Numenius is one of the most important authors who, in the Imperial Age, deal with the figure of Socrates. Socrates is important in the Platon­ic tradition, in particular in the sceptical tradition, when the Socratic dubitative “spirit” of the first Platonic dialogues became important to justify the “suspension of judgement.” Numenius criticises the whole Academic tradition by saying that the Academics (particularly the sceptics) betrayed the original doctrine of Plato and formulated a new image of Socrates. For Numenius, Socrates plays (...) a central role because Plato would have inherited his doctrine. What does Socrates’s doctrine consist in? According to Numenius, Socrates theorised a “doctrine of three Gods” (which can be likely found in the second Platonic epistle) which is strictly bound up with the main aspect of Plato’s thought. In fact, in Numenius’s view, Plato belongs to a genealogy which can be linked to Pythagoras himself. From this perspective, Numenius says that Socrates’s original thought is a theology which also belongs to the Pythagorean tradition and which Plato further developed. For Nume­nius, Socrates is not the philosopher of doubt, but a theologian who first theorised the existence of three levels of reality (Gods), which is also the kernel of Numenius’s metaphysical system. For this reason, Numenius puts Socrates within a theological genealogy that begins with Pythago­ras and continues with Socrates and Plato, and that the Academics and the Socratics failed to understand. (shrink)

With respect to Parmenides’ thought Melissus was regarded as a dissident thinker already in antiquity. His polemical introduction of the concept of void and the relative idea of infinite Being seemed particularly controversial. The aim of the present paper is to examine the origins of the Melissian understanding of void in order to trace its philosophical genesis to the criticism of the Atomist Leucippus. According to the philosopher from Abdera, the Eleatic fundamental principles had to conform to the obviousness of (...) bodies’ motion, which is why the Eleatic not-Being had to be understood as void. Melissus took issue with this view and criticized the idea of the void’s reality by means of a methodical argument. In the course of doing so, the philosopher from Samos distorted the original Parmenidean ontology, which is why his theories were often criticized severely as theoretically weak. (shrink)

Numenio appartiene all’ambito degli interpreti medioplatonici dei dialoghi di Platone; nel Medioplatonismo, infatti, si diffuse la tendenza a interpretare la filosofia di Platone come in chiave sistematica. Il dialogo più rilevante per questa operazione esegetica nel Medioplatonismo fu certamente il Timeo. In questo contributo intendo concentrarmi sull’interpretazione delle pagine 28a-29a del Timeo da parte di Numenio di Apamea ed esaminarne l’esegesi alla luce della sua prospettiva onto-teologica. Nel Timeo, l’utilizzo del verbo βλέπω ha la funzione di descrivere il fatto che (...) il demiurgo è contemplativo nei confronti del paradigma intelligibile. In Numenio, invece, l’associazione del verbo βλέπω al demiurgo è volta a mostrare il ruolo di mediatore che il secondo dio svolge tra il primo principio e la materia. In questo modo si mostrerà come i passi del Timeo vengano interpretati da Numenio alla luce della sua metafisica dualista. (shrink)

Numenius is an author who straddles the line between Middle Platonism and Neoplatonism. In this contribution, I focus on the differences between the second and the third God, which emerge from analyses of the relevant fragments. Numenius emphasizes, on several occasions, how the second God (i.e., the demiurge) has a dual nature. In this paper, I investigate the role of the demiurge in Numenius and examine in what sense the second and third God are “one.” On the one hand, Numenius (...) seems to be stressing the unity of the second and third levels of reality, but on the other hand, he also appears to be differentiating them. The present analyses concentrate on fragments 19F, 24F, 29T and 30T (respectively 11, 16, 21, and 22 in des Places’ edition). My purpose is to demonstrate that, according to Numenius, the second and the third God are one because they both can be regarded as demiurgic. Thus, Numenius conceives a kind of “double demiurgy,” which preserves the distinction between the second and the third God, who are distinguished from an ontological point of view, but who, at the same time, share a demiurgic function. The second God is then the paradigm, whereas the third God is immanent in matter as a ruling principle of the cosmos, which is similar to the World Soul, as he operates on matter in order to make it rationally ordered. (shrink)

