There exist important deductive systems, such as the non-normal modal logics, that are not proper subjects of classical algebraic logic in the sense that their metatheory cannot be reduced to the equational metatheory of any particular class of algebras. Nevertheless, most of these systems are amenable to the methods of universal algebra when applied to the matrix models of the system. In the present paper we consider a wide class of deductive systems of this kind called protoalgebraic logics. These include (...) almost all (non-pathological) systems of prepositional logic that have occurred in the literature. The relationship between the metatheory of a protoalgebraic logic and its matrix models is studied. The following results are obtained for any finite matrix model U of a filter-distributive protoalgebraic logic : (I) The extension U of is finitely axiomatized (provided has only finitely many inference rules); (II) U has only finitely many extensions. (shrink)

This paper is based on Lectures 1, 2 and 4 in the series of ten lectures titled “Algebraic Structures for Logic” that Professor Blok and I presented at the Twenty Third Holiday Mathematics Symposium held at New Mexico State University in Las Cruces, New Mexico, January 8-12, 1999. These three lectures presented a new approach to the algebraization of deductive systems, and after the symposium we made plans to publish a joint paper, to be written by Blok, further developing these (...) ideas. That project was still incomplete when Blok died. In fact, there is no indication that he had prepared a draft of the paper, and we do not know what new material he intended to include. I am therefore not in a position to complete the project as he had envisioned it. So, I have settled for the more limited objective of presenting the material from the three lectures, leaving to others the task of adapting the techniques used there to more general situations. (shrink)

Modal logics are studied in their algebraic disguise of varieties of so-called modal algebras. This enables us to apply strong results of a universal algebraic nature, notably those obtained by B. Jonsson. It is shown that the degree of incompleteness with respect to Kripke semantics of any modal logic containing the axiom □ p → p or containing an axiom of the form $\square^mp \leftrightarrow\square^{m + 1}p$ for some natural number m is 2 ℵ 0 . Furthermore, we show that (...) there exists an immediate predecessor of classical logic (axiomatized by $p \leftrightarrow \square p$ ) which is not characterized by any finite algebra. The existence of modal logics having 2 ℵ 0 immediate predecessors is established. In contrast with these results we prove that the lattice of extensions of S4 behaves much better: a logic extending S4 is characterized by a finite algebra iff it has finitely many extensions and any such logic has only finitely many immediate predecessors, all of which are characterized by a finite algebra. (shrink)

We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is (...) a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras. (shrink)

The rhetoric of 'needs' has been used to legitimate all major turns in UK health policy since 1936. This study identifies the ethical, policy and technical issues arising from the concept of needs. In the first part a theory of needs is developed, which takes into account both the philosophical traditions and the practical problems arising in daily health care. In a second part, health systems throughout the world are described and compared, addressing ethical as well as economical questions. Its (...) interdisciplinary approach will make The Need for Healthcare important reading not only for those interested in or employed in the health care sector but also for students of philosophy. (shrink)

The notion of an algebraic semantics of a deductive system was proposed in [3], and a preliminary study was begun. The focus of [3] was the definition and investigation of algebraizable deductive systems, i.e., the deductive systems that possess an equivalent algebraic semantics. The present paper explores the more general property of possessing an algebraic semantics. While a deductive system can have at most one equivalent algebraic semantics, it may have numerous different algebraic semantics. All of these give rise to (...) an algebraic completeness theorem for the deductive system, but their algebraic properties, unlike those of equivalent algebraic semantics, need not reflect the metalogical properties of the deductive system. Many deductive systems that don't have an equivalent algebraic semantics do possess an algebraic semantics; examples of these phenomena are provided. It is shown that all extensions of a deductive system that possesses an algebraic semantics themselves possess an algebraic semantics. Necessary conditions for the existence of an algebraic semantics are given, and an example of a protoalgebraic deductive system that does not have an algebraic semantics is provided. The mono-unary deductive systems possessing an algebraic semantics are characterized. Finally, weak conditions on a deductive system are formulated that guarantee the existence of an algebraic semantics. These conditions are used to show that various classes of non-algebraizable deductive systems of modal logic, relevance logic and linear logic do possess an algebraic semantics. (shrink)

The present paper is a study in abstract algebraic logic. We investigate the correspondence between the metalogical Beth property and the algebraic property of surjectivity of epimorphisms. It will be shown that this correspondence holds for the large class of equivalential logics. We apply our characterization theorem to relevance logics and many-valued logics.

