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)

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)

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)

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)

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.

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.

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)

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)

§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 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 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.

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.

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)

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)

We discuss Smirnovs problem of finding a common background for classifying implicational logics. We formulate and solve the problem of extending, in an appropriate way, an implicational fragment H of the intuitionistic propositional logic to an implicational fragment TV of the classical propositional logic. As a result we obtain logical constructions having the form of Boolean lattices whose elements are implicational logics. In this way, whole classes of new logics can be obtained. We also consider the transition from implicational logics (...) to full logics. On the base of the lattices constructed, we formulate the main classification principles for propositional logics. (shrink)

This paper is an abstract of the report which was presented on the Polish-Soviet meeting on logic . It is shown that one can consider a lineary-ordered Heyting’s and Brouwer’s algebras as truth-values for Lukasiewicz’s infinite-valued logic’s Lω.

The article examines the processes taking place in contemporary musical culture, and the emphasis is placed on the situation that has developed today in the musical life of Russia. It is noted that many contemporary composers in Russia are breaking with the domestic artistic traditions, focusing on the creative initiatives of composers living in the West. Among the Russian composers, the SoMa group composers are distinguished by a special intransigence to the principles of artistic creativity that tradionally developed in Russia, (...) they loudly declared: “Contemporary Russian music is us.” At the same time, it should be taken into account that Russian music is inextricably linked with the artistic traditions of Russia, which, first of all, is manifested in the reliance of the musical material on the songfulness that originates in the liturgical Orthodox singing. It is emphasized that today in Russia there are composers who maintain contact with the tradition, thereby preserving the achievements of Russian music. Among them, first of all, are the composers who are part of the MOST group. Moreover, the composers work in all cities of Russia – from Kaliningrad to Vladivostok – and increase the glory of Russia by their creativity. An interview is given with one of them – the Perm composer Nikita Shirokov. In conclusion, the author discusses the prospects for the development of the journal’s section – it is planned to publish materials and interviews related to the contemporary musical life in other countries. (shrink)

LetXbe a standard Borel space, and letEbe acountableBorel equivalence relation onX, i.e., a Borel equivalence relationEfor which every equivalence class [x]Eis countable. By a result of Feldman-Moore [FM],Eis induced by the orbits of a Borel action of a countable groupGonX.The structure of general countable Borel equivalence relations is very little understood. However, a lot is known for the particularly important subclass consisting of hyperfinite relations. A countable Borel equivalence relation is calledhyperfiniteif it is induced by a Borel ℤ-action, i.e., by (...) the orbits of a single Borel automorphism. Such relations are studied and classified in [DJK]. It is shown in Ornstein-Weiss [OW] and Connes-Feldman-Weiss [CFW] that for every Borel equivalence relationEinduced by a Borel action of a countable amenable groupGonXand for every probability measure μ onX, there is a Borel invariant setY⊆Xwith μ = 1 such thatE↾Y is hyperfinite. Motivated by this result, Weiss [W2] raised the question of whether everyEinduced by a Borel action of a countable amenable group is hyperfinite. Later on Weiss showed that this is true forG= ℤn. However, the problem is still open even for abelianG. Our main purpose here is to provide a weaker affirmative answer for general amenableG. We need a definition first. Given two standard Borel spacesX, Y, auniversally measurableisomorphism betweenXandYis a bijection ƒ:X→Ysuch that both ƒ, ƒ-1are universally measurable. Notice now that to assert that a countable Borel equivalence relation onXis hyperfinite is trivially equivalent to saying that there is a standard Borel spaceYand a hyperfinite Borel equivalence relationFonY, which isBorelisomorphic toE, i.e., there is a Borel bijection ƒ:X→YwithxEy⇔ ƒFƒ. We have the following theorem. (shrink)

Empirical research has transformed our understanding of autocratic institutions. Yet democratic theorists remain laser-focused on ideal democracies, often contending that political equality is necessary to generate democratic authority. Those analyses neglect most nonideal democracies and autocracies – regimes featuring inequality and practices like gerrymandering. This essay fills that fundamental gap, outlining the difficulties of applying theories of democratic authority to nonideal regimes and challenging long-standing views about democratic authority. Focusing on autocrats that lose elections, I outline the democratic authority of (...) nonideal, flawed procedures. Flawed elections are unjustifiably biased toward incumbents. But under certain conditions, ignoring an incumbent’s loss would require not treating one’s fellow citizens as equals. Under those conditions, therefore, citizens are bound to obey those electoral outcomes – that is, flawed procedures can possess democratic authority. (shrink)