This book provides an accessible, critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century: logicism, intuitionism and formalism.

During the Danish cartoons controversy in 2005–2006, a group of ambassadors to Denmark representing eleven predominantly Muslim countries requested a meeting with the Danish Prime Minister, Anders Fogh Rasmussen, to protest against the cartoons. Rasmussen interpreted their viewpoint as one of demanding limits to freedom of speech and he ignored their request for a meeting. Drawing on this case study, the article argues that it is an appropriate, and potentially effective, moral criticism of anyone who is in a position of (...) political power—taking into account reasonable constraints of feasibility and practicality—that they have refused to receive information, ideas, or opinions from individuals, or their representatives, with dissenting viewpoints. The article also articulates one possible theoretical ground for such a moral criticism: that they could be violating a fundamental moral right of people to submit information, ideas, or opinions to those who wield power over them and to be meaningfully heard—a right which can span state borders. (shrink)

Historical memory is considered in this article as one of the most important pillars of national identity. In addition to identifying some of the characteristic features of national, historical memory, the author shows that historical memory is influenced by two factors—the direct experience of the witnesses and participants of past events and official propaganda. As the direct witnesses of events disappear, the possibility of reconstructing and distorting historical memory increases. The ideas put forth in this article are formulated based on (...) the historical memory of World War II in the United States, Russia, Germany, and other European countries. (shrink)

The article discusses the issue of the nature of analytic philosophy. It is shown that in the 1920s–1940s it was a certain philosophical school, whose representatives were united by some initial principles. Analytic philosophers saw the main task of philosophy in the analysis of the language of natural sciences, in establishing logical connections between scientific propositions, in the empirical substantiation of scientific theories and in the elimination of speculative concepts and proposals from the language of science. The tool for such (...) analysis was the mathematical logic created at the beginning of the 20th century by G. Frege, A.N. Whitehead, B. Russell. Another characteristic feature of the analytic tradition was a negative attitude toward philosophical speculation. Adherents of this tradition believed that philosophy does not provide knowledge about the world, therefore, it is not a science. Analytic philosophers have made a significant contribution to the methodology of scientific knowledge, offering an accurate description of the hypothetical-deductive structure of scientific theory, methods of scientific explanation and prediction, verification, confirmation and refutation of scientific statements. In the late 1930s, most of the analytic philosophers emigrated to England and the United States. The analytic movement is gradually losing its integrity and loses the features of a philosophical school. There is a rejection of mathematical logic as the main means of analysis, the connection with the natural sciences has been lost. In the second half of the 20th century, analytic philosophy from a specific philosophical school turns into a certain style of thinking of the philosophers of various philosophical research areas and orientations. (shrink)

The author considers a problem of understanding. He claims that we understand texts, cultural objects rather than a man. He considers understanding as a process of interpretation of linguistic expressions and cultural objects. The author observes two sides of the meaning of linguistic expressions: a general (or social) one, which is common in a certain language community, and a personal one, which defines personal understanding. It is argued that mutual understanding is possible only on the stage of general meaning. However, (...) the exchange of personal meanings is a very sophisticated process. (shrink)

The paper discusses several problems of metaphilosophy that were explored in the philosophical literature in Russia. Metaphilosophy tries to understand what is philosophy, what problems philosophers are dealing with, which methods they employ in their investigations, the nature of philosophical statements and so on. Philosophers in Russia tended to think of philosophy as a special type of worldview that exists together with the ordinary worldview and religious worldview. The author defines worldview as a collection of basic beliefs about the surrounding (...) world, society, human being, the relations existing between individuals and society, about values and ideals. It is underscored that a worldview is always somebody’s worldview (it belongs either to an individual or a social group). The worldview problems explored by philosophers remain the same throughout thousands of years; what changes is how they are stated in different times. Every human being faces these problems if she has realized herself as an autonomous being and the reality splits for her into the I and the non-I. All philosophical problems revolve around three basic questions: what is the non-I (i.e. nature and society)? - this is the ontological question; what is I? (the anthropological question); what relations exist between the I and the non-I (the epistemological, axiological, ethical and other questions). The author also explores several stages of a philosophical investigation: an internal dissatisfaction with existing solutions, a search for a new perspective (meaning, idea, interpretation), development of the found solution. The author points at a number of characteristics that make philosophy different from science: philosophical statements and conceptions cannot be verified or refuted by experience, they are not universal. It is argued that the notion of truth in its classical interpretation cannot be applied to philosophical statements because the latter cannot be true or false. The author concludes that philosophical statements or conceptions express the subjective opinion of a given philosopher about the world and the human being. An obvious evidence for this is the existing pluralism of philosophical systems, schools, and trends. (shrink)

The author presents a philosophical critique of the basic ideas of logical semantics, as developed by Frege, Russell, and Wittgenstein. He argues that these logicians understated the importance of the sense of linguistic expressions.

