This article argues, against contemporary experimentalist criticism, that conceptual analysis has epistemic value, with a structure that encourages the development of interesting hypotheses which are of the right form to be valuable in diverse areas of philosophy. The article shows, by analysis of the Gettier programme, that conceptual analysis shares the proofs and refutations form Lakatos identified in mathematics. Upon discovery of a counterexample, this structure aids the search for a replacement hypothesis. The search is guided by heuristics. The heuristics (...) of conceptual analysis are similar to those in other interesting areas of scholarship, and so hypotheses generated by it are of the right form to be applicable to diverse areas. The article shows that the explanationist criterion in epistemology was developed and applied in this way. The epistemic value of conceptual analysis is oblique because it contributes not towards the main purpose of conceptual analysis but towards the reliable development of epistemically valuable hypotheses in philosophy and scholarship. (shrink)

Traditionally, intuitions about cases have been taken as strong evidence for a philosophical position. I argue that intuitions about concept deployment have epistemic value while intuitions about matters of fact have none. I argue this by use of the explanationist criterion which contends that S is justified in believing only those propositions which are part of the best explanation of S’s making the judgements she makes. This criterion accords with scientific practice. Bealer suggests, as a defence of intuition, that naturalists (...) rely on intuition in their arguments against intuition and thus that their arguments are self-undermining. But beliefs based on intuitions about the application of concepts, like ‘justification’ and ‘theory,’ are epistemically justified by the explanationist criterion. It is only intuitions about matters of fact which are rejected. Thus, epistemically-respectable intuitions about concepts are used to undermine intuitions about metaphysics. There is nothing self-undermining about this. (shrink)

