This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. (...) Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method. (shrink)

Dans cet article je présente une analyse critique de l’approche habituelle de l’identité mathématique qui a son origine dans les travaux de Frege et Russell, en faisant un contraste avec les approches alternatives de Platon et Geach. Je pose ensuite ce problème dans un cadre de la théorie des catégories et montre que la notion d’identité ne peut pas être « internalisée » par les moyens catégoriques standards. Enfin, je présente deux approches de l’identité mathématique plus spécifiques: une avec la (...) fibration catégorielle et l’autre avec des catégories supérieures faibles. (shrink)

Dans cet article je présente une analyse critique de l’approche habituelle de l’identité mathématique qui a son origine dans les travaux de Frege et Russell, en faisant un contraste avec les approches alternatives de Platon et Geach. Je pose ensuite ce problème dans un cadre de la théorie des catégories et montre que la notion d’identité ne peut pas être « internalisée » par les moyens catégoriques standards. Enfin, je présente deux approches de l’identité mathématique plus spécifiques: une avec la (...) fibration catégorielle et l’autre avec des catégories supérieures faibles. (shrink)

The popular view according to which category theory provides a support for mathematical structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics studies ‘invariant form’ (Awodey) categorical mathematics studies covariant and contravariant transformations which, generally, have no invariants. In this paper I develop a non-structuralist interpretation of categorical mathematics.

When the traditional distinction between a mathematical concept and a mathematical intuition is tested against examples taken from the real history of mathematics one can observe the following interesting phenomena. First, there are multiple examples where concepts and intuitions do not well fit together; some of these examples can be described as “poorly conceptualised intuitions” while some others can be described as “poorly intuited concepts”. Second, the historical development of mathematics involves two kinds of corresponding processes: poorly conceptualised intuitions are (...) further conceptualised while poorly intuited concepts are further intuited. In this paper I study this latter process in mathematics during the twentieth century and, more specifically, show the role of set theory and category theory in this process. I use this material for defending the following claims: (1) mathematical intuitions are subject to historical development just like mathematical concepts; (2) mathematical intuitions continue to play their traditional role in today's mathematics and will plausibly do so in the foreseeable future. This second claim implies that the popular view, according to which modern mathematical concepts, unlike their more traditional predecessors, cannot be directly intuited, is not justified. (shrink)

Category theory doesn't support Mathematical Structuralism but suggests a new philosophical view on mathematics, which differs both from Structuralism and from traditional Substantialism about mathematical objects. While Structuralism implies thinking of mathematical objects up to isomorphism the new categorical view implies thinking up to general morphism.

In addition to the “universal glue,” which is the local mechanical causation, the standard explanatory scheme of classical science presumes two “universal vessels,” which are global space and time. I call this outdated metaphysical setting “black-and-white” because it allows for only two principal scales. A prospective metaphysics able to bind existing sciences together needs to be “colored,” that is, allow for scale relativity and diversification by domain.

This article asks whether a country that suffers from serious environmental problems caused by another country could have a just cause for a defensive war? Danish philosopher Kasper Lippert-Rasmussen has argued that under certain conditions extreme poverty may give a just cause for a country to defensive war, if that poverty is caused by other countries. This raises the question whether the victims of environmental damages could also have a similar right to self-defense. Although the article concerns justice of war, (...) we will concentrate only on the issue of what can be just causes of war, instead of evaluating the entire justification of war. This is to say that we will limit our discussion to the question concerning just cause and leave aside more general questions concerning justness and moral permissibility of war. Our aim is to list the questions that must be made and settled if defensive war in the case of serious environmental problems is said to have (or not to have) a just cause. We will argue that there are three questions that are most important in this context. They are the question concerning liability, the question of collective responsibility, and the question whether environmental harms may create a “sufficient reason” for raising a war. (shrink)

In 1900 David Hilbert announced his famous list of then-opened mathematical problems; the problem number 6 in this list is axiomatization of physical theories. Since then a lot of systematic efforts have been invested into solving this problem. However the results of these efforts turned to be less successful than the early enthusiasts of axiomatic method expected. The existing axiomatizations of physical and biological theories provide a valuable logical analysis of these theories but they do not constitute anything like their (...) standard presentation,which can be used for transmission, evaluation, and justification of physical and biological knowledge. This state of theart in the axiomatization of physics is strong evidence that the standard notion of axiomatic theory stemming from Hilbert and Tarski is not appropriate for thet ask. However in the recent years in mathematics there emerged a new axiomatic approach best represented by the Homotopy Type theory (HoTT). We argue that the constructive axiomatic architecture used in HoTT has better chances to be successfully applied in physics as well as in computer science and engineering. (shrink)

In this article, I develop a general explanatory model of the liability and lesser evil justifications of harm. Despite their respective provenance in consequentialist and deontological ethics, both justifications are, at root, rich forms of the proportionality relationship between a shared set of underlying normative variables. The nature of the proportionality relationship, and the conditions under which it operates, differ between the two forms of justification. The article explores these differences in detail and the implications they have for the justification (...) of self-defense and war. (shrink)

According to traditional Judeo-Christian-Islamic theism, God is an omniscient, omnipotent, and morally perfect agent. This volume shows that philosophy of religion needs to take seriously alternative concepts of the divine, and demonstrates the considerable philosophical interest that they hold.

