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)

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)

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.

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)

This book examines three authors – Plutarch, Iamblichus and Augustine – who deeply impacted the ancient philosophical debates about divination, and highlights the complex relationship between philosophy and religion in Antiquity. Ce livre examine trois auteurs - Plutarque, Jamblique et Augustin - qui ont marqué les débats philosophiques antiques sur la divination et met en évidence la complexité des rapports entre philosophie et religion dans l’Antiquité.

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)

This book, the third in a series on the life course, has significance in today's world of research, professional practice, and public policy because it symbolizes the gradual reemergence of power in the social sciences. Focusing on "self-directedness and efficacy" over the life course, this text addresses the following issues: * the causes of change * how changes affect the individual, the family system, social groups, and society at large * how various disciplines--anthropology, sociology, psychology, epidemiology--approach this field of study, (...) with consideration given to common themes and differences Finally, an effort is made to develop a multidisciplinary perspective unique to the study of self-directedness and efficacy. (shrink)

This book, a history of a religious category of ancient philosophy, is the first synthesis on the notion of daimōn in the Platonic tradition. It focuses on the relationship between demonology and, respectively, cosmology, the philosophical hermeneutics of religion and theories of the soul. Histoire d’une catégorie religieuse de la philosophie ancienne, ce livre représente la première synthèse sur la notion de daimōn dans la tradition platonicienne. Il étudie les relations de la démonologie avec la cosmologie, l’herméneutique philosophique de la (...) religion et les théories de l’âme. (shrink)

In MemoriamElena Mamchur8 July, 1935–14 December, 2023. The principle of ‘maximum inheritance’, put forward by Elena Mamchur, presupposes its effect in scientific cognition even during ‘radical cha...

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.

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)

We propose that human reasoning relies on an inherence heuristic, an implicit cognitive process that leads people to explain observed patterns (e.g., girls wear pink) in terms of the inherent features of their constituents (e.g., pink is an inherently feminine color). We then demonstrate how this proposed heuristic can provide a unified account for a broad set of findings spanning areas of research that might at first appear unrelated (e.g., system justification, nominal realism, is–ought errors in moral reasoning). By revealing (...) the deep commonalities among the diverse phenomena that fall under its scope, our account is able to generate new insights into these phenomena, as well as new empirical predictions. A second main goal of this paper, aside from introducing the inherence heuristic, is to articulate the proposal that the heuristic serves as a foundation for the development of psychological essentialism. More specifically, we propose that essentialism—which is the common belief that natural and social categories are underlain by hidden, causally powerful “essences”—emerges over the first few years of life as an elaboration of the earlier, and more open-ended, intuitions supplied by the inherence heuristic. In the final part of the paper, we distinguish our proposal from competing accounts (e.g., Strevens' K-laws) and clarify the relationship between the inherence heuristic and related cognitive tendencies (e.g., the correspondence bias). In sum, this paper illuminates a basic cognitive process that emerges early in life and is likely to have profound effects on many aspects of human psychology. (shrink)

Arguments against the Russellian theory of definite descriptions based on cases that involve failures of uniqueness are a recurrent theme in the relevant literature. In this paper, I discuss a number of such arguments, from Strawson (1950), Ramachandran (1993) and Szabo (2005). I argue that the Russellian has resources to account for these data by deploying a variety of mechanisms of quantifier domain restrictions. Finally, I present a case that is more problematic for the Russellian. While the previous cases all (...) involve referential uses of descriptions (or some variations of such uses), the most effective objection to the uniqueness condition draws on genuine attributive uses. (shrink)

The author of the article turns to the modern discourse about man and his place in the humanities system. A retrospective analysis of the modern discourse about man allows us to distinguish three stages in its development: anti-humanism, anti-anthropology and post-anthropology. Despite the fact that the main topics around which he is focused are concentrated on criticism of "anthropocentrism" and "eurocentrism", the author concludes that the anti-anthropological narrative retains all the features of cultural and epistemological "narcissism". The anti-anthropological narrative continues (...) to function as a system of "recognizing oneself", as a system of "differentiating oneself and the other" and as a system of "justifying oneself through the other". (shrink)

The following study presents some considerations on different subjects regarding the field of art, from the art of using sounds in theatre and the importance of the Greek tragedy to the subtle differences between opera and theatre. The sound experiment is to be approached knowing that the audience is, in some way, deaf. The renewal of the sounds, even of those coming forth from the remote ages, is part of the author’s lust for a theater that celebrates real contact and (...) real feeling, with a unique expression of force, of intense colors and sharp energies. The main goal is to discover the actor’s or the opera singer’s work with the sounds, with the vibration of the words in his body, thus investigating the “meanings” of the pure sound. (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)

