A large Hilbert space is used for the calculation of the nuclear matrix elements governing the light neutrino mass mediated mode of neutrinoless double beta decay (Ovββ-decay) of76Ge,100Mo,116Cd,128Te, and136Xe within the proton-neutron quasiparticle random phase approximation (pn-QRPA) and the renormalized QRPA with proton-neutron pairing (full-RQRPA) methods. We have found that the nuclear matrix elements obtained with the standard pn-QRPA for several nuclear transitions are extremely sensitive to the renormalization of the particle-particle component of the residual interaction of the nuclear hamiltonian. (...) Therefore the standard pn-QRPA does not guarantee the necessary accuracy to allow us to extract a reliable limit on the effective neutrino mass. This behavior already known from the calculation of the two-neutrino double beta decay matrix elements, manifests itself in the neutrinoless double-beta decay but only if a large model space is used. The full-RQRPA, which takes into account proton-neutron pairing and considers the Pauli principle in an approximate way, offers a stable solution in the physically acceptable region of the particle-particle strength. In this way more accurate values on the effective neutrino mass have been deduced from the experimental lower limits of the half-lifes of neutrinoless double beta decay. (shrink)

Up to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic properties of the action. In classical logic there is a strong dichotomy: while over finitely many propositional variables everything is trivial, the study of the continuous transformations of the Cantor space is the subject of an extensive literature, and is far from (...) being a completed task. In many-valued logic this dichotomy disappears: already in the finite-variable case many interesting phenomena occur, and the present paper aims at displaying some of these. (shrink)

We give a self-contained geometric proof of the completeness theorem for the infinite-valued sentential calculus of Łukasiewicz.

ABSTRACT We characterize, for every subvariety V of the variety of all MV- algebras, the free objects in V. We use our results to compute coproducts in V and to provide simple single-axiom axiomatizations of all many-valued logics extending the Lukasiewicz one.

The volume collects twenty-eight original essays by colleagues and friends of Michela Pereira offered on the occasion of her seventieth birthday. As a pioneer of the re-evaluation of fundamental areas of the Western philosophical and scientific tradition, starting with alchemy, Michela Pereira has dedicated important studies to Hildegard of Bingen, Roger Bacon, Ramon Llull, in addition to being one of the most authoritative interpreters of the feminist movement in the modern world. «Seeing in the shadow», the title of this volume, (...) recalls a suggestive image coined by Hildegard to establish a connection between the work of creation, human nature and prophetic knowledge, three contexts around which the interests of Michela Pereira turn. The essays of the volume interpret these topics in many thought-provoking ways. Covering a wide temporal arc, from late Antiquity to Early Modern Times, and ranging from alchemy and medicine to spirituality, prophecy and myth, from the body-soul relation to performative arts, such as theatre and music, they also include brief editions of unedited medieval texts and an updated bibliography of Michela Pereira’s publications. (shrink)

The convergence of the Neoplatonic/Neopythagorean approach with the Aristotelian organization of the sciences is one of the most interesting features that characterizes the two influential mathematical treatises on On Arithmetics and On Music by Severinus Boethius. Basing his reasoning on Nicomachus and Ptolemy, Boethius follows the philosophical tradition that had tried to reconcile Plato’s and Aristotle’s views. This attitude is examined in the present paper as regards Boethius’ response concerning the relation between numbers, ethics and aesthetics. His view emerges as (...) coming out of a rather complex construction, which assigns the ethical scope of mathematics in indicating to the human mind how to correct the ratios that realize the best relationship in movements of the soul and the body. More precisely, its ethical aim is to correct the specific form of movement of human beings, that is their actions, exemplified in the way in which mathematical ratios represent the forms of government and musical ratios evoke and heal psychophysical affections. More complex, on the other hand, is the relationship between mathematics and beauty. In clear antithesis to the position taken by Augustine on the beauty of the rhythmic patterns that better represent the beauty of unity, Boethius does not relate the mathematical ratios of the consonances to an esthetical judgment by making use of the category of beauty. For him, the physical world is totally immersed in changes and movements, and this cannot but impede things from expressing the stable unity, which is required for contemplating the beautiful. (shrink)