In recent decades, more and more works have appeared, the authors of which are trying to predict possible scenarios for the future development of mankind. This article discusses 5 such scenarios: F. Fukuyama believes that all peoples and countries of the globe in the XXI century will develop in the direction of building a liberal-democratic society; Representatives of the Club of Rome in their latest report, based on statistical data of industrial development, substantiate the idea that by the middle of (...) the XXI century. the Earth’s biosphere will become unsuitable for human life and humanity will begin to die out; representatives of the transhumanist movement in their “Manifesto” set themselves the goal of replacing the human biological body with an artificial body by 1245 and thereby saving people from diseases, from old age and even from death itself; English economist D. Susskind in his book “The Future Without Jobs” predicts that in the next two to three decades, robots and artificial intelligence will force people out of all areas of production and discusses the question of how people who are deprived of the opportunity to work will live; Finally, the Israeli historian Yu.N. Harari in his extensive work “Homo Deus” paints a picture of the fact that scientific and technological progress will turn “reasonable man” into “divine man” in the near future. Assessing all these scenarios for the future development of mankind, one involuntarily comes to the conclusion that they all speak of the death of mankind in the near future. (shrink)

What is the identity of the best regime in Aristotle's Politics? Although there are a few references to the best regime in Book III, the obvious answer is the regime discussed in Books VII and VIII. Aristotle calls it the best regime on numerous occasions and discusses it at great length. Yet, this is not the complete answer. In Book IV Aristotle makes certain curious remarks on the best regime that, on examination, do not fit the best regime of Books (...) VII and VIII. They lead, instead, to the discovery of a systematic, though quiet, teaching on a very different best regime in Book III. The Politics actually contains a complicated yet coherent teaching on two best regimes. Grasping this teaching is key to arriving at a proper understanding of the distinctive character of Aristotle's political thought. (shrink)

In this paper we pay attention to the inconsistency in the derivation of the symmetric electromagnetic energy–momentum tensor for a system of charged particles from its canonical form, when the homogeneous Maxwell’s equations are applied to the symmetrizing gauge transformation, while the non-homogeneous Maxwell’s equations are used to obtain the motional equation. Applying the appropriate non-homogeneous Maxwell’s equations to both operations, we obtained an additional symmetric term in the tensor, named as “compensating term”. Analyzing the structure of this “compensating term”, (...) we suggested a method of “gauge renormalization”, which allows transforming the divergent terms of classical electrodynamics (infinite self-force, self-energy and self-momentum) to converging integrals. The motional equation obtained for a non-radiating charged particle does not contain its self-force, and the mass parameter includes the sum of mechanical and electromagnetic masses. The motional equation for a radiating particle also contains the sum of mechanical and electromagnetic masses, and does not yield any “runaway solutions”. It has been shown that the energy flux in a free electromagnetic field is guided by the Poynting vector, whereas the energy flux in a bound EM field is described by the generalized Umov’s vector, defined in the paper. The problem of electromagnetic momentum is also examined. (shrink)

The article is dedicated to the philosophical reaction by several Russian symbolists to the revolution of 1917. It demonstrates the “re-grouping” of Silver Age symbolism, which laid bare the underlying differences in its value foundations. The article considers this refracted unity in the ideational world of symbolism, in the journalistic writings of Vjacheslav Ivanov, Alexander Blok, Andrej Bely, and Maximilian Voloshin.