The first book of the Aristotelian Physics may be considered as a sort of general introduction to the whole work. In particular, chapters 2 and 3 result very interesting for the foundation of the science of nature according to Aristotle; indeed, in these two chapters, the Stagirite criticizes the position of the Eleates Parmenides and Melissus. These two philosophers are considered as those who claim that change does not exist because the existence of the not-being is impossible to suppose. For (...) this reason, since the Eleates deny that motion and change really exist, the refutation of their thesis results essential for the logical and ontological foundation of the Aristotelian science of nature. This paper wants to make light on the argumentations that Aristotle uses against Parmenides and Melissus. Indeed, since the Stagirite makes often use of his philosophical categories, it seems that his critics sound a little bit anachronistic. In many passages of the text is seems that Aristotle “simply” replace the presupposition of the Eleatic philosophy with the thesis of the evidence of moving and plurality, in general. The aim of this contribution is to reflect on the critics present in Ph. I 2–3 in order to underline the importance of the Eleatic philosophy for the Aristotelian science of nature. (shrink)

Richard McKirahan untersucht systematisch die aristotelische Diskussion des Denkens von Parmenides, Zeno und Melissus und bringt Licht in die obskureren und komplexeren Passagen. Er ergänzt seine Studie durch eine neuartige "aristotelisierende" Interpretation des Gedichts von Parmenides. Die Texte werden von einem umfassenden Essay der Herausgeber eingeleitet, der die Grundlinien des Bandes definiert und eine Bestandsaufnahme der Studien über die Beziehung zwischen Aristoteles und der Eleaticis vornimmt. Der zweite Teil des Bandes versammelt die Beiträge von neun Wissenschaftlern, die sich an einer (...) lebhaften Debatte über die von McKirahan angesprochenen Themen beteiligen. Mit Beiträgen von Alberto Bernabé | Mathilde Brémond | Bernardo Berruecos Frank | Néstor-Luis Cordero | Patricia Curd | Leonardo Franchi | Refik Güremen | Richard McKirahan | Massimo Pulpito | Barbara Sattler | Enrico Volpe. (shrink)

The Craig interpolation property is investigated for substructural logics whose algebraic semantics are varieties of semilinear pointed commutative residuated lattices. It is shown that Craig interpolation fails for certain classes of these logics with weakening if the corresponding algebras are not idempotent. A complete characterization is then given of axiomatic extensions of the “R-mingle with unit” logic that have the Craig interpolation property. This latter characterization is obtained using a model-theoretic quantifier elimination strategy to determine the varieties of Sugihara monoids (...) admitting the amalgamation property. (shrink)

This work presents a model-theoretic approach to the study of the amalgamation property for varieties of semilinear commutative residuated lattices. It is well-known that if a first-order theory T enjoys quantifier elimination in some language L, the class of models of the set of its universal consequences \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm T_\forall}$$\end{document} has the amalgamation property. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm Th}(\mathbb{K})}$$\end{document} be the theory of an elementary subclass (...) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{K}}$$\end{document} of the linearly ordered members of a variety \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{V}}$$\end{document} of semilinear commutative residuated lattices. We show that whenever \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm Th}(\mathbb{K})}$$\end{document} has elimination of quantifiers, and every linearly ordered structure in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{V}}$$\end{document} is a model of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm Th}_\forall(\mathbb{K})}$$\end{document}, then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{V}}$$\end{document} has the amalgamation property. We exploit this fact to provide a purely model-theoretic proof of amalgamation for particular varieties of semilinear commutative residuated lattices. (shrink)

These are the proceedings of the Workshop on Quantum Logic held in Erice (Sicily), December 2 - 9, 1979, at the Ettore Hajorana Centre for Scientific Culture. A conference of this sort was originally proposed by Giuliano Toraldo di Francia, who suggested the idea to Antonino Zichichi, and thus laid the foundation for the Workshop. To both of them we express our appreciation and thanks, also on behalf of the other participants, for having made this conference possible. There were approximately (...) fifty participants; their names and institutions are listed in the text. Quantum logic, which has now a history of some forty or more years, has seen remarkable growth during the sixties and seventies. The papers in the present volume presuppose, by and large, some acquaintance with the elements of the subject. These may be found in the well-known books by J.H. Jauch (Foundations of Quantum Hechanics; Reading, 1968), V.S. Varadarajan (Geometry of Quantum Theory: Princeton, 1968), and C. Piron (Foundations of Quantum Theory; New York, 1976). The initial program for the conference listed about twenty-five invited papers. But in the context of a very active and qualified attendance, other contributions were offered. This volume contains all of them. The program listed six main topics: I. Classification or different areas of quantum logic, and open problems. II. Comparison and unification of different approaches to quantum theories; problems of interpretation. III. Formal quantum logic; axiomatics. IV. Hodal interpretations of quantum logic. v vi FOREWORD V. Quantum set theory. (shrink)