This essay attempts to develop a new theoretical model for business ethics distinct from the two canonical business‐ethics theories, the stakeholder theory and the shareholder value theory. Milton Friedman argued that because managers are agents of the company's owners, their sole moral responsibility is to maximize owner returns. Thomas Pogge has recently suggested that such a view involves a kind of moral incoherence and that we should reject the efficacy of social arrangements like the principal‐agent relationship in altering moral obligations. (...) Both views fail to give proper account of the dispersal of moral responsibilities in business contexts. We must distinguish “minimal moral obligations” (stemming from justice and rights) from “maximal moral obligations” (stemming from all other moral considerations, including duties of aid, beneficence, and the virtues). Minimal obligations apply to all persons, but maximal obligations can be effected by social arrangements like the owner‐manager relationship. There may be moral obligations incumbent on owners that do not apply to managers. Understanding this distribution of responsibilities enables us to develop a new and attractive model of business ethics––“the ownership model”––which places greater emphasis on the rights and responsibilities of the owners of business than has been traditional in business ethics. (shrink)

In the wake of the considerable cultural changes and social shifts that the United States and all advanced industrial democracies have experienced since the late 1960s and early 1970s, social discourse around the disempowered has changed in demonstrable ways. In From Property to Family: American Dog Rescue and the Discourse of Compassion, Andrei Markovits and Katherine Crosby describe a “discourse of compassion” that actually alters the way we treat persons and ideas once scorned by the social mainstream. This “culture (...) turn” has also affected our treatment of animals inaugurating an accompanying “animal turn”. In the case of dogs, this shift has increasingly transformed the discursive category of the animal from human companion to human family member. One of the new institutions created by this attitudinal and behavioral change towards dogs has been the breed specific canine rescue organization, examples of which have arisen all over the United States beginning in the early 1980s and massively proliferating in the 1990s and subsequent years. While the growing scholarship on the changed dimension of the human-animal relationship attests to its social, political, moral and intellectual salience to our contemporary world, the work presented in Markovits and Crosby’s book constitutes the first academic research on the particularly important institution of breed specific dog rescue. (shrink)

This book provides an original and challenging perspective of religions as abstract complex adaptive systems, using an interdisciplinary approach to try to understand what religions are and how they function, two fundamental issues which, despite an intense struggle from several fields, have not yet been resolved. What is the source of religious belief? How do religions work and what are they made of? Why is religion so important for us that it has survived centuries of scientific progress and secularization? Why (...) are people religious even outside religion? The book addresses these questions using an interdisciplinary approach that seeks to untangle the Gordian knot of defining religion. In short, they can be considered entropy-reducing technologies. What differentiates them from other meaning-producing systems is their configuration which employs specific building blocks as tools for mitigating entropy, which are also subsystems and combine in various ways to build a unique configuration: rituals, myths, taboos, supernatural agents, authority, identity, superstitions, moral obligations, afterlife beliefs and the sacred. As a reaction to perturbances or pressure, systems can collapse. Inspired by Nicholas Nassim Taleb, it is, in this book, referred to as fragility—the negative reaction of systems to random events, and four parameters can be used to evaluate it in religious systems: monotonicity (the inability to learn from past mistakes), coupling (linking with other systems: such as political or economic), centralization and stress starvation. Several case studies are provided in order to test the theoretical claims made in this book, based on the author's field research in Romania, Japan, North Korea and Mongolia, and offering details that could be of interest to casual readers, students and researchers of religion. (shrink)

Digital inequality and digital justice are pressing issues in today's world. This work examines the socio-philosophical aspects of these problems and proposes measures to achieve digital justice. The authors draw attention to the fact that digital inequality can manifest itself in various forms, such as access to information, technology and resources, as well as opportunities to participate in the digital economy. This can lead to increased social inequalities and limited opportunities for the development of individuals and society as a whole. (...) To achieve digital justice, the authors propose a number of measures, such as improving access to digital technologies and resources, ensuring equal opportunities to participate in the digital economy, and protecting consumer rights and data privacy. They also draw attention to the need to promote digital literacy and education so that people can make effective use of digital technologies and resources. The authors also examine digital inequality and digital justice in the context of monopoly and free speech. They point out that some companies that declare their social responsibility may use their monopolistic position in the market to limit freedom of speech and access to information. In this context, the authors suggest strengthening the role of the state in regulating the digital economy and protecting consumer rights. In conclusion, the research is a valuable contribution to the field of research on digital inequality and digital justice. It emphasizes the need to take into account the socio-philosophical dimensions of these issues and suggests measures to achieve digital justice. It also draws attention to the importance of cultural and historical sensitivity in the development of digital policies and resources. (shrink)

