve the crisis that arose in mathematics in the early twentieth century. In European science in the late nineteenth century, the ideas of symbolic logic, based on the works of J. Bull, S. Jevons and continued by C. Pierce in the United States and E. Schroeder in Germany were getting popular. (...) The works by G. Frege and B. Russell should be considered more progressive towards the development of mathematical logic. The perspective of mathematical logic in solving the crisis of mathematics in Ukraine was noticed by Professor of Mathematics of Novorossiysk University Ivan Vladislavovich Sleshynsky. Sleshynsky is a Doctor of Mathematical Sciences, Professor of Novorossiysk University. After studying at the University for two years he was a Fellow at the Department of Mathematics of Novorossiysk University, defended his master’s thesis and was sent to a scientific internship in Berlin, where he listened to the lectures by K. Weierstrass, L. Kronecker, E. Kummer, G. Bruns. Under the direction of K. Weierstrass he prepared a doctoral dissertation for defense. He returned to his native university in 1882, and at the same time he was a teacher of mathematics in the seminary, Odesa high schools, and taught mathematics at the Odesa Higher Women’s Courses. Having considerable achievements in the field of mathematics, in particular, Pringsheim’s Theorem proved by Sleshinsky on the conditions of convergence of continuous fractions, I. Sleshynsky drew attention to a new direction of logical science. The most significant work for the development of national mathematical logic is the translation by I. Sleshynsky from the French language “Algebra of Logic” by L. Couturat. Among the most famous students of I. Sleshynsky, who studied and worked at Novorossiysk University and influenced the development of mathematical logic, one should mention E. Bunitsky and S. Shatunovsky. The second period of scientific work of I. Sleshynsky is connected with Poland. In 1911 he was invited to teach mathematical disciplines at Jagiellonian University and focused on mathematical logic. I. Sleshynsky’s report “On Traditional Logic”, delivered at the meeting of the Philosophical Society in Krakow. He developed the common belief among mathematicians that logic was not necessary for mathematics. His own experience of teaching one of the most difficult topics in higher mathematics – differential calculus, pushed him to explore logic, since the requirement of perfect mathematical proof required this. In one of his further works of this period, he noted the promising development of mathematical logic and its importance for mathematics. He claimed that for the mathematics of future he needed a new logic, which he saw in the “Principles of Mathematics” by A. Whitehead and B. Russell. Works on mathematical logic by I. Sleszynski prompted many of his students in Poland to undertake in-depth studies in this field, including T. Kotarbiński, S. Jaśkowski, V. Boreyko, and S. Zaremba. Thanks to S. Zaremba, I. Sleshynsky managed to complete the long-planned concept, a two-volume work “Theory of Proof”, the basis of which were lectures of Professor. The crisis period in mathematics of the early twentieth century, marked by the search for greater clarity in the very foundations of mathematical reasoning, led to the transition from the study of mathematical objects to the study of structures. The most successful means of doing this were proposed by mathematical logic. Thanks to Professor I. Sleshynsky, who succeeded in making Novorossiysk University a center of popularization of mathematical logic in the beginning of the twentieth century the ideas of mathematical logic in scientific environment became more popular. However, historical events prevented the ideas of mathematical logic in the domestic scientific space from the further development. (shrink)