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 paper investigates completions in the context of finitely generated lattice-based varieties of algebras. In particular the structure of canonical extensions in such a variety $${\mathcal {A}}$$ is explored, and the role of the natural extension in providing a realisation of the canonical extension is discussed. The completions considered are Boolean topological algebras with respect to the interval topology, and consequences of this feature for their structure are revealed. In addition, we call on recent results from duality theory to show (...) that topological and discrete dualities for $${\mathcal {A}}$$ exist in partnership. (shrink)

Anyone who has ever worked with a variety \ of algebras with a reduct in the variety of bounded distributive lattices will know a restricted Priestley duality when they meet one—but until now there has been no abstract definition. Here we provide one. After deriving some basic properties of a restricted Priestley dual category \ of such a variety, we give a characterisation, in terms of \, of finitely generated discriminator subvarieties of \. As an application of our characterisation, we (...) give a new proof of Sankappanavar’s characterisation of finitely generated discriminator varieties of distributive double p-algebras. A substantial portion of the paper is devoted to the application of our results to Cornish algebras. A Cornish algebra is a bounded distributive lattice equipped with a family of unary operations each of which is either an endomorphism or a dual endomorphism of the bounded lattice. They are a natural generalisation of Ockham algebras, which have been extensively studied. We give an external necessary-and-sufficient condition and an easily applied, completely internal, sufficient condition for a finite set of finite Cornish algebras to share a common ternary discriminator term and so generate a discriminator variety. Our results give a characterisation of discriminator varieties of Ockham algebras as a special case, thereby yielding Davey, Nguyen and Pitkethly’s characterisation of quasi-primal Ockham algebras. (shrink)

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

Exposition of the philosophy of Sri Madhwacharya, the 13th century ascetic and proponent of the 'dvaita - dualistic theism' school. This book outlines the philosophy of Sri Madhwacharya based on his works. The first few chapters deal with the epistemological basis of Sri Madhwacharya's philosophy. The significant contributions of Sri Madhwacharya to Indian philosophy - epistemological and ontological find special elucidation in this book. The concept of Sakshi which is most fundamental in the system with the associated concepts of space (...) and time are elaborated. The last two chapters are devoted to the enumeration and justification of the metaphysical categories of the system and the concept of Moksha according to Sri Madhwacharya. (shrink)

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.

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)

Filosofii︠a︡ naukovoho idealizmu -- Metodolohii︠a︡ i sot︠s︡iolohii︠a︡ prava -- Z istoriï politychnoï dumky.

Sections R1 to R3 attempt to take the sting out of hostile commentaries. Sections R4 to R5 engage Berlin and Kay and the World Color Survey to correct the record. Section R6 begins the formulation of a new theory of colour as an engineering project with a technological developmental trajectory. It is recommended that the colour space be abandoned.

In this target article the following hypotheses are discussed: (1) Colour is autonomous: a perceptuolinguistic and behavioural universal. (2) It is completely described by three independent attributes: hue, brightness, and saturation: (3) Phenomenologically and psychophysically there are four unique hues: red, green, blue, and yellow; (4) The unique hues are underpinned by two opponent psychophysical and/or neuronal channels: red/green, blue/yellow. The relevant literature is reviewed. We conclude: (i) Psychophysics and neurophysiology fail to set nontrivial constraints on colour categorization. (ii) Linguistic (...) evidence provides no grounds for the universality of basic colour categories. (iii) Neither the opponent hues red/green, blue/yellow nor hue, brightness, and saturation are intrinsic to a universal concept of colour. (iv) Colour is not autonomous. (shrink)

The late Jacob Klein’s important book is, remarkably, a lucid presentation of esoteric argument. Dealing with the famed Platonic triad, Theaetetus, Sophist, and Statesman, Klein settles the dispute about the missing dialogue, "The Philosopher," by first denying that it is missing and second showing that it is unnecessary. He argues, in short, that the triad is a dyad. That argument is reinforced by the distinction Klein strongly implies between the Socratic Theaetetus and the Eleatic Sophist and Statesman. "We can now (...) understand why the conversations of the ‘trilogy’ occur in two, not three, days and why the Sophist, the Statesman, and the Philosopher are dealt with in two, not three, dialogues". (shrink)