This book uses the conceptual tools of philosophy to shed light on digital media and on the way in which they bear upon our existence. At the turn of the century, the rise of digital media significantly changed our world. The digitizing of traditional media has extraordinarily increased the circulation of texts, sound, and images. Digital media have also widened our horizons and altered our relationship with others and with ourselves. Information production and communication are still undoubtedly significant aspects of (...) digital media and life. Recently, however, recording, registration and keeping track have taken the upper hand in both online practices and the imaginaries related to them. The essays in this book therefore focus primarily on the idea that digital media involve a significant overlapping between communication and recording. (shrink)

In his recent edition, with translation and commentary, of Aristotle, Eth. Nic. VI, Hans-Georg Gadamer reproposes his interpretation of Aristotle's practical philosophy as a model for his own hermeneutics, confirming in this way his tendency to identify practical philosophy with the intellectual virtue of phronesis. Furthermore, although he recognizes the primacy attributed by Aristotle to the theoretical life, Gadamer tends to undervalue it and to consider phronesis and sophia at the same level. In particular he believes that the theoretical life (...) was for Aristotle an ideal accessible only to the gods. Unlike Heidegger, who refuses Aristotle's position because of the primacy of theoretical life, but appropriates his practical philosophy, Gadamer thinks that today is still possible to follow Aristotle, but only if we reduce that primacy. The article shows how, according to Gadamer, what Aristotle says about theoretical life, if rightly understood, can still be accepted. /// Na sua edição recente, com tradução e comentário ao Livro VI da Ética a Nicómaco de Aristóteles, Hans-Georg Gadamer reaflrma a sua interpretação dafllosofia prática de Aristóteles como modelo para a sua hermenêutica, confirmando deste modo a sua tendência a identificar a filosofia pratica de Aristóteles com a virtude dianoética da phronesis. Além disso, e apesar de reconhecer o primado atribuido por Aristóteles à vida teorética, Gadamer tende a desvalorizá-lo e a considerar a phronesis e a sophia como estando no mesmo piano. Gadamer parece especialmente convencido de que a vida teoretica para Aristóteles constitui um ideal apenas acessivel aos deuses. Ao contrário de Heidegger, que refuta a posição de Aristóteles por causa do primado atribuido à vida teorética, mas se apropria da sua filosqfia prática, Gadamer pensa ser ainda possivel seguir Aristóteles, para o efeito apenas se exigindo uma redimensionação desse primado. Enfim, o artigo demonstra como, segundo Gadamer, aquilo que Aristoteles diz acerca da vida teorética pode, se correctamente entendido, ser aceite ainda hoje. (shrink)

Comparaison entre la philosophie pratique aristotélisante d'aujourd'hui, représentée en Allemagne surtout par H.G. Gadamer, J. Ritter et leurs élèves, et les théories d'Aristote sur la phronesis et l'ethos, visant à montrer que ces dernières, dans la pensée du Stagirite, ne remplissent pas, contrairement à ce que croient ces interprètes, le rôle de la philosophie pratique toute entière. Contrast between the aristotelizing practical philosophy of today, represented in Germany especially by H.G. Gadamer, J. Ritter and their followers, and Aristotle's theories on (...) phronesis and ethos, in order to show that these theories, in the Stagirite's thought, don't play, against the opinion of those interpreters, the rôle of the whole practical philosophy. (shrink)

John Rawls and Simone Weil presented two distinct conceptions of political justice, aimed at articulating a common ethos in an inherently heterogeneous society. The terms of the former, chiefly concerned with the distribution of primary goods, underwrite much of today's Western democracies political liberalism. The terms of the latter, chiefly concerned with the way interaction is organised in social activities in view of the body and soul's balancing pairs of needs, are less well known. We explain the sense in which (...) the overlapping consensus in Weil's notion of political justice is “thicker”, and may thus deserve more attention – alongside that of Rawls – for substantiating a democratic ethos within political liberalism. (shrink)

A literatura crítica sobre Aristóteles ainda discute se a forma é universal ou individual. A doutrina do livro Lambda da Metafísica afirma que as causas dos indivíduos são individuais, mas é no De generatione animalium que essa doutrina é justificada: o sêmen paterno transmite ao mênstruo uma série de movimentos que determinam a alma do feto e o seu desenvolvimento corporal. Portanto, o pai é causa motora do filho e produz sua alma, que pode ser individual.

The aim of this essay is to critically compare ancient ethics with modern ethics, considering them both under one particular aspect, namely, the relationship between ethics and intelligence. In fact, one of the most significant differences between ancient and modern ethics is precisely the divergence in how this relationship is conceived. With this in mind, an appendix is added, dedicated to the philosophy of the 20th Century, the time when the modern conception reaches a crisis point. In the conclusion, I (...) also intend to speak about Christian ethics, which, while not exactly a philosophical ethic, occupies its own peculiar place, so to speak, in the way the relationship between ethics and intelligence is conceived. (shrink)