§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)

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 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.

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)

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.

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)

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)

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)

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)

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)

So far I have taken prose and poetry where admittedly they exist, in literature, and attempted to discover the difference between them by taking pieces of prose or poetry which have the same or much the same subjects and comparing them with one another. In all these pairs of passages I thought I could detect this difference: that in the poem the subject as rendered in words acquires a life of its own, is a living thing, as it were, living (...) its own life like an animal or plant, is organic, and, in a word, concrete. While the prose, for all its constructive unity, is not self-subsistent, but is descriptive of a given subject, even though that subject is itself created by the writer, as in a novel, and, in a word, is analytic. It is not the greater passion or vividness of the poem, for prose may be vivid, as in Carlyle, and passionate, as in Burke. It is that the poet places himself and places his hearer within the subject itself, and works from within outwards, while the prosaist describes relatively from without. Both of them describe, the poet as well as the prosaist. But the prosaist builds up his subject so as to bring it before your mind. The poet starts with his subject in its integrity, places the hearer's mind within it, and his exposition is the unfolding life of the subject itself. (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)

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.

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)

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.

A major problem in the treatment of cancer is the specific targeting of anti‐tumor drugs to these abnormal cells. Ideally, such a drug should act over short distances to minimize damage to healthy cells, and target subcellular compartments that have the highest sensitivity to the drug. Photosensitizers, alpha‐emitting radionuclides and many other medicines could be considered as such drugs if they possessed cellular and subcellular specificity. The author describes a novel approach of using modular recombinant transporters to target photosensitizers and (...) alpha‐emitting radionuclides to the nucleus, where their action is most pronounced, of cancer cells. Photosensitizer‐transporter conjugates have up to 3000 times greater efficacy than free photosensitizers and display cell specificity in contrast to free photosensitizers. Alpha‐emitting radionuclides, conjugated with the modular transporters, acquired similar properties. The different modules of the transporters are interchangeable, meaning that they can be tailored for particular applications. BioEssays 30:278–287, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

So far I have taken prose and poetry where admittedly they exist, in literature, and attempted to discover the difference between them by taking pieces of prose or poetry which have the same or much the same subjects and comparing them with one another. In all these pairs of passages I thought I could detect this difference: that in the poem the subject as rendered in words acquires a life of its own, is a living thing, as it were, living (...) its own life like an animal or plant, is organic, and, in a word, concrete. While the prose, for all its constructive unity, is not self-subsistent, but is descriptive of a given subject, even though that subject is itself created by the writer, as in a novel, and, in a word, is analytic. It is not the greater passion or vividness of the poem, for prose may be vivid, as in Carlyle, and passionate, as in Burke. It is that the poet places himself and places his hearer within the subject itself, and works from within outwards, while the prosaist describes relatively from without. Both of them describe, the poet as well as the prosaist. But the prosaist builds up his subject so as to bring it before your mind. The poet starts with his subject in its integrity, places the hearer's mind within it, and his exposition is the unfolding life of the subject itself. (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.

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)

The thesis which I wish to recommend to you is that science is a form of art though not of fine art: that like art, it is a human invention, not less real for that, and having value, or being valuable, partly if not mainly because of that. I mean to indicate by this statement that for me at least a better insight can be got into the nature of science by considering it as a form of art, and asking (...) how it differs from and how it resembles fine art. (shrink)

In describing morality as an art, I do not merely mean that there is a fine art of conduct, of which good manners are an obvious instance: the delicate adjustment of behaviour to small or subtle changes in our circumstances, the variation of our responses with differences in the age, standing, consideration of the persons with whom we talk. That there is such an art of good life is true, but it only means that in the instruments of life, as (...) with our microscopes and telescopes, there are fine as well as coarse adjustments. Nor do I mean merely that, as Plato said, living is a craft, like weaving or carpentering, and that virtue is its technique. I mean something more than an analogy; and that the best way to understand morality is to see what it has in common with fine art, and at the same time the differences which, leaving it still an art, separate it from fine art. (shrink)

It is much more certain that the artist can help the philosopher than that the philosopher can help the artist. The purpose of this paper is to indicate the kind of questions about art which the philosopher asks, in order that those whose concern is with art, artists themselves in the first instance, and critics of art, may judge if these questions are interesting to them, and if so may co-operate with the philosophers in seeking to answer them. Now that (...) the sciences and the other occupations of man become so sharply separated from each other, philosophy has come to have a peculiar position. It deals with the questions which are left over from the sciences, and this gives it a specific and important office to perform. (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)

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)

Divine Providence and Human Agency develops an understanding of God and God's relation to creation that perceives God as sovereign over creation while, at the same time, allowing for a meaningful notion of human freedom. This book provides a bridge between contemporary approaches that emphasise human freedom, such as process theology and those influenced by it, and traditional theologies that stress divine omnipotence. This volume offers an important contribution to the debate of the doctrine of God in the context of (...) an evolutionary universe. (shrink)