A well-known result, going back to the twenties, states that, under some reasonable assumptions, any logic can be characterized as the set of formulas satisfied by a matrix 〈,F〉, whereis an algebra of the appropriate type, andFa subset of the domain of, called the set of designated elements. In particular, every quasi-classical modal logic—a set of modal formulas, containing the smallest classical modal logicE, which is closed under the inference rules of substitution and modus ponens—is characterized by such a matrix, (...) wherenow is a modal algebra, andFis a filter of. If the modal logic is in fact normal, then we can do away with the filter; we can study normal modal logics in the setting of varieties of modal algebras. This point of view was adopted already quite explicitly in McKinsey and Tarski [8]. The observation that the lattice of normal modal logics is dually isomorphic to the lattice of subvarieties of a variety of modal algebras paved the road for an algebraic study of normal modal logics. The algebraic approach made available some general results from Universal Algebra, notably those obtained by Jónsson [6], and thereby was able to contribute new insights in the realm of normal modal logics [2], [3], [4], [10].The requirement that a modal logic be normal is rather a severe one, however, and many of the systems which have been considered in the literature do not meet it. For instance, of the five celebrated modal systems, S1–S5, introduced by Lewis, S4 and S5 are the only normal ones, while only SI fails to be quasi-classical. The purpose of this paper is to generalize the algebraic approach so as to be applicable not just to normal modal logics, but to quasi-classical modal logics in general. (shrink)

Let S denote the variety of Sugihara algebras. We prove that the lattice (K) of subquasivarieties of a given quasivariety K S is finite if and only if K is generated by a finite set of finite algebras. This settles a conjecture by Tokarz [6]. We also show that the lattice (S) is not modular.

Kant’s formula of universal law (FUL) is standardly understood as a test of the moral permissibility of an agent’s maxim: maxims which pass the test are morally neutral, and so permissible, while those which do not are morally impermissible. In contrast, I argue that the FUL tests whether a maxim is the cause or determining ground of an action at all. According to Kant’s general account of causality, nothing can be a cause of some effect unless there is a law-like (...) relation between the putative cause and effect. Applied to the case of action, no maxim can be the cause of an agent’s action unless there is a law-like relation between maxims of that kind and actions of that kind. The special capacity to act according to maxims as law-like causes is what Kant calls a will; the basic constitutive principle of the will is a non-normative principle I call the categorical declarative. While the actions of a perfectly good will would be described by the categorical declarative alone, human action is determined not only by the causality of the will, but also by competing causes, namely those stemming from inclination. There is thus need for a causal test for putative maxims. The test contained in the FUL is meant to determine whether an action could be grounded solely on the agent’s maxim, or whether it requires a cause external to the will. This account permits one to build eventual distinctions concerning the morality of actions on prior and independent distinctions concerning their causality. (shrink)

In this paper we elaborate on the question how to bridge the gap between contemporary (New) music and the tradition of the past, often called ‘classical’ music. First we analyze the notion of tradition (in classical music) as being distinct from traditional music, nationalism and traditionalism. A central role in this paper is dedicated to the role of counterpoint education following J.J. Fux’s Gradus ad Parnassum in the development of Central-European classical music between the late Renaissance and late Romantic periods. (...) The developments in the 20th century New Music reveal several important trend breaks. The controversies raised during the early Renaissance, regarding the practice of polyphonic singing, are discussed with respect to their impact on music development in later ages. From these controversies and the re-discovery of Nicholas de Cusa’s view on mysticism, the experience of the non-experience in polyphonic music is elucidated. Herewith, an illuminative heuristic is found in the enfolding-unfolding paradigm both in music and pictural arts, from the Renaissance till the present. (shrink)