This paper examines the ability of countries in Central and Eastern Europe to ensure appropriate protection of research participants in the field of increasingly globalizing biomedical research. By applying an analytical framework for identifying gaps in policies and programs for human subjects protection to four countries of CEE—Belarus, Latvia, Lithuania, and Poland, substantial gaps in the scope and content of relevant policies and major impediments to program performance have been revealed. In these countries, public policies on the protection of research (...) participants lack consistency and reliable mechanisms for their implementation. Impediments to program performance most often relate to inadequacies in the national research ethics systems with regard to organizational structure, budgetary support, supervision, and training. The level of research ethics capacity varies from country to country and depends on socio-economic and political factors of post-communist transition. The breadth and depth of the problems identified suggest that the current level of protection for research participants in CEE might be inadequate to the challenges posed by the globalization of biomedical research. In CEE countries, there is a need for strengthening research ethics capacity through modification of relevant policies and improvement of program management. The differences among the countries call for further research on identifying the best approaches for filling the gaps in the policies and programs aimed at ensuring effective protection of research participants. (shrink)

The article analyzes the possibilities and limitations of artificial intelligence. The article considers the subjectivity of artificial intelligence, determines its necessity for solving intellectual problems depending on the possibility of representing the real world as a deterministic system. Methodological limitations of artificial intelligence, which is based on the use of big data technologies, are stated. These limitations cause the impossibility of forming a holistic representation of the objects of cognition and the world as a whole. As a tool for deterministic (...) description of the universe it is proposed to use empirical-metaphysical general theory of systems, which is an extension of existing general theories of systems due to ontological justification of the phenomenon of isomorphism and definition of a limited set of laws, rules, patterns and primitives of forms and relations of objects in the universe. The distinction of natural (human) and artificial intelligence is considered, including the realization of multisystem integration of intelligence in physical, biological, social and spiritual systems. A philosophically grounded approach to ensuring the evolutionary properties of artificial intelligence is formulated, based on the inclusion of non-equilibrium mechanisms through which stability is realized. (shrink)

Generic statements (e.g., “Birds lay eggs”) express generalizations about categories. In this paper, we hypothesized that there is a paradoxical asymmetry at the core of generic meaning, such that these sentences have extremely strong implications but require little evidence to be judged true. Four experiments confirmed the hypothesized asymmetry: Participants interpreted novel generics such as “Lorches have purple feathers” as referring to nearly all lorches, but they judged the same novel generics to be true given a wide range of prevalence (...) levels (e.g., even when only 10% or 30% of lorches had purple feathers). A second hypothesis, also confirmed by the results, was that novel generic sentences about dangerous or distinctive properties would be more acceptable than generic sentences that were similar but did not have these connotations. In addition to clarifying important aspects of generics’ meaning, these findings are applicable to a range of real-world processes such as stereotyping and political discourse. (shrink)

J. К. Galbraith begins his book on the history and current problems of money with the following statement: “There is much that is diverting in the history of money, but even more that provides a rich reflection of human behavior and human folly.”.

Aleksandr Pushkin (1799-1837) occupies a special place in the development of Russian culture. He was at the same time a great poet, the reformer of Russian literary language, a historian and a political thinker. In the enormous mass of work devoted to Pushkin, a certain number of articles are concerned with his ideas on economics and the reflection of socio-economic problems in his writing. Until now, however, this theme has been studied in only a fragmentary way and less from the (...) point of view of the professional economist than from that of a literary historian. In an attempt to enlarge and complete the idea we may have of Pushkin's economic views, I propose also to show the importance the politico-economic thought of Western Europe had for his work. One person comes to the fore when we study the subject from this angle: Nikolai Turgenev, a Decembrist, one of the “masters” of the poet's youth, who played an important role in the rapprochement of Russian and Western European cultures. (shrink)

This volume explores how understanding relates to conscious experience. In doing so, it builds bridges between different philosophical disciplines and provides a metaphysically robust characterization of understanding, both in and beyond science. The past two decades have witnessed growing interest from epistemologists, philosophers of science, philosophers of mind, and ethicists in the nature and value of intellectual understanding. This volume features original essays from leading scholars of understanding and the phenomenal experiences that underlie it. The chapters are divided into three (...) thematic sections. Part 1 provides theoretical characterizations of understanding, including Henk de Regt’s defense of a contextual theory of scientific understanding and a debate whether scientific inference and explanatory power are necessary or central features of understanding. Part 2 explores how conscious experience and understanding are related. The chapters articulate a phenomenal theory of understanding and address themes that are connected to understanding, including awareness, transformative experiences, and exemplification. Finally, Part 3 is devoted to domain-specific inquiries about understanding, such as logical proofs, particle physics, cognitive enhancement, and moral understanding. (shrink)