The first book-length philosophical study on the Presocratic influences in Plotinus’ Enneads.

_The first book-length philosophical study on the Presocratic influences in Plotinus’ Enneads._.

Archimedes’ Sand-Reckoner presents a system for naming extraordinarily large numbers, larger than the number of grains of sand that would fill the cosmos. Curiously, Archimedes addresses the treatise not to another specialist but to King Gelon II of Syracuse. While the treatise has thus been seen as evidence for the dynamics of patronage, difficulties in both Archimedes’ treatment of Gelon and his discussion of astronomical models make it fit incongruously within contemporary court and scientific contexts. This article offers a new (...) reading of the Sand-Reckoner based on a reconsideration of the relationship between author and addressee: deferring assumptions about the historicity of that relationship, it analyzes Gelon’s role in the treatise with respect to both the stylistic features of Archimedes’ prose and a broader tradition of narratives about a variety of cultural actors who engage with kings, speaking not so much truth as wit to power. Such a reading resolves the social and scientific difficulties of the treatise, and develops the literary-experimental qualities of Hellenistic science. In turn, the article proposes a revised approach, sensitive to broader patterns of authorship, to understanding ancient scientific authors’ relationship to royal authority. It concludes, finally, that the royal patronage seemingly exemplified by the Sand-Reckoner had greater significance as a cultural trope than as a social institution. (shrink)

A topic common to both Plato’s and Aristotle’s discussions of theories of the soul is the doctrine of the soul as a harmony of the parts of the body. Plato’s Phaedo as well as Aristotle’s De anima and Eudemus present this theory and argue against the identification of the soul as a harmony. This paper has two focuses, one philosophical and one historical. First, I will focus on the argumentation used by Aristotle in his dialogue Eudemus, which is often associated (...) with Aristotle’s early attachment to Plato. On the basis of the argumentation against the harmonia theory, I will try to show that the Eudemus is not a dialogue that depicts Aristotle’s Platonic phase. Instead, by comparing the arguments of the Eudemus with both Plato and Aristotle’s mature thought, I will argue that the argumentation of the Eudemus seems to be an indirect attack on Plato’s view on the Forms and on the nature of the soul, and that it seems to be consistent with Aristotle’s mature work On the Soul. Second, given that Aristotle discusses this topic twice, I will try, also on the basis of conclusions about the Eudemus and on later reception of Aristotle’s arguments, to show why this is the case. (shrink)

> καὶ πῶς τις ἀνάξει αὐτοὺς εἰς φῶς, ὥσπερ > > ἐξ Ἅιδου λέγονται δή τινες εἰς θεοὺς ἀνελθεῖν; > > Plato Republic 521c This study reconstructs Empedocles’ eschatology and cosmology, arguing that they presuppose one another. Part one surveys body and soul in Empedocles and argues that the transmigrating daimon is a long-lived compound made of the elements air and fire. Part two shows that Empedocles situates our current life in Hades, then considers the testimonies concerning different cosmic levels (...) in Empedocles and compares them with the afterlife schemes in Pindar’s Second Olympian Ode and Plato’s Phaedo myth. Part three offers a new edition of section d lines 5–10 of the Strasbourg papyrus of Empedocles that reinforces the connection between transmigration and different cosmic locations for souls. Part four reconstructs Empedocles’ cosmology, identifies three different levels or habitats of soul, and, more tentatively, suggests that Empedoclean “long-lived gods” are best understood as stars. (shrink)

Presocratic philosophy as a historical category was defined by Aristotle as physics, or physical philosophy, because φύσις (understood as a single genus of being, among others) was its object of study, its practitioners being since tagged accordingly as φυσικοί or φυσιόλογοι. The central part of the paper deals briefly with the four pioneering Heraclitean uses of the word φύσις (frs. DK B106, B1, B112, and B123), in which the sense of the only Homeric use of the term seems to be (...) deepened and continued. Φύσις in Heraclitus has an ontological sense (covering the rationale of genuine and unitary being), and appears always in epistemic contexts, as the object of search, criterion of knowledge, basis for action and language, susceptible of show­ing and concealing. Contrasting with Aristotle’s outlook, Plato’s Phaedo 95e ff. sheds a different light on φύσις, suggesting Plato’s acknowledgement of a wider metaphysical reach of Presocratic thought, and stressing historical continuity of the philosophical project as such. In particular, the meaning of the word φύσις in Plato and Heraclitus isn’t natural or physical reality, but reality tout court, or the nature of things (their essential being: the what, how and why of things that are). (shrink)