Traditional Western conceptions of immortality characteristically presume that we come into existence at a particular time , live out our earthly span and then die. According to some, our death may then be followed by a deathless post-mortem existence. In other words, it is assumed that we are born only once and die only once; and that – at least on some accounts – we are future-sempiternal creatures. The Western secular tradition affirms at least ; the Western religious tradition – (...) Christianity, Judaism, Islam – generally affirms both and . The Indian tradition, however, typically denies both and . That is, it maintains both that we all have pre-existed beginninglessly, and that we have lived many times before and must live many times again in this world. The Indian picture, then, is that we have died and been reborn innumerable times previous to this life and we will be reborn many times in the future. This is sometimes called the Indian belief in reincarnation. The difficulty with this usage is that the term ‘reincarnation’ suggests a belief in an immortal soul that transmigrates or reincarnates. However Buddhism, while affirming rebirth, specifically denies the existence of an eternal soul. Thus the term ‘rebirth’ is preferable for referring to the generally espoused Indian doctrine. (shrink)

Besides serving us at the growing edge of science and beyond, metaphor figures even in our first learning of language; or, if not quite metaphor, something akin to it. We hear a word or phrase on some occasion, or by chance we babble a fair approximate ourselves on what happens to be a pat occasion and are applauded for it. On a later occasion, then, one that resembles the first occasion by our lights, we repeat the expression. Resemblance of occasions (...) is what matters, here as in metaphor. We generalize our application of the expression by degrees of subjective resemblance of occasions, until we discover from other people's behavior that we have pushed analogy too far and exceeded the established usage. If the crux of metaphor is creative extension through analogy, then we have forged a metaphor at each succeeding application of that early word of phrase. These primitive metaphors differ from the deliberate and sophisticated ones, however, in that they accrete directly to our growing store of standard usage. They are metaphors stillborn. It is a mistake, then, to think of linguistic usage as literalistic in its main body and metaphorical in its trimming. Metaphor, or something like it, governs both the growth of language and our acquisition of it. What comes as a subsequent refinement is rather cognitive discourse itself, at its most dryly literal. The neatly worked inner stretches of science are an open space in the tropical jungle, created by clearing tropes away. W. V. Quine is the Edgar Pierce professor emeritus of philosophy at Harvard University. His many influential works include Methods of Logic, Word and Object, and The Roots of Reference. "On the Nature of Moral Values," his previous contribution to Critical Inquiry, appeared in the Spring 1979 issue. (shrink)