Mainstream political liberals hold that state coercion is legitimate only if it is justified on the grounds of reasons that all may reasonably be expected to accept. Critics argue that this public justification principle is self-defeating, because it depends on moral justifications that not all may reasonably be expected to accept. To rebut the self-defeat objection, I elaborate on the following disjunction: one either agrees or disagrees that it is wrong to impose one’s morality on others by the coercive power (...) of the state. Those who disagree reject PJP, they understand politics as war. Those who agree accept PJP, they understand politics as competition. Political competitors abide by PJP to avoid politics as war, by enforcing PJP on political combatants they engage in a war that is unavoidable. In both cases their exercise of political power has a justification that is reasonably acceptable to all. (shrink)

When is it right to go to war? The most persuasive answer to this question has always been 'in self-defense'. In a penetrating new analysis, bringing together moral philosophy, political science, and law, David Rodin shows what's wrong with this answer. He proposes a comprehensive new theory of the right of self-defense which resolves many of the perplexing questions that have dogged both jurists and philosophers. -/- Winner of the American Philosophical Association Frank Chapman Sharp Memorial Prize.

Nishi Shah has argued that the norm of truth is a prescriptive norm which regulates doxastic deliberation. Also, the acceptance of the norm of truth explains why belief is subject to norms of evidence. Steglich-Petersen pointed out that the norm of truth cannot be prescriptive because it cannot be broken deliberatively. More recently, Pascal Engel suggested that both the norms of truth and evidence are deliberately violated in cases of epistemic akrasia. The akratic agent accepts these norms but in some (...) cases he is not motivated by them. In this paper I will argue that Shah cannot use Engel's suggestion because, given his definition of doxastic deliberation, epistemic akrasia is impossible in the context of deliberation about belief. Furthermore, epistemic akrasia is in conflict with the phenomenon of doxastic transparency that Shah tries to explain. (shrink)

The article is devoted to the study of the nature of consciousness within the framework of the information concept. The paper proposes a definition of consciousness as an informational environment in which an extended model of reality is realized. The process of realization of this extended model is defined as thinking. The result of thinking is information objects that form a system in the form of information environment. Information objects are reflections of the real world properties, not directly, but by (...) means of translation through a special object – a carrier of consciousness. In the case of human consciousness, such a carrier is a human being (represented in the form of his nervous system). As a result, consciousness can be qualified as a simulacrum of reality, i.e., a model of a model: an information model of the carrier of consciousness, which in turn is a means of physical modeling of the real "big" world. Possible mechanisms mediating thinking are considered. For this purpose, two new concepts are introduced: neural circuit and neurophysical pattern. An approach to the study of self-consciousness based on the localization of the consciousness carrier in the multidimensional space of states of initial real objects, as well as their reflections in the form of information objects is proposed. This localization is ensured by the presence of feedbacks. Summarizing the results of the study, the article states the following connection between consciousness, self-consciousness and subjectness: under certain conditions (when consciousness is localized in the state space of the carrier of consciousness), consciousness acquires the property of self-consciousness, a special case of which (when the initiator of changes determining localization is the carrier of consciousness) is self-consciousness endowed with subjectness. (shrink)

When is it right to go to war? The most persuasive answer to this question has always been 'in self-defense'. In a penetrating new analysis, bringing together moral philosophy, political science, and law, David Rodin shows what's wrong with this answer. He proposes a comprehensive new theory of the right of self-defense which resolves many of the perplexing questions that have dogged both jurists and moral philosophers. By applying the theory of self-defense to international relations, Rodin produces a (...) far-reaching critique of the canonical Just War theory. The simple analogy between self-defense and national defense - between the individual and the state - needs to be fundamentally rethought, and with it many of the basic elements of international law and the ethics of international relations. (shrink)

In the article an idea is conducted that practice of education goes away the roots to the deep layers of human civilization. The author of the article concentrated the attention on the analysis of work of Socrates and Aristotle. It is shown that Socrates first began consciously to use the bottom- up reasoning and give general determinations, work on concepts. On the initial stage of educating Socrates induced students the system of questions to find truth, that in modern pedagogical anthropology (...) is one of main tasks in education. By means of the skilfully put questions Socrates tricked into a student to confession of those positions that are true. The author of the article pays attention to that Socrates used the new for that time methods of educating constantly, for example, conversation, unlike sophists that preferred to the lecture. The feature of conversations of Socrates consisted in that the simplest vital cases came into question at first, but after themes became complicated. Comparisons, metaphors, turns, satire, were thus used, that facilitated perception of sense of conversation to the students. In the article the analysis of anthropological and pedagogical ideas is given in labours of Aristotle. It is shown that Aristotle studying a man, his " nature" and " essence", did not stop thereon, and set by the question of improvement of human family by means of education. Aristotle considered that education must be under control the state, and nobody can doubt in that a legislator must belong with exceptional attention to education of young people, as in the states, where small attention is spared the questions of education, the political system suffers from it. (shrink)