One of the aims of the Neoplatonists is to demonstrate that ancient Presocratic thought is, in fact, a Preplatonic thought. According to the Neoplatonists, Presocratics, who were not far from the truth, employed an inaccurate and ambiguous language, whereas Plato spoke about the truth in a more appropriate and clear way. That is why the Presocratics are not necessarily erroneous and their theoretical originality and their terminology can be incorporated into the Neoplatonic philosophy. I would like to show how some (...) Presocratic theories are embedded in the Neoplatonic metaphysical system of the three Hypostases. Regarding the One and the Intellect, Plotinus, Proclus and the Anonymous Author of the Prolegomena to Platonic Philosophy read and employ some Presocratic texts in order to harmonize the Platonic and the Presocratic accounts. Although the Neoplatonists see themselves as continuing the Greek philosophical tradition started by the Presocratics, their interpretation of Presocratic thought illustrates the birth of exegetic philosophy which is able to apply ancient concepts and predicates to its own metaphysical theory. (shrink)

Sometime between 1589 and 1591, a momentous discovery was announced in Florence; or, at least, a discovery thought to be momentous by its promoter: "The true form of the octave is the octuple [ratio 8:1] and not the duple [2:1]".1 Thus taken out of context, we might be forgiven if we failed either to share the author's enthusiasm or to recognize the importance of his finding. But the fact remains that, sadly, nobody else did either: not only did his contemporaries (...) decline to adopt this dramatic solution to the problem of the musical consonances,2 but even those who may take an almost perverse interest at times in the forgotten or the misbegotten—among others, historians of... (shrink)

In Philolaus’ cosmology, the earth revolves around a central fire along with the other heavenly bodies, including a planet called the counter-earth which orbits below the earth. His theory can account for most astronomical phenomena. A common criticism of his theory since ancient times is that his counter-earth does no work in the system. Yet ancient sources say the planet was supposed to account for some lunar eclipses. A reconstruction of Philolaus’ cosmology shows how lunar eclipses occurring at certain times (...) of day cannot be explained by earth blocking the sun’s light. The counter-earth could explain these eclipses. (shrink)

In this paper, three problems that have hardly been noticed or even gone unnoticed in the available literature in the cosmology of Philolaus are addressed. They have to do with the interrelationships of the orbits of the Earth, the Sun, and the Moon around the Central Fire and all three of them constitute potentially insurmountable obstacles within the context of the Philolaic system. The first difficulty is Werner Ekschmitt’s claim that the Philolaic system cannot account for the length of the (...) day (νυχϑήμερον). It is shown that this problem can be solved with the help of the distinction between the synodic day and the sidereal day. The other two problems discussed in this paper are concerned with two hitherto unnoticed deficiencies in the explanation of lunar eclipses in the Philolaic system. The Philolaic system cannot account for long-lasting lunar eclipses and according to the internal logic of the system, during lunar eclipses the Moon enters the shadow of the Earth from the wrong side. It is almost unbelievable that nobody, from the Pythagoreans themselves up to recent authors, has noticed these two serious deficiencies, and especially the latter, in the cosmology of Philolaus the Pythagorean. (shrink)

The discovery of incommensurability by the Pythagoreans is usually ascribed to geometric or arithmetic questions, but already Tannery stressed the hypothesis that it had a music-theoretical origin. In this paper, I try to show that such hypothesis is correct, and, in addition, I try to understand why it was almost completely ignored so far.

Drawing on recent scholarship and delving systematically into Iamblichean texts, these ten papers establish Iamblichus as the great innovator of Neoplatonic philosophy who broadened its appeal for future generations of philosophers.