Fallibilism is ubiquitous in contemporary epistemology. I argue that a paradox about knowledge, generated by considerations of truth, shows that fallibilism can only deliver knowledge in lucky circumstances. Specifically, since it is possible that we are brains‐in‐vats (BIVs), it is possible that all our beliefs are wrong. Thus, the fallibilist can know neither whether or not we have much knowledge about the world nor whether or not we know any specific proposition, and so the warrant of our knowledge‐claims is much (...) reduced and second‐order skepticism is generated. Since this is the case in both skeptical and everyday contexts, contextualism cannot resolve the paradox. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Pragmatism's Evolution: Organism and Environment in American Philosophy by Trevor PearceAlexander KleinTrevor Pearce. Pragmatism's Evolution: Organism and Environment in American Philosophy. Chicago: The University of Chicago Press, 2020. Pp. 384. Paperback, $35.00.Pragmatist pioneers were young lions in the days of Darwin. Evolutionary-biological thinking infused this philosophical movement from the start. And yet the last time a major monograph appeared on classic pragmatism and evolutionary biology—Philip Wiener's Evolution and (...) the Founders of Pragmatism (New York: Harper Torchbooks, 1949)—the author could personally thank Ralph Barton Perry, William James's junior colleague and eventual biographer. John Dewey himself wrote the foreword.Almost seventy-five years later, we have Trevor Pearce's painstakingly researched Pragmatism's Evolution. The author has graduate training in both biology and philosophy and is a former student of William Wimsatt and Robert Richards's (343). The book offers an intricate portrait of how debates about evolutionary biology informed the thinking of a loose-knit group of pragmatists between the years 1860 and 1910. While a remarkable variety of figures are discussed, ten pragmatists command the most attention: Chauncey Wright, C. S. Peirce, Francis Ellingwood Abbot, John Fiske, William James, Josiah Royce, John Dewey, Jane Addams, G. H. Mead, and W. E. B. Du Bois (18). Call them "the American Ten."Without downplaying Darwin, an overarching theme is the special significance of Herbert Spencer. Despite many specific disagreements with him (see e.g. 74, 207–8, 253–54, 281), the American Ten all accepted something more fundamental from Spencer: an intellectual framework that explains mind and morality in terms of functional relationships between organism and environment.After an introduction outlining what Pearce identifies as four chronological "cohorts" of pragmatists (more on this concept below), he examines the 1860s and 1870s reception of Darwin (chapter 1) and Spencer (chapter 2), showing how senior pragmatists like Wright, Peirce, and James defended evolution during this period. In chapter 2, we meet the Metaphysical Club's arch Spencerian, John Fiske, and we get a reading of James's critique of Spencer's psychology and sociology. Chapter 3 gives a highly detailed, reference-work-like portrait of the second cohort's training in evolutionary biology during the 1880s—chiefly Royce, Dewey, Addams, Mead, and Du Bois. In chapter 4, we learn that in the 1880s and 1890s, idealists like Edward Caird, Samuel Alexander, David George Ritchie, and Josiah Royce all co-opted ideas from evolutionary biology, which they apparently thought compatible with Hegelian dialectics. Chapter 5 shows that central planks of Peirce's metaphysics and Dewey's ethics are responsive to an 1890s dispute over the causes of the biological variation upon which selection acts (the so-called "factors" debate). The final two chapters show how pragmatist ethics (chapter 6) and epistemology (chapter 7) were infused with substantive ideas about evolution and about scientific experiment more generally.The depth and use of historical scholarship on offer here are both remarkable. On depth, Pearce draws from nineteen special collections and archives housed at institutions from California to Manchester, UK. The reference list (published on Pearce's website) runs [End Page 160] to 118 pages and was apparently too long for inclusion in the book. Archival research and lengthy bibliographies are to be expected in today's history of philosophy. But the sheer range of sources Pearce draws from is, by any measure, impressive.The use to which he puts those sources is provocative. Close reading, and in particular argument reconstruction, is usually the stock in trade for historians of philosophy. Pearce takes a different approach (7), seeking interpretive insight through a kind of philosophical network analysis. The nodes are mainly philosophers, scientists, and social critics. Unlike digital network analyses, Pearce connects his nodes by hand, via a great multiplicity of social, educational, and intellectual relations. We learn who studied evolution where, with whom, and when; what specific texts were assigned in classes taken, in classes taught; who attacked whom, who sided with whom; and so on.The resulting networks are rich, though they can be difficult to track due to their complexity. At its best, the book uses networks to produce genuine insights that... (shrink)

Each of the five volumes in the Stone Art Theory Institutes series—and the seminars on which they are based—brings together a range of scholars who are not always directly familiar with one another’s work. The outcome of each of these convergences is an extensive and “unpredictable conversation” on knotty and provocative issues about art. This fourth volume in the series, _Beyond the Aesthetic and the Anti-Aesthetic_, focuses on questions revolving around the concepts of the aesthetic, the anti-aesthetic, and the political. (...) The book is about the fact that now, almost thirty years after Hal Foster defined the anti-aesthetic, there is still no viable alternative to the dichotomy between aesthetics and anti- or non-aesthetic art. The impasse is made more difficult by the proliferation of identity politics, and it is made less negotiable by the hegemony of anti-aesthetics in academic discourse on art. The central question of this book is whether artists and academicians are free of this choice in practice, in pedagogy, and in theory. The contributors are Stéphanie Benzaquen, J. M. Bern­stein, Karen Busk-Jepsen, Luis Camnitzer, Diarmuid Costello, Joana Cunha Leal, Angela Dimitrakaki, Alexander Dumbadze, T. Brandon Evans, Geng Youzhuang, Boris Groys, Beáta Hock, Gordon Hughes, Michael Kelly, Grant Kester, Meredith Kooi, Cary Levine, Sunil Manghani, William Mazzarella, Justin McKeown, Andrew McNamara, Eve Meltzer, Nadja Millner-Larsen, Maria Filomena Molder, Carrie Noland, Gary Peters, Aaron Richmond, Lauren Ross, Toni Ross, Eva Schürmann, Gregory Sholette, Noah Simblist, Jon Simons, Robert Storr, Martin Sundberg, Timotheus Vermeulen, and Rebecca Zorach. (shrink)

