This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is (...) of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures. (shrink)

The first book to be devoted to the logic behind the application of ethical theories, this collection of essays explores the question of how many different moral traditions (utilitarianism, natural rights theory, Marxism, Christian moral theology, and Kantianism among others) view the relation between theory and concrete judgments. By considering many applications of moral theory in medical ethics the authors illustrate their point.

Muzykalʹnai︠a︡ ėstetika i kulʹturologii︠a︡ -- Istorii︠a︡ muzyki -- Istorii︠a︡, teorii︠a︡ muzykalʹnogo ispolnitelʹstva -- Tradit︠s︡ionnai︠a︡ kulʹtura.

In this paper, I consider a variety of objections against the covering-law model of scientific explanation, show that Aristotle was already aware of them and had solutions for them, and argue that these solutions are correct. These solutions involve the notions of nonHumean causality and of essential properties. There are a great many familiar objections, both methodological and epistemological, to introducing these concepts into the methodology of science, but I show that these objections are based upon misunderstandings of these concepts.

The techniques of natural duality theory are applied to certain finitely generated varieties of Heyting algebras to obtain optimal dualities for these varieties, and thereby to address algebraic questions about them. In particular, a complete characterisation is given of the endodualisable finite subdirectly irreducible Heyting algebras. The procedures involved rely heavily on Priestley duality for Heyting algebras.

The correctness of application of orientalist discourse of E. Said to the colonial policy of the Russian Empire is analyzed in the article on the example of P. I. Rychkov research. By studying integration of Bashkirs in the structure of the Russian state, the author came to the conclusion that Russia’s policy in the East was based on the experience of the management of non-Russian peoples, which was developed in the 16-17th centuries. The establishment of ‘cultural distance‘ is typical only (...) for a small group of educated administrators of past-Petrine era. Most of the officials of the region, as in the preceding period, and during the time of Rychkov and Tatishchev preferred to rely on traditional methods of Bashkir management, which was developed in the period of their voluntary accession. Managerial stereotypes of 16-17th centuries, had significant influence on policy towards South-Eastern peoples of Russia even in the 19th century. The Russian administration inherent in the desire to integrate the non-Russian peoples in the General class structure of the state on the basis of analogies or correspondences, the objective of which was social and cultural rapprochement of the two societies. (shrink)

Psychoactive drugs are being prescribed to millions of Americans at an increasing rate. In many cases these drugs are necessary in order to overcome debilitating emotional problems. Yet in other instances, these drugs are used to supplant, not supplement, interpersonal therapy. The process of overcoming emotional obstacles by introspection and the attainment of self knowledge is gradually being eroded via the gratuitous use of psychoactive medication in order to rapidly attain a release from the common problems that life inevitably presents (...) us with. In this paper, I argue that Kant’s formula of humanity, which maintains that persons ought never to treat others or themselves soley as a means to an end, proscribes this. Moreover, Kant argues that we have an imperfect duty of self development, and I argue that we fail to adhere to such a duty whenever we seek to evade the process of introspection and self knowledge in favour of the expedient results that drugs may provide us with as we attempt to overcome the emotional hurdles in our lives. (shrink)

Both syntactic and semantic solutions are given for the entailment problem of duality theory. The test algebra theorem provides both a syntactic solution to the entailment problem in terms of primitive positive formulae and a new derivation of the corresponding result in clone theory, viz. the syntactic description of $\operatorname{Inv(Pol}(R))$ for a given set R of finitary relations on a finite set. The semantic solution to the entailment problem follows from the syntactic one, or can be given in the form (...) of an algorithm. It shows, in the special case of a purely relational type, that duality-theoretic entailment is describable in terms of five constructs, namely trivial relations, intersection, repetition removal, product, and retractive projection. All except the last are concrete, in the sense that they are described by a quantifier-free formula. It is proved that if the finite algebra $\underline{M}$ generates a congruence-distributive variety and all subalgebras of $\underline{M}$ are subdirectly irreducible, then concrete constructs suffice to describe entailment. The concept of entailment appropriate to strong dualities is also introduced, and described in terms of coordinate projections, restriction of domains, and composition of partial functions. (shrink)

Georgians' acquaintance with Islam was with the first Arab raids. From the first Muslim Arab domination, Georgians started to become Muslims with cultural interaction. Islam spread especially in Eastern Georgia during the time of Muslim Arabs, Seljuks and Mongols. The spread of Islam in Western Georgia started with the Ottomans. The Ottoman Empire's contact with Georgia begins with the conquest of Trabzon by Fatih Sultan Mehmed. When the Ottomans contacted the region, the geography of Georgia was divided into small kingdoms. (...) With the conquest of Trabzon, the Georgian border was reached and in 1479, Acaristan, Borcka and Maçahel surroundings joined the Ottoman lands. On the one hand, Sukhumi was captured from the north. Then, continuing to advance in the region, Yavuz Sultan Selim paid tribute to the Kingdom of Güryel and Imeret (Açıkbaş) in 1508 during his governorship of Trabzon. Thus, the Ottoman borders had reached beyond the Black Sea coast into Western Georgia. As a result of the increasing relations around Adjaria, which came under Ottoman rule, Islamization began to spread rapidly among the people. Contrary to what is claimed, the spread of Islam in the region did not spread from the ruling strata to the lower, but from the popular strata to the ruling strata. This process was surprisingly fast. In the process of Islamization, many mosques, masjids and schools were built in Adjara, especially with the help of the people. The foundations operating in the region and the mosques and masjids serving under them show that, contrary to the claims of Russian and Georgian historians, Islamization took place rapidly at the beginning of the 17th century in Adjara. In this process, many mosques, masjids and schools were built in the region. In this research, based on the numerous Hurufat records belonging to Adjara, Batumi, Gönye, Çürüksu and Maçahel, the Islamization process will be evaluated by making a social reading with the data obtained from the religious structures established in the rural settlements of the Adjara geography and their officials. Evaluations were made on the Islamization process in Adjara by making a social reading. (shrink)

In Denmark, which alone in Western Europe has not accepted brain death as the criterion of death, the newly established Danish Council of Ethics has issued a report suggesting that in Denmark the criterion of death should still be the cessation of cardiac activity. The council bases its conclusion on the concept of death in everyday experience and its ethical implications.

[opening paragraph]: Buddhist inquiry into the natural world proceeds from a radically different point of departure than western science, and its methods differ correspondingly. Early pioneers of the scientific revolution, including Copernicus, Kepler, and Galileo, expressed an initial interest in the nature of physical objects most far removed from human subjectivity: such issues as the relative motions of the sun and earth, the surface of the moon, and the revolutions of the planets. And a central principle of scientific naturalism is (...) the pure objectification of the natural world, free of any contamination of subjectivity. This principle of objectivism demands that science deals with empirical facts testable by empirical methods entailing testability by third-person means; and such facts must, therefore, be public rather than private, which is to say, they must be accessible to more than one observer. (shrink)