In lieu of an abstract, here is a brief excerpt of the content:Hebdomads: Boethius Meets the Neopythagoreans1Sarah Pessin1the thesis of this article is three-fold. First, I suggest, uncontroversially, that Boethius was in many ways influenced by Neopythagorean ideas. Second, I recommend that in light of our appreciation of his Neopythagorean inclinations in at least some of his writings, we understand his esoteric reference to the “hebdomads”—at the outset of his treatise often called by that name—as a reference to (...) something Neopythagorean. This I suggest in light of the fact that, as I will discuss, the “hebdomad” plays an important role within the Neopythagorean literature of Nicomachus of Gerasa, an author with whose writings Boethius was intimately familiar. Lastly, I suggest—following Dillon’s analysis of the Triad and the Hebdomad within Nicomachus’ works—an interpretation of the ‘hebdomad’ within the Neopythagorean corpus which, if correct, would make appropriate Boethius’ reference to it at the outset of a treatise on the nature of God and creation.2In his introductory remarks to the Quomodo Substantiae,2 a short but difficult theological treatise on the nature of goodness and its relation to being (esse), Boethius gives his reader fair warning:... tu ne sis obscuritatibus brevitatis adversus, quae cum sint arcani fida custodia turn id habent commodi, quod cum his solis qui digni sunt conloquuntur. [End Page 29]... do not you take objection to obscurities consequent on brevity, which are the sure treasure-house of secret doctrine and have the advantage that they speak only with those who are worthy.3While itself somewhat obscure, this statement seems to suggest that a clear explication of the treatise would involve the clarification of certain notions which Boethius chooses not to clarify, and hence, the uninitiated reader will be met with obscurity.4 Consider this suggested reading especially in light of what immediately follows: After listing nine brief axioms, we are told that: “These preliminaries are enough then for our purpose. The intelligent interpreter of the discussion will supply the arguments appropriate to each point.”5 What is most important to note in support of the claim that Boethius is intentionally obscuring the content of the work which follows, is that he never refers to these obscure axioms again—not in way of explaining them, or even in way of helping the reader use them to elucidate the subject matter which follows, (which is apparently what they are capable of doing). Furthermore, this lack of explanation and expansion on his part appears—as evidenced in the above quote—to be in line with his intended purposes in this treatise. It seems that the “intelligent interpreter” to whom he refers is the reader who is knowledge-able of certain ideas which Boethius prefers not to elaborate upon in this treatise, and who should at least in theory therefore be able to arrive at a full understanding of the arguments which follow.6The veil of obscurity which we seem to meet in the terse nature of the content of the treatise itself, then, also seems apparent in Boethius’ esoteric reference to the “hebdomads” at the outset of the treatise:You ask me to state and explain somewhat more clearly that obscure question in my Hebdomads concerning the manner in which substances are good in virtue of existence without being substantial goods. You urge that this demonstration is necessary because the method of this kind of treatise is not clear to all... But I think over my Hebdomads with myself, and I keep my speculations in my own memory rather than share them with any of those pert and frivolous persons who will not tolerate an argument unless it [End Page 30] is made amusing.7 Wherefore do not you take objection to obscurities stemming from brevity... 8Boethius’ reference to his “hebdomads” here is perplexing.Looking to the Greek word for ‘seven,’ (‘hepta’), it has been suggested that these ‘hebdomads,’ (lit., ‘groups of seven,’ or simply ‘sevens’), might simply refer to a weekly meeting group (i.e., a ‘seminar’), which Boethius attended, and which provided him the impetus to compose the treatise in question. Others suggest that this ‘group of sevens’ refers to the list of axioms which follows (which some... (shrink)

Porphyry’s position in the ancient hermeneutic tradition should be considered separately from his place in the Platonic tradition. He shows considerable respect for allegorizing interpreters with links to Pythagoreanism, particularly Numenius and Cronius, prominent sources in On the Cave of the Nymphs. The language of Homer’s Cave passage is demonstrably distinctive, resembling the Shield passage in the Iliad, and such as to suggest an ecphrasis to early imperial readers. Ecphrasis in turn suggested deeper significance for the story. While largely content (...) to follow Numenian trends in interpreting Homer’s cave symbolically and in relation to multiple belief-systems, Porphyry shows occasionally signs of wanting to adhere more closely to Homeric evidence, resorting to symbolic interpretation mainly when no more straightforward truth is on offer. (shrink)

In this paper, I argue that Bryson’s Oikonomikos is a fascinating example of the oikonomia genre in several different respects. Although the problematic transmission of this Neopythagorean text makes studying it a challenge, such effort is well-rewarded with an elaborate argument which paints the human bodily constitution, the central bodily functions and oikonomic activities as intrinsically linked. Focusing on Bryson’s argument which roots oikonomic behaviour in human biology, I explore the underlying conceptualisation of human nature and contextualise it within (...) relevant philosophical and scientific traditions. (shrink)