ABSTRACT The individual-community relationship has always been one of the most fundamental topics of social sciences. In sociology, this is known as the micro-macro relationship while in economics it refers to the processes, through which, individual actions lead to macroeconomic phenomena. Based on philosophical discourse and systems theory, many sociologists even use the term "emergence" in their understanding of micro-macro relationship, which refers to collective phenomena that are created by the cooperation of individuals, but cannot be reduced to individual actions. (...) "Emergence" theories attempt to explain the nature of society as a complex system by examining how individuals and their relationships lead to the creation of integrated and macro-social phenomena such as markets, educational systems, cultural beliefs, and shared social practices. As a prelude to activity, every researcher has to answer the question from the methodological point of view, how is it possible to study the behavior of social groups and how can we gain knowledge about the laws related to social groups? Anyone who deals with humanities and social sciences or any reality and phenomenon that affects human beings, inevitably deals with the reality that is emerging. In fact, emergence occurs when one level of reality emerges radically from another level. Examples of emergent levels of reality include how the mind emerges from the body; or the way society emerges from human beings. Therefore, when there is an emerging factor, different scientific disciplines should be used, because it is inevitable to talk about social affairs, psychology and neurobiology, as well as physical and even chemical. -/- INTRODUCTION Since its beginning in the 19th century, sociology has faced the fundamental question of what a social phenomena stands for? At a glance, sociologists deal with the study of social groups, collective behavior, institutions, social structures, social networks, and social dynamics, and ultimately all such phenomena are composed of individuals. Therefore, social phenomena seem to have no independent ontological status, and in this case, sociology is ultimately about reducible individuals. Different approaches about the micro-macro relationship, using the concept of "emergence", argue that although collective phenomena are created by individuals, they cannot be reduced to individual action. The term "emergence" is used to distinguish "emergent results" from " Procedural results". Results are called Procedural that can only be calculated by adding or subtracting the causes that act together. On the contrary, they are emergent outcomes that are qualitatively novel compared to the causes from which they originate. An example of such emergent results is mental characteristics that emerge from neural processes, but are not considered among the characteristics of neural processes of components - which are their origin. Philosophical debates about emergentism and reductionism focus on the mind-brain relationship, but as many philosophers have noted, they can be generalized to apply to any hierarchical set of features. The cognitive revolution reactivated a 19th century controversy between theorists of Identity and dualism. The theorists of Identity believe in reductionist materialism and elimination of metaphysics, according to which the mind is nothing more than the biological, while the dualists believe that the mind and the brain are distinct from each other. Emergence has been considered as a third way between the theories of Identity and dualism. -/- METHODOLOGY Interdisciplinarity Is fundamentally indicated by the dominance of open systems as well as social and emerging systems at different levels. Therefore, as long as we are facing a new emergentism, there will necessarily be different fields and an interdisciplinary method. The commonality of social sciences and cognitive sciences on the issue of emergence provides the possibility of interaction and exchange of concepts between these two for deeper research. Therefore, in this research, apart from the concepts of Subvenience and downward causation, we have used multiple realization and wildly disjunctive, which are used to explain the emerging concept in cognitive sciences, including neurobiology, psychology, and philosophy. For analytical and interdisciplinary approaches, after examining the concepts of subvenience, and wildly disjunctive, Individualistic and collectivist emergentism have been reviewed. And then their adequacy is criticized and evaluated in meeting strong emergence conditions. -/- FINDINGS Philosophers of the mind have been able to define the conditions of irreducibility and downward causation, which are essential for strong emergence, by using the principle of subvenience with the help of multiple realization and wildly disjunctive principles. Therefore, by definition, emergentist individualism suffers from the problem of how to explain downward causality and irreducibility, and emergentist collectivism faces the challenge of reification. The analysis of the challenges facing the two methodological approaches of individualism and collectivism leads us to three unresolved issues about the emerging phenomenon, which are realism, downward causality, and mechanism. Despite the differences in the stances of these two approaches regarding the aforementioned triple problems, individualists and collectivists both agree that some social characteristics are reducible; and some others are irreducible due to their complexity, the determination of which, depends on the case study of the mechanism of emergence of each social characteristic. -/- CONCLUSION