A pergunta, “Tudo é número?” no título do famoso artigo de 1989 de Zhmud, deixa aberto um desafio para o extremamente importante testemunho aristotélico de que “tudo é número” era a definição fundamental da filosofia pitagórica. Tal desafio não é nada simples, especialmente quando se considera que, até então, as histórias tanto da filosofia quanto da matemática antiga parecem não ter dúvidas de que esta afirmação é correta. Este artigo pretende submeter à avaliação crítica a alegação de Aristóteles de que (...) os pitagóricos acreditavam que “tudo é número”. Nossa análise dos muitos modos nos quais Aristóteles enuncia a tese de que “tudo é número” revelará, para além de variações meramente semânticas, uma contradição teórica fundamental que o próprio Aristóteles parece incapaz de resolver. De fato, três versões diferentes da doutrina estão presentes na doxografia aristotélica: uma identificação dos números com objetos sensíveis; uma identificação dos princípios dos números com os princípios das coisas que existem; uma imitação dos objetos pelos números. Enquanto as versões e parecem identificar, em termos que lembram Platão, os números com a causa material da realidade, a versão, a saber, números como causas formais da realidade, é uma reconstrução aristotélica da teoria pitagórica. Aristóteles teria sido levado a tal reconstrução pela dificuldade que encontrou para aceitar a noção pitagórica material de número, e por considerá-la, para seu gosto, fortemente marcada pela recepção da mesma teoria no ambiente da Academia. (shrink)

This paper examines the relation between Pythagorean and Heraclitean political views. I argue that for Pythagoras, Heraclitus, and Archytas the cosmological and musical notions of harmony (ἁρμονία) and the related notion of concord (ὁμόνοια) have an intrinsic political significance. These thinkers variously reflect upon political harmony and concord, and agree that a crucial condition for it is law (νόμος), which according to Pythagoras and Heraclitus has a divine origin. I begin with the Heraclitean fragments 22 B51, 54, 72, and 114 (...) DK, in which social and political reflection is connected with the theory of the harmony of opposites. In the case of Pythagoras and early Pythagoreanism, the intense, albeit indirect political influence in Magna Graecia—as transmitted by Iamblichus and Porphyry—offers evidence for social and political ideas determined by a reflection on the cosmological role of harmony and number. Finally, Archytas’ political application of rational calculation in fragment 47 B3 DK, which aims at producing concord by establishing the just measures of wealth in the city, together with the testimony on Archytas’ intense and fruitful political activity, can be taken as confirmation that the thinker’s wider cosmological views were indeed intertwined with his political reflection and action. (shrink)

At Phaedo 86b7–c2 Simmias puts forward the theory that the soul is the attunement of bodily elements. Many scholars have claimed that this theory originates in the Pythagoreans, especially Philolaus. The claim is largely based on their reading of the Phaedo, since we have scarce doxographical evidence. In this paper I show that the dialogue in question does not constitute any evidence for the Pythagorean origin of Simmias’ attunement theory, and that it rather represents the theory as stemming from a (...) materialistic world view that had become widespread among people at that time. I also pursue the question how and why, then, the attunement theory was able to attract many people, by examining its relation to Socrates’ affinity argument. (shrink)