This essay considers the origins of the arithmological genre, the first specimen of which was an anonymous Neopythagorean treatise of the first century BCE. Arithmology as a special genre of philosophical writings dealing with the properties of the first ten numbers should be distinguished from number symbolism, which is a universal cultural phenomenon related to individual significant numbers. As our analysis shows, the philosophical foundations of arithmology were laid down in the treatise of Plato’s successor Speusippus On Pythagorean Numbers, (...) who relied on the Platonic doctrine of the ten ideal numbers, whereas in ancient Pythagoreanism arithmological notions, unlike number symbolism, are not attested. In the first century BCE, an epoch of revival of Platonism and Aristotelianism, Speusippus’ ideas received a second birth, thus marking the beginning of arithmology as a popular genre. (shrink)

This chapter investigates the Neopythagorean roots of Plotinus’ concept of number. Porphyry’s reports of Plotinus’ use of Neopythagorean sources in his teachings are quickly confirmed in the Enneads. In addition to Numenius’ influence on the definition of multiplicity as “separation,” this chapter reveals the programmatic significance of Moderatus’ distinction between the monad as the principle of numbers and the one as the principle of enumerated things on Plotinus’ two kinds of number. This discovery also shows Plotinus’ use of (...) Moderatus’ definition of mathematical number in the formulation of the outward and inward directions of multiplicity. Next, the chapter examines the elements from Nicomachus of Gerasa’s Introduction to Arithmetic in Plotinus’ concept of multiplicity. The final conclusion of the chapter shows that Plotinus views multiplicity exclusively as number, which preserves it from dissipating into infinity and thus non-existence. (shrink)

In Pythagorean Women, classical scholar Sarah B. Pomeroy discusses the groundbreaking principles that Pythagoras established for family life in Archaic Greece, such as constituting a single standard of sexual conduct for women and men. Among the Pythagoreans, women played an important role and participated actively in the philosophical life. While Pythagoras encouraged women to be submissive to men, his reasoning was based on the desire to preserve harmony in the home. -/- Pythagorean Women provides English translations of all the earliest (...) extant examples of literary Greek prose by Neopythagorean women, shedding light on their attitudes about marriage, the home, music, and the cosmos. Pomeroy sets the Pythagorean and Neopythagorean women vividly in their historical, ecological, and intellectual contexts, illustrated with original photographs of sites and artifacts known to these women. (shrink)

The question of the self and person in Islamic philosophy can be considered from several different perspectives. The term “philosophy,” falsafa, in Islam refers solely to the Greek tradition of thought represented by such thinkers as al‐Fārābī, Avicen‐ na, and Averroës. Even some of those who unquestionably belong to this tradition – Suhrawardī and Mullā ṣadrā, for example – tend to avoid the term “falsafa” in favor of the Arabic synonym “ḥikma” (lit. wisdom). There are other Islamic intellectual traditions that (...) are unquestionably philosophic in one sense or another or that have important implications even for thinkers working strictly within the Graeco‐ Islamic tradition of falsafa. The most basic tradition of thought about the self and person is Quranic Islam, which sets the fundamental terms of reference for moral and religious thought about the person in the Islamic world. (The Quran is always considered by Muslims to be the word of God, not of Muhammad.) The rich tradition of Islamic legal thought about the person may be considered an extension of Quranic thought on the subject. For convenience, in the present article this tradition will be referred to as “Quranic” or “Islamic,” but it must be remembered that thinkers of other traditions in the Islamic world also considered themselves to be “Quranic” and “Islamic,” though perhaps in different senses. The second tradition that I will discuss is Graeco‐Islamic philosophy, which I will refer to as “philosophy.” This represents the tradition of Plato and Aristotle, combined in various proportions and sometimes with conspicuous elements of Neoplatonism and Neopythagoreanism. The third tradition is Sufism, Islamic mysticism, which developed important and influential ideas about the self and person. (shrink)

Intent upon harmonizing doctrines of their predecessors, some Neoplatonic commentators are faced with a problem of resolving doctrinal discrepancies so as to restore the συµφωνία in the history of philosophy. This article considers a particular example of this attempt ats harmonization: how Simplicius reconciles Aristotle's Categories with the Neopythagorean doctrine of the Pseudo-Archytas. The chronological inversion introduced by the counterfeiter produces remarkable effects on the late Platonic doctrine about general terms, to the extent that a commentator such as Simplicius (...) works to reduce the dissonance between Archytas' and Aristotle's words. This paper has three aims: to restore the general grid that Simplicius uses for reading and commenting on Archytas through Aristotle; to identify the exegetical strategies aimed at a doctrinal reconciliation; to consider a specific case, provided by the doctrine of weight, which engenders a new physical theory by Simplicius. (shrink)