An emergence that is consistent with reductionism is called a weak emergence. And strong emergence includes the principle of irreducibility and downward causality. According to strong emergence, the characteristics of social phenomena have downward causal power, which cannot be reduced to the causal forces. The principle of subvenience, together with multiple realization and wildly disjunctive, can provide the conditions of irreducibility and downward causality, which are essential conditions of strong emergence. Based on the philosophical analysis of two methodological approaches, individualist and collectivist, it can be concluded that emergentist individualism suffers from the problem of how to explain downward causality and irreducibility, and reification collectivism faces the challenge of reification. The analysis of the problems faced by these two approaches leads us to three unresolved issues, which are realism, downward causality, and mechanism. individualist emergentists acknowledge the existence of emergent social characteristics, but despite this, they believe that these characteristics are not real but merely analytical constructs that require explanation based on individuals and their mutual actions. But collectivists argue that emergentism yields a categorical ontology and supports social realism. They accept the dependence of social characteristics on individuals, but claim that social entities and structures are ontologically independent. Individualists and collectivists both agree that some social characteristics are reducible; and others are irreducible due to their complexity; and the only way to recognize this is to engage in empirical studies of the mechanisms and temporal processes of "emergence" that create social characteristics. -/- NOVELTY The newness of this compact article is as follows: a) Presenting an interdisciplinary approach using the analysis of philosophy of cognitive sciences, including the philosophy of mind, neurobiology and psychology to formulate the issue of social emergence; b) Criticizing individualist and collectivist methodological approaches to the issue of social emergence and explaining the sufficiency and shortcomings of both in providing weak and strong emerging conditions; c) Explaining and categorizing the challenges facing methodological approaches in explaining the phenomenon of social emergence, in three categories: realism, downward causality, and mechanism. BIBLIOGRAPHY Beckermann, A., Flohr, H., & Kim, J. (eds.) (1992). Emergence or reduction? Essays on the prospects of nonreductive physicalism. Berlin: Walter de Gruyter. Bhaskar, R. (1979). The possibility of Naturalism. New York: Routledge. Bhaskar, R., Danermark, B. & Price, L. (2018). Interdisciplinarity and wellbeing: A critical realist general theory of interdisciplinarity. London and New York: Routledge. Blau, P.M. (1981). Introduction: diverse views of social structure and their common denominator. In Blau, P.M. & Merton, R.K. (eds.), Continuity in Structural Inquiry (pp. 1–23). Beverly Hills: Sage. Blau, P.M. (1987). Microprocess and macrostructure. In K.S. Cook (ed.), Social Exchange Theory (pp. 83–100). Newbury Park, CA: Sage. Brooks, R.A., & Maes, P. (eds). (1994). Artificial life IV; proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems. Cambridge, Mass: MIT Press. Clark, A. (1997). Being there: Putting brain, body, and world together again. Cambridge, Mass.: MIT Press. Coleman, J. S. (1987). Microfoundations and macrosocial behavior. In: J. C. Alexander, B. Giesen, R. Munch, & Neil J. Smelser (Eds.). The Micro-Macro Link (pp. 153–73). Berkeley: University of California. Coleman, J. S. (1990). Foundations of social theory. Cambridge, MA: Harvard University Press. Elster, J. (1985). Making sense of Marx. New York: Cambridge University Press. Fodor, J.A. (1974). Special sciences (Or: The disunity of science as a working hypothesis). Synthese, 28(2), 97–115. Fodor, J.A. (1989). Making mind matter more. Philosophical Topics, 17, 59-79. Giddens, A. (1984). The constitution of society: Outline of the theory of structuration. Berkeley: University of California Press. Hempel, C.G. (1965). Aspects of scientific explanation and other essays in the philosophy of science. New York: The Free Press. Horgan, T. (1993). From supervenience to superdupervenience: meeting the demands of a material world. Mind, 102, 555-586. Humphreys, P. (1997). How properties emerge”. Philosophy of Science, 64, 1-17. Kim, J. (1999). Making sense of emergence. Philosophical Studies, 95, 3–36. Kincaid, H. (1997). Individualism and the unity of science. New York: Rowman & Littlefield. Lewis, D.K. (1986). The plurality of worlds. Oxford: Oxford University Press. Nigel, G., & Conte, R. (eds.) (1995). Artificial societies; The computer simulation of social life. London: UCL Press. O’Connor, T. (1994). Emergent properties. American Philosophical Quarterly, 31, 91-104. Popper, K.R. (1968). Conjectures and refutations: The Growth of Scientific Knowledge. New York: Harper & Row. Sawyer, R. K. (2001). Emergence in sociology: contemporary philosophy of mind and some implications for sociological theory. American Journal of Sociology, 107, 551-585. Sawyer, R. K. (2004). The mechanisms of emergence. Philosophy of the Social Sciences, 34, 260–282. Sawyer, R. K. (2005). Social emergence: societies as complex systems. Cambridge: Cambridge University Press. Sawyer, R.K. (2003). Nonreductive individualism: Part 2, Social causation. Philosophy of the Social Sciences, 33, 203–224. Winch, P. (1993). The idea of a social science and its relation to philosophy‭ (SAMT, Trans.). Tehran, Iran: SAMT. (shrink)

