The purpose of the conference "On Pythagoreanism", held in Brasilia in 2011, was to bring together leading scholars from all over the world to define the status quaestionis for the ever-increasing interest and research on Pythagoreanism in the 21st century. The papers included in this volume exemplify the variety of topics and approaches now being used to understand the polyhedral image of one of the most fascinating and long-lasting intellectual phenomena in Western history. Cornelli's paper opens the volume by charting (...) the course of Pythagorean studies over the past two centuries. The remaining contributions range chronologically from Pythagoras and the early Pythagoreans of the archaic period (6th-5th centuries BCE) through the classical, hellenistic and late antique periods, to the eighteenth century. Thematically they treat the connections of Pythagoreanism with Orphism and religion, with mathematics, metaphysics and epistemology and with politics and the Pythagorean way of life. (shrink)

The history of Pythagoreanism is littered with different and incompatible interpretations. This observation directs this book towards a fundamentally historiographical rather than philological approach, setting out to reconstruct the way in which the tradition established Pythagoreanism s image.".

This volume presents the first Italian translation with commentary of the Doric Pseudo-Pythagorean texts, which are ascribed to Archytas and Brontinus and deal with metaphysical, logical, and epistemological questions. These texts probably date from the 1st century BCE and are the product of a re-emerging dogmatic interpretation of Plato's dialogues.

This paper examines Plato's ideas on cause-effect relations in the "Phaedo." It maintains that he sees causes as things (not events, states of affairs or the like), with any information as to how that thing brings about the effect relegated to a strictly secondary status. This is argued to make good sense, so long as we recognise that aition means the "thing responsible" and exploit legal analogies in order to understand what this amounts to. Furthermore, provided that we do not (...) pre-suppose that we already know what can and what cannot count as a cause, Plato proves to have an attractive case for his principle that all causation is a matter of like causing like. Once we appreciate this, we are a little closer to understanding his more idiosyncratic principle, which although puzzling is ubiquitous in his writings and often invoked as a premise in key arguments, that opposites cannot cause opposites. The last part of the paper turns to formal causes, defending Plato's advocacy of them, and examining their role in the "Parmenides'" Third Man Argument. The main proposal is that Plato's conception of Forms as causes opens the door to a better version of that argument's "Non-identity" premise than those currently available. (shrink)

In the twenty-fourth aporia of Theophrastus' Metaphysics, there appears an important, if ‘bafflingly elliptical’, ascription to Plato and the ‘Pythagoreans’ of a theory of reduction to the first principles via ‘imitation’. Very little attention has been paid to the idea of Platonic and ‘Pythagorean’ reduction through the operation of ‘imitation’ as presented by Theophrastus in his Metaphysics. This article interrogates the concepts of ‘reduction’ and ‘imitation’ as described in the extant fragments of Theophrastus’ writings – with special attention to his (...) Metaphysics – in an attempt to make sense of how, precisely, Theophrastus characterizes the metaphysical systems of Plato and the ‘Pythagoreans’. A fuller examination of Aporia 24 produces important new understandings of the nature of the Early Academy in the mid fourth century B.C.E. Specifically, by ascribing the concept of reduction via ‘imitation’ to Plato and the ‘Pythagoreans’, Theophrastus is actually describing theories about the structure of the universe held by an important Platonist competitor and the contemporary head of the Academy in Athens, Xenocrates of Chalcedon (396/5–314/13 B.C.E.), who (a) took it upon himself to establish a Platonic doctrine that could be associated with his master’s writings and (b) coordinated that doctrine with the philosophical precepts of the Pythagoreans. As a consequence, we are prompted to question Aristotle’s famous ascription of a theory of ‘imitation’ to the metaphysics of the genuine contemporary or recently deceased Pythagoreans (such as Philolaus of Croton or Archytas of Tarentum) and consider how Xenocrates’ writings on Plato and the ‘Pythagoreans’ might be informing both Theophrastus’ and Aristotle’s descriptions of the Platonic and Pythagorean philosophical system(s). (shrink)

This paper discusses Aristotle’s statement (Metaph. A 9, 991a8-9) that both Anaxagoras and Eudoxus claimed that things are the result of a mixture of original elements, in relation to Plato’s metaphysics. Eudoxus used this immanentistic thesis to reform one central component of Plato’s Theory of Form, that is the “participation”. The first part of the paper analyzes some Anaxagorean aspects in Plato’s metaphysics, showing that Plato shares with Anaxagoras the “Transmission Theory of Causality” (as called by Dancy), but he refuses (...) its immanentistic version. The second part interprets Hip. Maj. 301b2-301c2 as a refusal of a immantestic interpretation of verbs like prosgivgnomai and kosmei'tai. It is also rejected Morgan’s thesis according to which Hippias supports an aware mereological metaphysical theory. The third part contests that Phaed. 100-106 is a defense of an immanentistic metaphysics abandoned by Plato in his later works. The meaning of the expression to; ejn hJmi'n does not include a mereological approach to the causality. In Plato’s metaphysics there is no strong contradiction between transcendence and immanence. The fourth part shows that the Parmenides refuses any immanentistic version of the relationship between Forms and things. Lastly, I will argue that from a Platonic point of view the only acceptable version is the separated interpretation of Transmission Theory of Causality. (shrink)

This paper pursues two tasks: first, to criticize a number of prominent contemporary interpretations of the Pyrrhonism of Sextus Empiricus, especially Jonathan Barnes’s; and second, to outline an alternative interpretation of Sextus that (a) reconciles the opposing sides of the long-standing dispute over the scope of Pyrrhonian suspension of judgment, and (b) suggests a sympathetic alternative to some of the most influential accounts of the Pyrrhonian way of life.

In this paper, we examine Sextus Empiricus' treatise Against the geometers . We first set this treatise in the overall context of the sceptic's polemics against the liberal arts. After a discussion of Sextus' attitude to the quadrivium , we discuss the structure, the sources and the target of the Against the geometers . It appears that Euclid is not Sextus' source, and neither he, nor the professional geometers, seem to be Sextus' main targets. Of course, Sextus never really makes (...) clear his precise target, but his attacks are rather directed against geometry as a means of modelling the physical world, thus ruining the support geometry was intended to bring to the physical part of dogmatic philosophy. (shrink)