As is well known, Lucian’s masterpiece Verae Historiae can be read as a travesty of Homer’s Odyssey. The present paper argues that with his fantastic voyage Lucian reacts not just to the Odyssey itself but also to the recent interpretation of the Odyssey by the Middle Platonic and Neopythagorean philosopher Numenios of Apameia. Lucian’s purpose, therefore, in writing the Verae Historiae was presumably to give back to Odysseus some of the resilience that interpretations like that of Numenios had taken (...) away from him, and in general to set mythological poetry free once again from the constraints the philosophers had laid on it. (shrink)

This anthology, the largest collection of Pythagorean writings ever to appear in English, contains the four ancient biographies of Pythagoras and over 25 Pythagorean and Neopythagorean writings from the Classical and Hellenistic periods. The material of this book is indispensable for anyone who wishes to understand the real spiritual roots of Western civilization.

The genre of the plague treatise, still little studied, testifies to the cultural transformations that swept western Eurasia after the Black Death apocalypse of the mid-fourteenth century, with recurrent outbreaks for centuries thereafter. Ottoman contributions to this genre are exemplary: they allow us to track the emergence of an imperial-scientific early modernity. This article presents the most comprehensive and innovative Islamicate plague treatise extant, Taşköprīzāde Aḥmed’s (d. 1561) Treatise on Healing Epidemic Diseases. Therein the celebrated Ottoman polymath makes a strong (...) case, advanced by arguments both religious and rational, for occult science as the most empirical method for preventing and curing the plague. To this end, he devotes the theoretical first half of the treatise to a critique of fatalist scholars and sufis, who prefer tawakkul to tasabbub, or blind faith to “scientific method”; the practical second half is devoted to what he considers to be the most medically effective scientific discipline of his era, lettrism (ʿilm al-ḥurūf)—a Neopythagorean science encapsulating the new “cosmological imaginary” of Western early modernity generally, wherein the world was seen by many thinkers and doers as a mathematical and hence magically tractable text. Our distaste for occult science notwithstanding, Taşköprīzāde must here be named another early modern empiricist. (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)

The 1962 publication of J. H. Waszink's edition of Calcidius' commentary on Plato's "Timaeus" focussed attention on the question of Calcidius' source for a group of chapters where he presents an interpretation of Plato's account of the creation of soul. I discuss three attempts to answer this question: that of Waszink himself, who argues that the source is Porphyry who was here influenced by the Neopythagorean/Platonist Numenius, that of J. M. Van Winden, who claims Numenius as the direct source, (...) and that of Werner Deuse, who offers reasons for excluding Numenius as either directly or indirectly responsible. I show the weakness of Deuse's critique, but then argue that neither Waszink nor Van Winden has given sufficient consideration to the possibility that Plotinus, either alone or through Porphyry as intermediary, is behind Calcidius' interpretation, where the doctrines of the unity of the soul and of a higher soul that does not descend, both characteristic of Plotinus' psychology, are prominent. However, there is an important but uniformly overlooked feature of this exegesis that rules out both Plotinus and Porphyry as possible sources. This leaves Numenius as the only serious candidate. If, then, the origin of the doctrines of the unity of the soul and of the undescended higher soul can be traced to the work of Numenius, there is the strong possibility that in his formulation of these same doctrines Plotinus was indebted to Numenius. (shrink)

This chapter examines the relationship between Plotinus’ concept of the origin of multiplicity as “separation from the One” and Plato’s presentation of the Demiurge’s composition of the universe in the Timaeus. The two terms characterize the “top-down” approach in Ennead VI.6 and the “bottom-up” approach in the Timaeus. The two works achieve the same goal—the explanation of the universe—with the same means—according to number—but from opposite starting points. The missing conceptual link between the two approaches, the chapter discovers, is found (...) in Numenius’ concept of the Three Gods, ordering the universe: the Father, the Maker, and the Creation. The characteristics of Numenius’ First God convey the dichotomy between rest, as being and stability, and motion, as change, in the first principle. The explicit paradox of ontological stability and innate motion in Numenius’ First God is implicitly present in Plotinus’ explanation of the origin of the universe as “separation.” This chapter concludes that Plotinus induces the concept of multiplicity as a measurement of the ontological distance from the One. It also opens the possibility for stronger Neopythagorean influences. (shrink)