La dimensione teorica della musica occidentale, nella sua evoluzione storica, ha inevitabilmente fatto uso di concetti essenziali alla definizione di come il suono è musicalmente organizzato o organizzabile. Fra questi, risultano imprescindibili le nozioni di materia, forma e ordine, che implicano rispettivamente, nei pur diversi ambiti linguistici e contesti storico-filosofici di riferimento, ciò di cui è fatta la musica, ciò a cui la materia sonora tende, e come tale tensione è realizzata. Scopo di questo contributo è una valutazione d’insieme sulla (...) valenza filosofica e l’uso di tali concetti nel pensiero musicale occidentale altomedievale e in quello del Novecento, che nonostante la distanza cronologica presentano convergenze significative. Nel Medioevo, un lungo processo di elaborazione teorico-pratica permise la matematizzazione dello spazio musicale, attraverso l’adattamento di moduli melodici, trasmessi oralmente, alle strutture scalari desunte dalla teoria greco-boeziana. La forma e l’ordo musicali furono quindi riferiti ai criteri fisico-matematici atti a distinguere nella materia sonora, in sé disorganica e indefinita, ciò che è musicale da ciò che non lo è. Tale concezione sparisce con l’affermarsi del sistema tonale, ove il suono fisico è concepito come “pre-formato” e “pre-ordinato” nella gamma scalare e nei vincoli attrattivi “naturali” degli armonici. In conseguenza, i concetti di forma e ordine abbandonano il contesto acustico, andando a definire i criteri teorici della composizione artistica, in linea con l’idea filosofica del loro esprimere la coerenza logico-sintattica dell’“insieme organico” . Nell’ambito del pensiero musicale del Novecento, la crisi del sistema tonale e la messa a punto di nuove modalità e tecniche di produzione del suono hanno riorientato la valenza significante e l’uso di questi tre concetti, implicando il loro tornare a imporsi sugli elementi primari della fisica del suono, non solo l’altezza, ma soprattutto il timbro, il volume e la durata. Già Schönberg, nel 1911, affermava come “l’ordine che chiamiamo forma artistica” è “un necessario espediente” elaborato “a causa della nostra incapacità a comprendere l’indistinto e il non-ordinato”, che è la condizione propria della materia sonora. In its historical development, the Western theory of music has inevitably made use of specific concepts to define how the sound is musically organized or organizable. Among these notions, those of matter, form and order signify – in spite of the different linguistic areas and the various historical and philosophical backgrounds – that from which music is made, that to which it tends and how such tendency is realized. This paper aims to evaluate the philosophical implications and the use of these three concepts in the musical theories of the high Middle Ages and of the twentieth century, since, in spite of their chronological distance, they present significant similarities. A long process of theoretical and practical adjustments of the melodic structures of liturgical chants to the scale-systems of the Greek and Boethian theory contributed to developing what would become a familiar notion throughout the Middle Ages: that musical intervals can be expressed in mathematical terms. According to this view, the words forma and ordo signify the mathematical measures that are applied to the “matter” of sound, which is considered as inorganic and indefinite in itself. This conception gradually disappears when the tonal system begins to emerge, since this new modality of composition implies that the physical sound is “pre-formed” and “pre-ordered” within the musical scale, according to the “natural” links of the harmonics. Consequently, the concepts of “form” and “order” do not refer any more to the context of sound generation, but are now used to define the theoretical criteria of the artistic composition, so to accomplish the new philosophic idea of their expressing the logical-syntactic coherence of the “organic-whole” . In the early twentieth century, when the tonal system starts to be replaced by new methods of composition and when new modalities and techniques of sound production emerge, those three concepts are used, again, to express the basic elements of the physics of sound: not only its height, but also its timbre, volume, and duration. In 1911, Schönberg argued that the order that we call “artistic form” is a necessary device, elaborated “because of our incapacity to comprehend the indistinct and unordered thing”, that is the own condition of the matter of sound. (shrink)

