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 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)

Kant’s critique/doctrine distinction tracks the difference between a canon for the understanding’s proper use and an organon for its dialectical misuse. The latter reflects the dogmatic use of reason to attain a doctrine of knowledge with no antecedent critique. In the 1790s, Fichte collapses Kant’s distinction and redefines dogmatism. He argues that deriving a canon is essentially dialectical and thus yields an organon: critical idealism is properly a doctrine of science or Wissenschaftslehre. Criticism is furthermore said to refute dogmatism, by (...) which Fichte means Spinozism. Schelling repudiates Fichte’s position in his Philosophical Letters by reviving Kant’s distinction. First, ‘critique’ for Schelling names a canon that is valid for all systems—including Spinozism—and thus favours none—not even the Wissenschaftslehre. Second, Schelling coins ‘dogmaticism’ to refer to what Kant calls ‘dogmatism’: reason’s uncritical claim to doctrine. Hence, he says all systems—even Fichte’s—are susceptible to the ‘enthusiasm’ of mistaking themselves for doctrines or ‘objects of knowledge’, instead of subjectively valid ‘objects of freedom’. I reconstruct Schelling’s argument for reviving Kant’s distinction, while noting two consequences for German idealism. First, if criticism favours no system, a system’s origin cannot be an act of knowledge, e.g., intellectual intuition, but only an act of endorsement. Second, if dogmaticism entails enthusiasm, a system’s goal cannot be absolute knowledge, but only infinite striving. Hence, by retrieving Schelling’s notion of dogmaticism, we can both gain a better understanding of the Letters and register the impact of a core Kantian distinction on the German idealist project. (shrink)

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)

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.

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)

Meillassoux seeks knowledge of transcendental reality, blaming Kant for the ‘correlationist’ proscription of independent access to either thought or being. For Meillassoux, correlationism blocks an account of the meaning of ‘ancestral statements’ regarding reality prior to humans. I examine three charges on which Meillassoux’s argument depends: (1) Kant distorts ancestral statements’ meaning; (2) Kant fallaciously infers causality’s necessity; (3) Kant’s transcendental idealism cannot grasp ‘the great outdoors’. I reject these charges: (1) imposes a Cartesian misreading, hence Meillassoux’s false assumption that, (...) for Kant, objects don’t exist without subjects; (2) misreads Kant, who infers causality’s necessity from the possibility of experience; (3) casts Kant’s idealism as subjective, ignoring his perspectival portrayal of it. (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)

Information can be public among a group. Whether or not information is public matters, for example, for accounts of interdependent rational choice, of communication, and of joint intention. A standard analysis of public information identifies it with (some variant of) common belief. The latter notion is stipulatively defined as an infinite conjunction: for p to be commonly believed is for it to believed by all members of a group, for all members to believe that all members believe it, and so (...) forth. This analysis is often presupposed without much argument in philosophy. Theoretical entrenchment or intuitions about cases might give some traction on the question, but give little insight about why the identification holds, if it does. The strategy of this paper is to characterize a practical-normative role for information being public, and show that the only things that play that role are (variants of) common belief as stipulatively characterized. In more detail: a functional role for “taking a proposition for granted” in non-isolated decision making is characterized. I then present some minimal conditions under which such an attitude is correctly held. The key assumption links this attitude to beliefs about what is public. From minimal a priori principles, we can argue that a proposition being public among a group entails common commitment to believe among that group. Later sections explore partial converses to this result, the factivity of publicity and publicity from the perspective of outsiders to the group, and objections to the aprioricity of the result deriving from a posteriori existential presuppositions. (shrink)

Bazzocchi disposes the text of the Tractatus in a user-friendly manner, exactly as Wittgenstein's decimals advise. This discloses the logical form of the book by distinct reading units, linked into a fashioned hierarchical tree. The text becomes much clearer and every reader can enjoy, finally, its formal and literary qualities.

Knowledge of mechanisms is critical for causal reasoning. We contrasted two possible organizations of causal knowledge—an interconnected causal network, where events are causally connected without any boundaries delineating discrete mechanisms; or a set of disparate mechanisms—causal islands—such that events in different mechanisms are not thought to be related even when they belong to the same causal chain. To distinguish these possibilities, we tested whether people make transitive judgments about causal chains by inferring, given A causes B and B causes C, (...) that A causes C. Specifically, causal chains schematized as one chunk or mechanism in semantic memory led to transitive causal judgments. On the other hand, chains schematized as multiple chunks led to intransitive judgments despite strong intermediate links. Normative accounts of causal intransitivity could not explain these intransitive judgments. (shrink)

1. Sae sidae rŭl yŏrŏ gan saramdŭl -- 2. Ŏdum ŭi sidae.

A directory of archives and manuscript repositories, with links to web pages for the repositories and to online finding aids. Searchable by: collection name; city; state; National Inventory of Documentary Sources (NIDS) number; and National Union Catalog of Manuscript Collections (NUCMC) number.

Est-il possible de trouver une herméneutique œcuménique pour que toutes les confessions chrétiennes puissent lire les Saintes Ecritures ensemble ? C'est à cette question que tente de répondre l'A. dans cet article. Après avoir formulé précisément la nature de sa problématique théologique en introduction, l'A. axe sa première partie sur l'état actuel de la question posée. En seconde partie, il propose un modèle possible d'herméneutique transconfessionnelle. En dernière partie, il procède à une étude comparative entrre les diverses confessions sur la (...) réflexion scripturaire. (shrink)

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)