One of the main issues that dominates Neoplatonism in late antique philosophy of the 3rd–6th centuries A.D. is the nature of the first principle, called the ‘One’. From Plotinus onward, the principle is characterized as the cause of all things, since it produces the plurality of intelligible Forms, which in turn constitute the world’s rational and material structure. Given this, the tension that faces Neoplatonists is that the One, as the first cause, must transcend all things that are characterized by (...) plurality—yet because it causes plurality, the One must anticipate plurality within itself. This becomes the main mo- tivation for this study’s focus on two late Neoplatonists, Proclus (5th cent. A.D.) and Damascius (late 5th–early 6th cent. A.D.): both attempt to address this tension in two rather different ways. Proclus’ attempted solution is to posit intermediate principles (the ‘henads’) that mirror the One’s nature, as ‘one’, but directly cause plurality. This makes the One only a cause of unity, while its production of plurality is mediated by the henads that it produces. Damascius, while appropriating Proclus’ framework, thinks that this is not enough: if the One is posed as a cause of all things, it must be directly related to plurality, even if its causality is mediated through the henads. Damascius then splits Proclus’ One into two entities: (1) the Ineffable as the first ‘principle’, which is absolutely transcendent and has no causal relation; and (2) the One as the first ‘cause’ of all things, which is only relatively transcendent under the Ineffable. -/- Previous studies that compare Proclus and Damascius tend to focus either on the Ineffable or a skeptical shift in epistemology, but little work has been done on the causal framework which underlies both figures’ positions. Thus, this study proposes to focus on the causal frameworks behind each figure: why and how does Proclus propose to assert that the One is a cause, at the same time that it transcends its final effect? And what leads Damascius to propose a notion of the One’s causality that no longer makes it transcendent in the way that a higher principle, like the Ineffable, is? The present work will answer these questions in two parts. In the first, Proclus’ and Damascius’ notions of causality will be examined, insofar as they apply to all levels of being. In the second part, the One’s causality will be examined for both figures: for Proclus, the One’s causality in itself and the causality of its intermediate principles; for Damascius, the One’s causality, and how the Ineffable is needed to explain the One. The outcome of this study will show that Proclus’ framework results in an inner tension that Damascius is responding to with his notion of the One. While Damascius’ own solution implies its own tension, he at least solves a difficulty in Proclus—and in so doing, partially returns to a notion of the One much like Iamblichus’ and Plotinus’ One. (shrink)

Eugene Afonasin highlights the wealth of information on Pythagoras and his tradition preserved in Clement of Alexandria’s Stromateis and presents them against the background of Later Platonic philosophy. He  rst outlines what Clement knew about the Pythagoreans, and then what he made of the Pythagorean ideal and how he reinterpreted it for his own purposes. Clement clearly occupies an intermediate position between the Neopythagorean biographical tradition, rmly based on Nicomachus, and that more or less vague and difuse literary situation (...) which preceded the later developments, and in this respect is a very good source, worth studying for its own sake and as supplementary material which can help to understand the great Pythagorean synthesis attempted by Iamblichus. Developing their variants of the “exhortation to philosophy” (protreptikoi logoi), these men were much concerned with the educational value of the Pythagorean way of life rather than biographical circumstances, designed to place the ancient sage in the proper cultural context. (shrink)

This thesis is a study of Archaic and Early Classical philosophical poetry within the competitive context which characterized the poetic production of that period. In particular, I evaluate the ideas and arguments of Xenophanes, Parmenides, Epicharmus and Empedocles in the context of the social and cultural aspects of Archaic poetic performance in order to evaluate their response to traditional agonism. As I argue, these figures entered the poetic contest not only to defeat their poetic adversaries, but also to transform and (...) redefine the terms of the competition itself. Chapter 1 is devoted to the analysis of three institutionalized forms of poetic agonism: sympotic games, rhapsodic contests, and dramatic performances. In chapter 2, I evaluate the socio-political import of Xenophanes' poetry and argue that his conception of the greatest god serves to substantiate his moral prescriptions aimed at eliminating civic conflict. In chapter 3, I examine Parmenides' original notion of alētheia as logical deduction, whereby he provides a solution to the problem of the truth-status of poetry stemming from the Muses' ability to inspire both genuine and false accounts, as narrated in Hesiod's Theogony. Chapter 4 provides an analysis of Empedocles' polemic allusions to his poetic and philosophical predecessors. I argue that Empedocles' confidence in his poetic authority is ultimately grounded on his self-declared divine status, which grants him a unique and comprehensive poetic knowledge. In chapter 5, I evaluate Epicharmus' philosophical fragments against the background of early rhetoric and argue that, through the use of philosophically inspired arguments, Epicharmus aimed to make manifest philosophy's agonistic potential and to show how it could be exploited to one's own advantage. (shrink)