Robert Grosseteste’s utilization of Greek and Arabic Aristotelian commentators represents an intriguing aspect of his approach to Aristotle. This study centres on Grosseteste’s quotations from John Philoponus’ Commentary on Posterior Analytics, which Grosseteste employed to complement his own commentary on this Aristotelian work. After revisiting the debated medieval circulation of segments of Philoponus in connection with James of Venice’s Aristotelian translations, the article delves into the Renaissance Latin versions of Philoponus’ commentary. This includes the previously overlooked translation by Maurizio Zamberti (...) (1516, unpublished) and the initial Venetian editions (1534, 1539, 1542). The Venetian prints were derived from an anonymous and unfamiliar Latin version that followed James of Venice’s translation and terminology. This distinctive feature, along with the marginalia referencing Lincolniensis (i.e., Grosseteste) in Philippus Theodosius’ revised text (Venice 1542), allows for a comparison of passages from Grosseteste and Philoponus to validate their correspondences. The final segment of this study investigates Grosseteste’s sparse and elusive references to Aristotle’s On the Soul in light of the possibility that they may stem from fragments of Philoponus’ commentary accompanying James of Venice’s translation of that Aristotelian work. (shrink)

The half-open real unit interval an automorphism-invariant positive normalized linear functional onH. SinceHis representable as a uniformly dense set of continuous functions on its maximal spectrum, such functionals—in this context usually called states—amount to automorphism-invariant finite Borel measures on the spectrum. Different choices for the unit may be algebraically unrelated, but our second main result shows that the corresponding measures are always absolutely continuous w.r.t. each other, and provides an explicit expression for the reciprocal density.

In classical propositional logic, a theory T is prime iff it is complete. In Łukasiewicz infinite-valued logic the two notions split, completeness being stronger than primeness. Using toric desingularization algorithms and the fine structure of prime ideal spaces of free ℓ -groups, in this paper we shall characterize prime theories in infinite-valued logic. We will show that recursively enumerable prime theories over a finite number of variables are decidable, and we will exhibit an example of an undecidable r.e. prime theory (...) over countably many variables. (shrink)

This article presents a study and a critical edition of the short anonymous treatise on the rainbow starting with the incipit Inter omnes impressiones. The text was known to Nicole Oresme who engages with it twice: in his Questiones in Meteorologica de prima lectura and in Le livre du ciel et du monde. This Tractatus de iride, previously unknown to scholars, is transmitted in three late thirteenth-century manuscripts. It uses Robert Grosseteste’s theories of the rainbow as caused by the refraction (...) of sunlight and of colour as light incorporated in aereal particles. However, contrary to Grosseteste, the Tractatus de iride adopts the idea of different degrees of incorporation of light, which is also found in the scientific writings by Adam of Exeter, a Franciscan scholar belonging to the same Oxonian circle as Grosseteste. Moreover, the Tractatus de iride develops original propositions in regard to the role of individual raindrops, the importance of the angle from which the rainbow is observed, and the idea of the spirituality of the colours in the medium, which were central also for Roger Bacon’s and Nicole Oresme’s own theories of the rainbow. (shrink)

Hume's Reception in Early America: Expanded Edition brings together the original American responses to one of Britain's greatest men of letters, David Hume. Now available as a single volume paperback, this new edition includes updated further readings suggestions and dozens of additional primary sources gathered together in a completely new concluding section. From complete pamphlets and booklets, to poems, reviews, and letters, to extracts from newspapers, religious magazines and literary and political journals, this book's contents come from a wide variety (...) of sources published in colonial America and the early United States between 1758 and 1850. As well as classics by Thomas Jefferson, John Adams and Alexander Hamilton, it contains scores of unknown and hard-to-locate items, many of which have not been reprinted since their original publication. These responses are divided into four parts covering Hume's Essays; his Philosophical Writings; his History of England; and his Character and Death. Each of those parts has a separate introductory essay, and every selection is introduced by a short headnote that sets the piece in its historical context and provides bibliographical references. Packed with new insights into Hume and American thought and culture, Hume's Reception in Early America reveals the relevance and impact of Hume on American political, philosophical, historical, religious, and aesthetic debates. (shrink)

This is a welcome reprint of a book that continues to grow in importance.