The investigations of Aza A. Takho-Godi, devoted to the evolution of concepts and terms in European culture, were ahead of their time and, as it turns out today, paved the way for historical semantics, which turned out to be a kind of independent version of the “history of concepts”: a direction of humanitarian thought aimed at identifying cultural, social, and political functions concepts in their historical dynamics and in relation to a wide field of cultural interactions of a particular era. (...) The impressive results of “historical semantics” in the version of Takho-Godi are connected not only with the masterful and strictly substantiated identification of the developing conceptual core of lexemes, not only with the penetrating intuitions of the living word, but also with the vision of an absolute spiritual context in which semantic worlds are driven not by mechanical causality and not by historical chance, but by a kind of teleology. (shrink)

The First World War forced the Russian intelligentsia to rethink its values—values that had been constructed in the nineteenth century. Distancing itself from pacifism and cultural relativism, it began to search for a moral meaning to the war that broke out in 1914—i.e. to defend the war as morally right and having a higher spiritual purpose. Russian philosophers were central to these debates, as they tried to interpret the war, and the relationship between war and peace, from a metaphysical point (...) of view. The paper will look at philosophical, ethical and religious aspects of these debates, and some of the philosophers who participated in them. (shrink)

Late Edmund Husserl’s examination of the crisis of the European sciences is the point of departure of this paper. Husserl’s views about wrong objectivisation and naturalization of reason in science and philosophy have prepared the ground for dissatisfaction with reason in various trends of 20th century Social and Political Philosophy. This intellectual climate has naturally bred the radical criticism against the social project of Enlightenment practiced by the first generation Frankfurt School. Later on, the Modern reason misfortunes in social and (...) political sphere are epitomized by Emanuel Levinas’ uprising against fundamentalontology for the sake of responsibility to the Other as well as by Julia Kristeva’s appeal to reestablish the social contract on new sensibility and new rationality. Finally, Jean Boaudrillard puts the univocal diagnosis that reason has surrendered to the code of consumerist simulacrum. In the second part of the paper, some suggestions proposed by the above philosophers (except for Baudrillard) about resolving the deadlock prepared by the Modern reason are viewed briefly. A conclusion is made that Baudrillard’s pessimistic position seems to be the most plausible and relevant in the current socio‐political and philosophical climate. (shrink)

The purpose of the present essay is to explain how the basic notions of Modern philosophy, forming Descartes’ optimistic attitude towards knowledge and human relations, were altered in order to be critically implemented into Vico’s more sober teaching. Several decades after Descartes took up the fight against skepticism, an Italian thinker, Giambattista Vico, critically approached the Cartesian project of Modernity. While Descartes believed that the essence of a human being consists in applying reason properly and using free will according to (...) its guidance in order to achieve the greatest success in science, mathematics, and philosophy, Vico insisted that human imagination and ingenuity ought to be directed to the humanities and legal studies and should aim at practical results. This was the eighteenth century Humanistic reply to Descartes. (shrink)

The proposed paper makes an overview of ideas about the failure of the Modern reason as they are launched in the 20th century Continental Philosophy. It begins with Edmund Husserl’s views about wrong objectivism and naturalism in science and philosophy, proceeds to the radical criticism against the project of Enlightenment practiced by the first generation Frankfurt School, and pays attention to Hans-Georg Gadamer’s dissatisfaction with cliché language and thinking dominating both public and private discourse today. Further examination of the Modern (...) reason misfortunes discusses Emanuel Levinas’ uprising against fundamental ontology for the sake of ethics and responsibility to the Other, Julia Kristeva’s appeal to reestablish the social contract on new sensibility and new rationality, and Jean Boaudrillard’s observation that reason has surrendered to the code of simulacrum. In the second part of the paper, some suggestions proposed by the above philosophers (except Baudrillard) about resolving the deadlock of the Modern reason are viewed briefly. A conclusion is made that Baudrillard’s pessimistic position seems to be the most plausible and relevant in the current socio-political and philosophical climate. (shrink)

The article examines the main ideological content of the work of the community of scientists and philosophers, which entered the history of philosophy under the name “The Vienna Circle”. Representatives of this association viewed their main methodological task in the logical analysis of the language of science in order to eliminate metaphysical – pseudoscientific – concepts. They investigated the structure of scientific theories, the functions of the theory – explanation and prediction, the processes of justification, confirmation and refutation of theories. (...) Their results were widely recognized, set down essential influence on scientific problems as well as style of philosophical and academic studies, and are still included in textbooks on the philosophy of science. The members of the Vienna Circle created the first holistic concept of science, which gave impetus to subsequent developments in the philosophy of science and served as example for the construction of similar concepts. The socio-ideological prerequisite of this philosophical movement was the task of creating a new scientific view of the world, opposing philosophical pessimism and anti-scientism. This worldview, however, was not naive-scientististic, but presented a synthetic project at the intersection of natural science, philosophy, art and social pedagogy. (shrink)