The aim of the study was to determine the acceptance and perception of Nigerian patients to medical photography. A self-administered questionnaire was distributed among Nigerian patients attending oral and maxillofacial surgery and plastic surgery clinics of 3 tertiary health institutions. Information requested included patients' opinion about consent process, capturing equipment, distribution and accessibility of medical photographs. The use of non-identifiable medical photographs was more acceptable than identifiable to respondents for all purposes (P = 0.003). Most respondents were favourably disposed to (...) photographs being taken for inclusion in the case note, but opposed to identifiable photographs being used for other purposes most especially in medical websites and medical journals. Female respondents preferred non-identifiable medical photographs to identifiable ones (P = 0.001). Most respondents (78%) indicated that their consent be sought for each of the outline needs for medical photography. Half of the respondents indicated that identifiable photographs may have a negative effect on their persons; and the most commonly mentioned effects were social stigmatization, bad publicity and emotional/psychological effects. Most of the respondents preferred the use of hospital-owned camera to personal camera/personal camera-phone for their medical photographs. Most respondents (67.8%) indicated that they would like to be informed about the use of their photographs on every occasion, and 74% indicated that they would like to be informed of the specific journal in which their medical photographs are to be published. In conclusion, non-identifiable rather than identifiable medical photography is acceptable to most patients in the studied Nigerian environment. The use of personal camera/personal camera-phone should be discouraged as its acceptance by respondents is very low. Judicious use of medical photography is therefore advocated to avoid breach of principle of privacy and confidentiality in medical practice. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 62.3 (2001) 401-423 [Access article in PDF] Petrarch and the Genealogy of Asceticism W. Scott Blanchard The morality of thought lies in a procedure that is neither entrenched nor detached. --Theodor Adorno Perhaps no author within or outside of the canon of Western literature wrote as extensively on the topic of solitude as did Francesco Petrarch. While many of our modern associations with (...) the term may find some of their origins traceable as far back as Petrarch's career, the term "solitude" carried with it much different associations in his century than it does for us today, influenced as we are by the Romantic tradition and especially by Wordsworth's absorption with the idea of solitude as an ideal state for self-conscious reflection on the individual's personal history and its meaning. No less than three of Petrarch's major prose works--the De otio religioso, the De vita solitaria, and the Secretum--confront the topic of solitude directly, and we can also point to many letters, poems, and portions of his treatises that either directly or indirectly reflect Petrarch's virtual obsession with solitude. In Petrarch we are confronted with an author who was at once the most politically connected intellectual of his century--we are even tempted to call him a "public intellectual"--and yet who constantly invoked his desire for solitude, for an escape from the many distractions and seductions that the cities and courts of his society offered. For Petrarch these were invariably places where desire lurked and power held sway, so that the life of solitude was often invoked as an alternative--a counter-cultural locus, perhaps--where freedom from temptation and subjection was imagined as an escape from the negotium of worldly life. There is much in Petrarch's writings on the solitary life that is wishful and that we might characterize as merely compensatory in a life that was otherwise quite active and engaged, but there is also a [End Page 401] strain of thought in these works that indicates a certain intransigence beneath Petrarch's overdetermined attachment to the idea, if not the practice, of withdrawal and detachment. An inquiry into Petrarch's idealization of the solitary life may even yield a somewhat reactionary aspect of his complex mind, a conservative strain in an author who was in almost every other way the literary herald of a humanism that was at the center of the cultural avant-garde of the Trecento. Is the Petrarch that in so many accounts of his character is construed as the "first modern man" actually something else, a reluctant ascetic holdover from the Middle Ages? How did Petrarch use his unique understanding of the life of solitude, of ascesis, as a pose from which to construct his sense of himself as an author and intellectual? Or are we simply confronted in the figure of a worldly and an ascetic Petrarch with yet another set of contradictions so appropriate to the "immensely complex" author whose poetic signature was the oxymoron? 1"Asceticism" and "solitude" are of course not synonymous terms, but any examination of a number of Petrarch's works as they fall within what might be called a genealogy of asceticism must recognize from the start that Petrarch's brand of asceticism was somewhat unique, especially insofar as it was deeply influenced by ancient Stoicism as well as by his reading in authors from the early Christian era. The most useful expression for our purposes may be the medieval concept of the "contemplative life," since much of the analysis in what follows will focus on how Petrarch often used his self-proclaimed pose of detachment and withdrawal as a technique for carrying on what were otherwise quite engaged dialogues with those worldly formations of power and authority that are normally conceived of as belonging to the "active" sphere of human existence. 2 For despite Petrarch's participation in or association with a number of political and civic ventures during his long and productive career, he likely never would have freely chosen... (shrink)

Named for the famous Chinese minister of state, Guan Zhong, the Guanzi is one of the largest collections of ancient Chinese writings still in existence. With this volume, W. Allyn Rickett completes the first full translation of the Guanzi into English. This represents a truly monumental effort, as the Guanzi is a long and notoriously difficult work. It was compiled in its present form about 26 B.C. by the Han dynasty scholar Liu Xiang and the surviving text consists of some (...) seventy-six anonymous essays dating from the fifth century B.C. to the first century B.C.The forty-two chapters contained in this volume include several which present Daoist theories concerning self-cultivation and the relationship between the body and mind as well as the development of Huang-Lao political and economic thought. The "Dizi zhi" chapter provides one of the oldest discussions of education in China. The "Shui di" chapter refers to the circulation of blood some two thousand years before the discoveries of William Harvey in the West. Other chapters deal with various aspects of statecraft, Yin-Yang and Five Phases thought, folk beliefs, seasonal calendars, and farming. Perhaps the best-known chapters are those that deal with various methods of controlling and stimulating the economy. They constitute one of the world's earliest presentations of a quantity theory of money. Throughout the text, Rickett provides extensive notes. He also supplies an introduction to the volume and a comprehensive index. (shrink)