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 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.

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)

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)

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.

In the paper the following questions are discussed: What is logical consequence? What are logical constants? What is a logical system? What is logical pluralism? What is logic? In the conclusion, the main tendencies of development of modern logic are pointed out.

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)

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)

Ecotage, or the destruction of property for the sake of promoting environmental ends, is beginning to (re)establish itself both as a topic of public discussion and as a radical activist tactic. In response to these developments, a small but growing academic literature questions whether, and if so under what conditions, ecotage can be morally justified. This paper contributes to the literature by arguing that instances of ecotage are pro tanto justified insofar as they are instances of effective and proportionate self- (...) and/or other-defense. Having elucidated and defended its central claim, this paper concludes by briefly considering some other morally relevant features of ecotage that might tell for or against its overall justification in particular cases. (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)

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 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)

In lieu of an abstract, here is a brief excerpt of the content:Kennedy Institute of Ethics Journal 13.1 (2003) 51-52 [Access article in PDF] Congress Considers Incentives for Organ Procurement Alexander S. Curtis [Tables]During the 108th Congressional session, several bills pertaining to ethical incentives for organ donation likely will be introduced. In some cases, they will be similar to bills before the 107th Congress (see Table 1). Bills in both the House of Representatives and the Senate address the establishment (...) and maintenance of donor registries, financial reimbursements for medical and nonmedical expenses incurred by qualifying donors, the presentation of commemorative medals, and tax credits.A bill entitled "Gift of Life Congressional Medal Act" (introduced last year by Senate majority leader Bill Frist (R-TN) as Senate Bill 325), and its corresponding bill of the same title (passed in the House of Representatives last year as H.R. 708), would establish a congressional commemorative medal honoring "any organ donor, or the family or family member of any organ donor." The medal is to be designed and struck with "suitable emblems, devices, and inscriptions" by the Secretary of the Treasury. The eligible donor or donor's family member would be presented with the medal by the Secretary of Health and Human Services. This bill would establish qualifying donations as those of human kidneys, livers, hearts, lungs, pancreases, or any other organ, but excludes corneas and eyes.Another bill, introduced by Representative Michael Bilirakis (R-FL) entitled "Organ Donation Improvement Act" (H.R. 624), would award grants or contracts to states, transplant centers, and qualified organ procurement organizations for the purpose of providing travel, subsistence, and incidental nonmedical expenses to individuals who make living donations. In order to receive reimbursement, the donating individuals must reside in states other than the states in which the intended recipients reside and the annual income of those receiving the organs cannot exceed $35,000. The bill also would appropriate $15,000,000 to make grants to states and public and nonprofit entities for the purpose of carrying out studies, public education demonstrations, and outreach activities "designed to increase the number of organ donors within the state." The bill would be effective from time of enactment through 2005. [End Page 51]Two other bills proposed within the House of Representatives in 2002 called for amendment to the Internal Revenue Code. The "Gift of Life Tax Credit Act (introduced as H.R. 1872 by Representative James Hansen (R-UT)) and the "Help Organ Procurement Expand Act" (introduced as H.R. 2090 by Representative Chris Smith (R-NJ)) present a refundable credit to individuals or to the estates of those who agree either to be living donors or to donate their organs upon death. The "Gift of Life Tax Credit Act" refunds $10,000 to the estates of eligible individuals "for the taxable year which includes the date of the individual's death." The "Help Organ Procurement Expand Act" offers a refund of $2,500 to qualified persons. Donations of kidneys, livers, pancreases, islet cells, lungs, and intestines are accepted, however several conditions restrict permissible donors. The "Gift of Life Tax Credit Act" requires that the legally competent individual's death not be due to a suicide and that the intention to donate was clearly declared. The "Help Organ Procurement Expand Act" prohibits donations from individuals who were killed with physician assistance, died as a result of a suicide, have been indicted or convicted of a felony or a misdemeanor offense, or are actively under criminal investigation for a possible felony offense. The "Help Organ Procurement Expand Act" also restricts procuring organs from unborn children or human fetuses and under circumstances in which the living donor would be subject to "unacceptable levels of medical risk of death or permanent debilitation." Alexander S. Curtis is a research assistant at the Kennedy Institute of Ethics, Georgetown University, Washington, DC. He received his bachelor's degree from Miami University.... (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)

The problem of freedom is researched in various ways by the religions of the world, by the scientific theories and by the mythological consciousness of people. The article pays great attention to the myth and its influence on the realm of freedom and on our interpretation of reality. The author understands a myth as a certain free fiction of a man in order to interpret reality in his own way and sometimes to create his own artistic image of the world. (...) Often the myth stimulates the ability of the imagination and thus it participates in the creation and existence of personality. It is argued that the traces of the myth can be found in most ways of orientation in the material and ideal worlds as well as in the systems of human interests and relationships, in the original human desire of freedom. The problem of freedom is central to all human history. Freedom of conscience, freedom of speech, political freedoms - one can name a large number of different freedoms, but the freedom of creativity should be considered as principal freedom. It should be noted also the freedom of thought, which can lead a cognizing person beyond the worlds of substances and energies, to the place where the Eternal Creator should abide. As the world religions believe, we inherit the capacity for creativity and self-knowledge from God. The very same creative freedom exists historically. Freedom of thought is accompanied by spontaneity and mystery. Spontaneity of consciousness and freedom of creativity create a system of meanings that determine the course of human history, while history is perceived by an observer as a completely unique, cognizable phenomenon. (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.

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.

This chapter focuses on the ontological nature of the past and our experience of the present in relation to the actual. It is argued that philosophers mistakenly equate the real with the actual. The actual is what is presented to us in experience, but what is presented to us in experience is confined to the present; so one might think that it follows that only the present is real. This presentist theory is subsequently rejected. Past, present and future are real (...) and certain mental acts such as memories of the past and expectations of the future have as their content objects at those times; these objects are just as real as the objects of present experiences. This paves the way for a distinctive brand of eternalism that is defended in the remainder of this chapter. (shrink)

Let Γ be a collection of relations on the reals and let M be a set of reals. We call M a perfect set basis for Γ if every set in Γ with parameters from M which is not totally included in M contains a perfect subset with code in M. A simple elementary proof is given of the following result (assuming mild regularity conditions on Γ and M): If M is a perfect set basis for Γ, the field of (...) every wellordering in Γ is contained in M. An immediate corollary is Mansfield's Theorem that the existence of a Σ 1 2 wellordering of the reals implies that every real is constructible. Other applications and extensions of the main result are also given. (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)

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 book presents the first detailed account of Werner Heisenberg’s failed attempt to find a theory of everything in the autumn of his career. It further investigates what we can learn from his failure in relation to the search for a final theory of physics, an endeavour that continues to define research in fundamental physics to this day. Thereby it provides the first historically informed contribution to the current debate on post-empirical physics and the state of particle physics.

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 a 1936 manuscript submitted to the Physical Review, Albert Einstein and Nathan Rosen famously claimed that gravitational waves do not exist. It has generally been assumed that there was a conceptual error underlying this fallacious claim. It will be shown, through a detailed study of the extant referee report, that this claim was probably only the result of a calculational error, the accidental use of a pathological coordinate transformation.