The MV-algebra S m w is obtained from the (m+1)-valued ukasiewicz chain by adding infinitesimals, in the same way as Chang's algebra is obtained from the two-valued chain. These algebras were introduced by Komori in his study of varieties of MV-algebras. In this paper we describe the finitely generated totally ordered algebras in the variety MV m w generated by S m w . This yields an easy description of the free MV m w -algebras over one generator. We characterize (...) the automorphism groups of the free MV-algebras over finitely many generators. (shrink)

In this volume specialists of medieval music and philosophy put the medieval 'musica' into the context of ideas and institutions in which it existed. The significance of 'musica' cannot be understood from a modern point of view since 'music' does not match the medieval 'musica'.

We examine the role of religious identity in promoting strategic renewal in privately held founder family firms. Religious identity in these firms refers to their collective sense of being that reflects their founders’ and owner family members’ espoused religious values and beliefs, thereby distinguishing themselves from others in what is central, distinct, and enduring about their organization. We propose that such a religious identity determines family firms’ spiritual capital, which influences strategic renewal activities such as conflict resolution and resource allocation. (...) Specifically, we argue that spiritual capital can be a double-edged sword when family firms pursue strategic renewal. We discuss the implications of our work for future research. (shrink)

We examine the role of religious identity in promoting strategic renewal in privately held founder family firms. Religious identity in these firms refers to their collective sense of being that reflects their founders’ and owner family members’ espoused religious values and beliefs, thereby distinguishing themselves from others in what is central, distinct, and enduring about their organization. We propose that such a religious identity determines family firms’ spiritual capital, which influences strategic renewal activities such as conflict resolution and resource allocation. (...) Specifically, we argue that spiritual capital can be a double-edged sword when family firms pursue strategic renewal. We discuss the implications of our work for future research. (shrink)

Few figures of the Middle Ages command the attention of so many modern disciplines as Robert Grosseteste (c. 1170-1253). Theology, Philosophy, History, and Science are all areas which his life and thought continue to have significance and to inspire re-interpretation. Accompanied by a series of original commentaries, this new edition of Grosseteste's work, with English translation, draws together the perspectives of modern scientists and medieval specialists. Volume I of a six volume series, Knowing and Speaking presents two of the earliest (...) of Grosseteste's works, the treatises On the Liberal Arts and On the Generation of Sounds. These are accompanied by a significant Middle English treatise on the Seven Liberal Arts whose anonymous fifteenth-century author translated and excerpted passages from Grosseteste's treatises in a re-imagining of their structure and function.0Each work is treated separately within the volume, which is constructed in three parts. On the Liberal Arts sets Grosseteste's thoughts on the arts subjects and emphasises moral concerns about the purpose of learning. On the Generation of Sounds builds on the theories and statements of On the Liberal Arts in connection to the production of sound, elaborating the earlier position, relating the generation of sounds to human vocal and speech production. (shrink)

Editor James Fetzer presents an analytical and historical introduction and a comprehensive bibliography together with selections of many of Carl G. Hempel's most important studies to give students and scholars an ideal opportunity to appreciate the enduring contributions of one of the most influential philosophers of science of the 20th century.

Ethics in business and economics is often attacked for being too superficial. By elaborating the conclusions of two such critics of business ethics and welfare economics respectively, this article will draw the attention to the ethics behind these apparently well-intended, but not always convincing constructions, by help of the fundamental ethics of Emmanuel Levinas. To Levinas, responsibility is more basic than language, and thus also more basic than all social constructions. Co-operation relations in organizations, markets and value networks are generated (...) from personal relations and personal responsibilities. It is not sufficient to integrate ethics in an impersonal, rational system, neither in business organizations nor in the world economy. Ethics has its source not in rationality, but in the personal. (shrink)