In this fresh interpretation of Heidegger, Alexander S. Duff explains Heidegger's perplexing and highly varied political influence. Heidegger and Politics argues that Heidegger's political import is forecast by fundamental ambiguities about the status of politics in his thought. Duff explores how, in Being and Time as well as earlier and later works, Heidegger analyzes 'everyday' human existence as both irretrievably banal but also supplying our only tenuous path to the deepest questions about human life. Heidegger thus points to two (...) irreconcilable attitudes toward politics: either a total and purifying revolution must usher in an authentic communal existence, or else we must await a future deliverance from the present dispensation of Being. Neither attitude is conducive to moderate politics, and so Heidegger's influence tends towards extremism of one form or another, modified only by explicit departures from his thought. (shrink)

This paper studies the notion of virtuality in the Bohr-Kramers-Slater theory of 1924. We situate the virtual entities of BKS within the tradition of the correspondence principle and the radiation theory of the Bohr model. We show how, in this context, virtual oscillators emerged as classical substitute radiators and were used to describe the otherwise elusive quantum transitions. They played an effective role in the quantum theory of radiation while remaining categorically distinct and ontologically separated from the quantum world of (...) the Bohr model. The notion of virtuality thus differs markedly from its counterpart in quantum mechanics or QFT. (shrink)

A survey is given of three-valued paraconsistent propositionallogics connected with Jaśkowski’s criterion for constructing paraconsistentlogics. Several problems are raised and four new matrix three-valued paraconsistent logics are suggested.

My object in these lectures is to show that Science is a form of Art, though not of fine art; in other words, that it is one example of a process of which fine art is the most obvious example, the process of making out of certain materials a result into which the mind itself enters. Clearly enough the material of the artist, whatever it be, marble or paints or tones or words, is moulded by the artist into a shape (...) which it would not possess unless something in the artist’s mind found expression in it. Science also is a product of the mind’s interference and is artificial. But it differs from fine art, I shall try to show, in this respect: in fine art the material is controlled from the mind, or at least it is principally controlled from the mind. In science the material is the facts of nature ; but while science would not be except for the mind of the scientist, the work is controlled from the side of the material itself, and his mind is instrumental to the product rather than in some sense intrinsic to it as in fine art. (shrink)