This paper examines the challenge that psychoanalytic theory cannot be refuted. It does so by considering the theory in its orthodox Freudian form, and in the main branches into which it can be divided ? the theory of Instincts, of Development, of Psychic Structure, of Mental Economics or Defence, and of Symptom Formation. The essential character of the generalizations and concepts of these branches will just be indicated; and we shall ask of each branch whether it is possible to refute (...) it. A considerable amount of scientific enquiry has been done into the concepts and generalizations of psychoanalysis. Relevant examples of these enquiries will be noted; and the question asked whether these scientific studies have in fact done anything to refute or support the various branches of psychoanalytic theory. The general upshot will be that the challenge is both important and a mistake. (shrink)

A number of recent arguments purport to show that imprecise credences are incompatible with accuracy-first epistemology. If correct, this conclusion suggests a conflict between evidential a...

One of the most recent controversies to arise in the field of bioethics concerns the ethics for the Groningen Protocol: the guidelines proposed by the Groningen Academic Hospital in The Netherlands, which would permit doctors to actively euthanise terminally ill infants who are suffering. The Groningen Protocol has been met with an intense amount of criticism, some even calling it a relapse into a Hitleresque style of eugenics, where people with disabilities are killed solely because of their handicaps. The purpose (...) of this paper is threefold. First, the paper will attempt to disabuse readers of this erroneous understanding of the Groningen Protocol by showing how such a policy does not aim at making quality-of-life judgements, given that it restricts euthanasia to suffering and terminally ill infants. Second, the paper illustrates that what the Groningen Protocol proposes to do is both ethical and also the most humane alternative for these suffering and dying infants. Lastly, responses are given to some of the worries expressed by ethicists on the practice of any type of non-voluntary active euthanasia. (shrink)

In our time, a time of fundamental societal changes associated with the development of the world socialist system, which conditions the progressive course of mankind's social development, the problem of the prevention of war has come to be of immense importance. This problem has not only the greatest practical significance, but also a theoretical, philosophical aspect. The philosophical aspect of this problem is reflected, in the first place, in the fact that some hold the view that a new world war (...) is predestined by history, and represents a fatal inevitability, so that struggle against it is "Utopian." This view denies the possibility of peaceful coexistence among the given countries differing in societal and political systems. Such a position is in irreconcilable contradiction with the teachings of Marxism-Leninism, which stand opposed to the bourgeois conceptions of Karl Jaspers, W. Schmidt, Raymond Aron, G. Wetter, and many others who employ pseudoscientific argumentation to propagate the idea that such peaceful coexistence is impossible. (shrink)

Neuronal aggregates involved in conscious awareness are not evenly distributed throughout the CNS but comprise key components referred to as the neural network correlates of consciousness (NNCC). A critical node in this network is the posterior cingulate, precuneal, and retrosplenial cortices. The cytological and neurochemical composition of this region is reviewed in relation to the Brodmann map. This region has the highest level of cortical glucose metabolism and cytochrome c oxidase activity. Monkey studies suggest that the anterior thalamic projection likely (...) drives retrosplenial and posterior cingulate cortex metabolism and that the midbrain projection to the anteroventral thalamic nucleus is a key coupling site between the brainstem system for arousal and cortical systems for cognitive processing and awareness. The pivotal role of the posterior cingulate, precuneal, and retrosplenial cortices in consciousness is demonstrated with posterior cingulate epilepsy cases, midcingulate lesions that de-afferent this region and are associated with unilateral sensory neglect, observations from stroke and vegetative state patients, alterations in blood flow during sleep, and the actions of general anesthetics. Since this region is critically involved in self reflection, it is not surprising that it is similarly a site for the NNCC. Interestingly, information processing during complex cognitive tasks and during aversive sensations such as pain induces efforts to terminate self reflection and result in decreased processing in posterior cingulate and precuneal cortices. (shrink)