Fichte assigns ‘intellectual intuition’ a new meaning after Kant. But in 1799, his doctrine of intellectual intuition is publicly deemed indefensible by Kant and nihilistic by Jacobi. I propose to defend Fichte’s doctrine against these charges, leaving aside whether it captures what he calls the ‘spirit’ of transcendental idealism. I do so by articulating three problems that motivate Fichte’s redirection of intellectual intuition from being to acting: (1) the regress problem, which states that reflecting on empirical facts of consciousness leads (...) only to further facts and so cannot yield a first principle; (2) the rhapsody problem, which states that the categories form a haphazard set and so lack necessity unless they derive from a first principle; and (3) the nihilism problem, which states that a first principle cannot lie outside our cognition of it, lest it be the cause of our cognition and, being first, the cause of all our actions, reducing us to machines. Crucially, Fichte’s three motivating problems are in fact aspects of a single problem. Leaving any aspect unsolved spoils putative solutions to the other two. Consequently, Fichte requires a single unified solution to all three, which his doctrine of intellectual intuition provides. (shrink)

Levinas did not present any new ethical theories; he did not even give any normative recommendations. But his phenomenological investigations help us to understand how the idea of ethics emerges and how we try to cope with it. The purpose of this paper is to suggest some implications from a reading of Levinas on how ethical challenges are handled within a management perspective. The paper claims that management, both in theory and in practice, is necessarily egocentric and thus ethically biased. (...) Therefore, ethics, defined as the idea that it is possible to do otherwise than pursue one's own interest, must have its source outside the scope of management. Levinas identifies this source as the call for responsibility from the Other, beyond the reach of managerial control. He also suggests how this idea of ethics is put into practice, especially in economic life: the existence of money makes it both possible and necessary to compare unique and incomparable others. Management tools may be used in the service of always more justice, as it also may be used for the opposite purpose. Instead of trying to draw a normative conclusion from Levinas, we may distinguish between two ways of experiencing reality: one through language and knowledge, covering both descriptive and normative knowledge, including business ethics, and the other through the particular events of encounters, from where this knowledge is continuously questioned through the call for responsibility, and thereby may provide possibilities for continuous improvements towards always more justice. (shrink)

Levinas did not present any new ethical theories; he did not even give any normative recommendations. But his phenomenological investigations help us to understand how the idea of ethics emerges and how we try to cope with it. The purpose of this paper is to suggest some implications from a reading of Levinas on how ethical challenges are handled within a management perspective. The paper claims that management, both in theory and in practice, is necessarily egocentric and thus ethically biased. (...) Therefore, ethics, defined as the idea that it is possible to do otherwise than pursue one's own interest, must have its source outside the scope of management. Levinas identifies this source as the call for responsibility from the Other, beyond the reach of managerial control. He also suggests how this idea of ethics is put into practice, especially in economic life: the existence of money makes it both possible and necessary to compare unique and incomparable others. Management tools may be used in the service of always more justice, as it also may be used for the opposite purpose. Instead of trying to draw a normative conclusion from Levinas, we may distinguish between two ways of experiencing reality: one through language and knowledge, covering both descriptive and normative knowledge, including ‘business ethics’, and the other through the particular events of encounters, from where this knowledge is continuously questioned through the call for responsibility, and thereby may provide possibilities for continuous improvements towards always more justice. (shrink)

Two attitudes are possible: one, that the world is an absolute jungle and that the exercise of coercive power by rulers is only a manifestation of this; and the other, that it is both necessary and right that there should be this exercise of power, that through it the world is much less of a jungle than it could possibly be without it, so that one should in principle be glad of the existence of such power, and only take exception (...) to its unjust exercise. (shrink)

The familiar issue of corporate social responsibility takes on a new topic. Added to the list of concerns from affirmative action and environmental integrity is their growing contributions to education. At first glance, the efforts may appear to be ordinary gestures of communal good will in terms of providing computers, sponsoring book covers, and interactive materials provided by Scholastic Magazine. A closer view reveals a targeted market of student life who are vulnerable to commercials placed in these formats. Among the (...) most effective corporate intervention is Channel One News. It offers a newsworthy show but with mandatory commercial viewing. This increasing trend of corporations intervening to assist schools that need more money and/or equipment is disingenuous.In this essay, I present the background of this commercialization of education and demonstrate the violations against student autonomy and integrity. Although there may be utilitarian merits to some interventions, I argue that these infringe upon the moral value of personhood. Advertising in schools in its current practice is immoral on deontological grounds. (shrink)