Democracy as one of the forms of a governance and political process is at the same time a political value. The value’s aspects of democracy are closely connected with the character of democratic political regime, democratic process and democratic political culture of society. in the structure of democratic values one may roughly point out horizontal facet of them and vertical one. Horizontal values include following values: general social domain; the sphere of political institutions; the aspects of political process and procedures; (...) cultural sphere. As a rule, these values are out of doubt, though this fact doesn’t preclude there critic from various opponents of democracy. On the contrary, it’s a hierarchy of democratic values, which is the vertical facet of them is the point at scientific andpolitical debates. This fact also causes various approaches to democracy. The problems of democratic values inseparably linked with the questions about there universal character. Under an analysis of the universal character of democratic values it’s necessary to take into account its socioantropological aspect. The point is about developing essence of the human being under the impact of diverse internal and external factors. (shrink)

The article examines the situation that has developed in the contemporary age and being named differently: postmodernism, post-postmodernism, digital modernism, metamodernism, etc. It is noted that, despite the difference in naming, all the terms indicate a global crisis of culture and man. The three most important signs of this crisis are identified: degradation of a man – the predominance of his animal nature; total technicism; oblivion of national traditions, sacred things. These features are briefly explained. It is concluded that the (...) basis of these signs is the loss of human spirituality. It is stated that music has extraordinary opportunities to elevate the spiritual needs of a person. It is emphasized that these opportunities contributed to the strengthening of the impact of religious practices within various worships – shamanism, Zoroastrianism, Sufism, and others, which ensured the maintenance of the humanity of the world. It is believed that the use of spiritual-creative possibilities of music will help overcome the existing global crisis and prepare the formation of the era of culture and man, the era called a New Humanism by M. Eliade. It is argued that there are composers in Russia and in other countries today who purposefully use the spiritual-creative potential of music in their work to overcome the crisis that has arisen. We offer an interview with one of them – Russian composer Dmitry Stefanovich. In conclusion, it is noted that the following articles will continue to analyze the processes taking place in contemporary culture, and, in this regard, there will be presented stories about music and interviews with composers from Russia and other countries. (shrink)

Crown under Law is an investigation of the constitutional idea through an exploration of the political thought of Richard Hooker and John Locke. It should appeal to academics within a number of disciplines including history of ideas, political philosophy, philosophy of law, and theology.

In this paper we define n+1-valued matrix logic Kn+1 whose class of tautologies is non-empty iff n is a prime number. This result amounts to a new definition of a prime number. We prove that if n is prime, then the functional properties of Kn+1 are the same as those of ukasiewicz's n +1-valued matrix logic n+1. In an indirect way, the proof we provide reflects the complexity of the distribution of prime numbers in the natural series. Further, we introduce (...) a generalization K n+1 * of Kn+1 such that the set of tautologies of Kn+1 is not empty iff n is of the form p , where p is prime and is natural. Also in this case we prove the equivalence of functional properties of the introduced logic and those of n+1. In the concluding part, we discuss briefly a partition of the natural series into equivalence classes such that each class contains exactly one prime number. We conjecture that for each prime number the corresponding equivalence class is finite. (shrink)

Book Review: P.P. Tolochko. Ukraine between Russia and the West: Historical and Nonfiction Essays. Saint Petersburg: Saint Petersburg University of Humanities and Social Sciences, 2018. - 592 pp. ISBN 978-5-7621-0973-4This author discusses the problem of scientific objectivity and reviews a book written by the medievalist-historian P.P. Tolochko, full member of the National Academy of Sciences of Ukraine, honorable director of the NASU Institute of Archaeology. The book was published by the Saint Petersburg University of Humanities and Social Sciences in the (...) autumn of 2018. The book presents a collection of articles and reports devoted to processes in Ukraine and, first of all, in Ukrainian historical science, which, at the moment, is experiencing an era of serious reformation of its interpretative models. The author of the book shows that these models are being reformed to suit the requirements of the new ideology, with an obvious disregard for the conduct of objective scientific research. In this regard, the problem of objectivity of scientific research becomes the subject of this review because the requirement of objectivity can be viewed not only as a methodological requirement but also as a moral and political position, opposing the rigor of scientific research to the impact of ideological, political and moral systems and judgments. It is concluded that in this sense the position of P.P. Tolochko can be considered as the act of profound ethical choice. (shrink)