Achieving space domain awareness requires the identification, characterization, and tracking of space objects. Storing and leveraging associated space object data for purposes such as hostile threat assessment, object identification, and collision prediction and avoidance present further challenges. Space objects are characterized according to a variety of parameters including their identifiers, design specifications, components, subsystems, capabilities, vulnerabilities, origins, missions, orbital elements, patterns of life, processes, operational statuses, and associated persons, organizations, or nations. The Space Object Ontology provides a consensus-based realist framework (...) for formulating such characterizations in a computable fashion. Space object data are aligned with classes and relations in the Space Object Ontology and stored in a dynamically updated Resource Description Framework triple store, which can be queried to support space domain awareness and the needs of spacecraft operators. This paper presents the core of the Space Object Ontology, discusses its advantages over other approaches to space object classification, and demonstrates its ability to combine diverse sets of data from multiple sources within an expandable framework. Finally, we show how the ontology provides benefits for enhancing and maintaining longterm space domain awareness. (shrink)

The present study investigated whether individual differences between psychologists in thinking styles are associated with accuracy in diagnostic classification. We asked novice and experienced clinicians to classify two clinical cases of clients with two co-occurring psychological disorders. No significant difference in diagnostic accuracy was found between the two groups, but when combining the data from novices and experienced psychologists accuracy was found to be negatively associated with certain decision making strategies and with a higher self-assessed ability and preference for a (...) rational thinking style. Our results underscore the idea that it might be fruitful to look for explanations of differences in the accuracy of diagnostic judgments in individual differences between psychologists (such as in thinking styles or decision making strategies used), rather than in experience level. (shrink)

Achieving space situational awareness requires, at a minimum, the identification, characterization, and tracking of space objects. Leveraging the resultant space object data for purposes such as hostile threat assessment, object identification, and conjunction assessment presents major challenges. This is in part because in characterizing space objects we reference a variety of identifiers, components, subsystems, capabilities, vulnerabilities, origins, missions, orbital elements, patterns of life, operational processes, operational statuses, and so forth, which tend to be defined in highly heterogeneous and sometimes inconsistent (...) ways. The Space Domain Ontologies are designed to provide a consensus-based realist framework for formulating such characterizations in a way that is both consistent and computable. Space object data are aligned with classes and relations in a suite of ontologies built around the existing Space Object Ontology. They are stored in a dynamically updated Resource Description Framework triple store, which can be queried to support space situational awareness and the needs of spacecraft operators and analysts. This paper provides an overview of the Space Domain Ontologies and their development and use. It presents the motivation for and advantages of the Space Domain Ontologies, including the benefits they provide for enhancing and maintaining long-term space situational awareness. (shrink)

The dorsal anterior cingulate cortex is a key node in the human salience network. It has been ascribed motor, pain-processing and affective functions. However, the dynamics of information flow in this complex region and how it responds to inputs remain unclear and are difficult to study using non-invasive electrophysiology. The area is targeted by neurosurgery to treat neuropathic pain. During deep brain stimulation surgery, we recorded local field potentials from this region in humans during a decision-making task requiring motor output. (...) We investigated the spatial and temporal distribution of information flow within the dACC. We demonstrate the existence of a distributed network within the anterior cingulate cortex where discrete nodes demonstrate directed communication following inputs. We show that this network anticipates and responds to the valence of feedback to actions. We further show that these network dynamics adapt following learning. Our results provide evidence for the integration of learning and the response to feedback in a key cognitive region. (shrink)

Necessary Existence breaks ground on one of the deepest questions anyone ever asks: why is there anything? Pruss and Rasmussen present an original defence of the hypothesis that there is a necessarily existing being capable of providing an ultimate foundation for the existence of all things.

First Published in 1998. Routledge is an imprint of Taylor & Francis, an informa company.