§1. I will start with a quick definition of descriptive set theory: It is the study of the structure of definable sets and functions in separable completely metrizable spaces. Such spaces are usually called Polish spaces. Typical examples are ℝn, ℂn, Hilbert space and more generally all separable Banach spaces, the Cantor space 2ℕ, the Baire space ℕℕ, the infinite symmetric group S∞, the unitary group, the group of measure preserving transformations of the unit interval, etc.In this theory sets are (...) classified in hierarchies according to the complexity of their definitions and the structure of sets in each level of these hierarchies is systematically analyzed. In the beginning we have the Borel sets in Polish spaces, obtained by starting with the open sets and closing under the operations of complementation and countable unions, and the corresponding Borel hierarchy. After this come the projective sets, obtained by starting with the Borel sets and closing under the operations of complementation and projection, and the corresponding projective hierarchy.There are also transfinite extensions of the projective hierarchy and even much more complex definable sets studied in descriptive set theory, but I will restrict myself here to Borel and projective sets, in fact just those at the first level of the projective hierarchy, i.e., the Borel (), analytic () and coanalytic () sets. (shrink)

We prove the following Main Theorem: $ZF + AD + V = L(R) \Rightarrow DC$ . As a corollary we have that $\operatorname{Con}(ZF + AD) \Rightarrow \operatorname{Con}(ZF + AD + DC)$ . Combined with the result of Woodin that $\operatorname{Con}(ZF + AD) \Rightarrow \operatorname{Con}(ZF + AD + \neg AC^\omega)$ it follows that DC (as well as AC ω ) is independent relative to ZF + AD. It is finally shown (jointly with H. Woodin) that ZF + AD + ¬ DC (...) R , where DC R is DC restricted to reals, implies the consistency of ZF + AD + DC, in fact implies R # (i.e. the sharp of L(R)) exists. (shrink)

We consider first-order infinite-valued Łukasiewicz logic and its expansion, first-order rational Pavelka logic RPL∀. From the viewpoint of provability, we compare several Gentzen-type hypersequent calculi for these logics with each other and with Hájek’s Hilbert-type calculi for the same logics. To facilitate comparing previously known calculi for the logics, we define two new analytic calculi for RPL∀ and include them in our comparison. The key part of the comparison is a density elimination proof that introduces no cuts for one of (...) the hypersequent calculi considered. (shrink)

The paper discusses functional properties of some four-valued logics which are the expansions of four-valued Belnap’s logic DM4. At first, we consider the logics with two designated values, and then logics defined by matrices having the same underlying algebra, but with a different choice of designated values, i.e. with one designated value. In the preceding literature both approaches were developed independently. Moreover, we present the lattices of the functional expansions of DM4.

The structure of covariant observables—normalized positive operator measures (POMs)—is studied in the case of a type I symmetry group. Such measures are completely determined by kernels which are measurable fields of positive semidefinite sesquilinear forms. We produce the minimal Kolmogorov decompositions for the kernels and determine those which correspond to the extreme covariant observables. Illustrative examples of the extremals in the case of the Abelian symmetry group are given.

This essay argues that the thinker whose teaching played a key role in the formation of the Russian political and legal paradigm was not Marx but Hegel. It analyzes the impact of the Hegelian philosophy on the development of the Russian constitutional tradition, and examines its political implications.