Chapter six examines the relationship between Plotinus’ concepts of number and multiplicity, and Porphyry’s organization of the Enneads. Porphyry’s thematical arrangement of the Enneads is traditionally considered to be more detrimental than beneficial for understanding Plotinus’ thought. The chapter re-examines this issue and discovers that Porphyry fuses Plotinus’ philosophy with Neopythagorean numerical symbolism to reveal the central organizing theme of Plotinus’ universe. In the Neopythagorean tradition, the number six is considered to be the first perfect number and the (...) hexad is identified as the number of Soul, while the completion of the universe is represented by the number nine, which is “called ‘ennead’ as if it were the ‘henad’ of everything within it, by derivation from the ‘one’.” The individual treatises are consequently grouped in nines, because they enclose the numerical essence of the universe from “henad” to “ennead.” Porphyry’s arrangement of the Enneads encrypts numerically the perfect unity of Plotinus’ universe, for which Ennead VI.6 provides the conceptual blueprint. (shrink)

The Middle Platonic tradition forms the main focus of these studies, many of which derive from Professor Whittaker's work on the writings of Alcinous (formerly attributed to Albinus) and their place and importance in that tradition. He follows the transmission of different texts, and the development of the commentaries upon them, from Classical times through the Byzantine world up to the Renaissance and beyond. Most of the articles, however, deal with the evolution of Platonic thought in the first centures A.D., (...) its interaction with other schools of thought, such as Neopythagoreanism, and the influence of Hellenistic philosphy upon the growth of Early Christian thought and theology. Additional notes and references have now been supplied. (shrink)

Ancient Greek Philosophy routinely relied upon concepts of number to explain the tangible order of the universe. Plotinus' contribution to this tradition, however, has been often omitted, if not ignored. The main reason for this, at first glance, is the Plotinus does not treat the subject of number in the Enneads as pervasively as the Neopythagoreans or even his own successors Lamblichus, Syrianus, and Proclus. Nevertheless, a close examination of the Enneads reveals that Plotinus systematically discusses number in relation to (...) each of his underlying principles of existence--the One, Intellect, and Soul. Plotinus on Number offers the first comprehensive analysis of Plotinus' concept of number, beginning with its origins in Plato and the Neopythagoreans and ending with its influence on Porphyry's arrangement of the Enneads. It's main argument is that Plotinus adapts Plato's and the Neopythagoreans' cosmology to place number in the foundation of the intelligible realm and in the construction of the universe. Through Plotinus' defense of Plato's Ideal Numbers from Aristotle's criticism, Svetla Slaveva-Griffin reveals the founder of Neoplatonism as the first post-Platonic philosopher who purposefully and systematically develops what we may call a theory of number, distinguishing between number in the intelligible realm and number in the quantitative, mathematical realm. Finally, the book draws attention to Plotinus' concept as a necesscary and fundamental linke between Platonic and late Neoplatonic schools of philosophy. (shrink)

The aim of this paper is to show that John Wyclif’s theory of space is at once an interpretation of the Platonic theory of place and a Neopythagorean conception of magnitudes and numbers. The result is an original form of mathematical atomism in which atoms are point-like entities with a particular situation in space. If the core of this view comes from Boethius’ De arithmetica, John Wyclif is also influenced by Robert Grosseteste’s metaphysics, which includes the Boethian number theory (...) within the Christian tale of the creation of the world ex nihilo. John Wyclif, however, adds some novelty to this theory concerning the epistemological status of this hypothetical description of the creation of the world out of atoms. First, according to Wyclif, whereas geometry is concerned with sensible and imaginable beings, arithmetic, which is purely intellectual, has access to the deep mathematical structure of the universe. He then suggests a subordination of geometry under arithmetic, which he considers the most solid basis for his metaphysics. As a result, with the attribution of numbers and units to every level of reality, it becomes possible to reform our natural imagination, so that it can imagine the atomic structure of matter and space. (shrink)

El presente trabajo se propone rastrear la influencia de la tradición platónica Acerca de los primeros principios, en sus diversas formulaciones, sobre la filosofía de Orígenes de Alejandría. La lectura origeniana de los autores platónicos y su afinidad con ellos se confirman en las fuentes históricas. El alejandrino adopta y asimila numerosos aspectos de la doctrina y la terminología de los seguidores de Platón. Sin embargo, también toma distancia de ellos en algunos puntos neurálgicos de su concepción de lo divino (...) y de la creación del mundo. Se analizan especialmente los papeles que cumplen en la teoría origeniana las categorías académicas de lo absoluto y lo relativo, la noción mesoplatónica y filoniana del agente demiúrgico y una original adaptación del esquema causal derivativo neopitagórico. -/- The present paper intends to trace the influence of the Platonic tradition On first principles;, considering its different versions, on the philosophy of Origen of Alexandria. Origen's knowledge of the Platonists and his affinity with them are confirmed by the historical sources. The Alexandrian adopts and assimilates many aspects of the doctrine and terminology of Plato's followers. However, he also departs from them regarding some of the essential elements in his conception of the divine and of the world's creation. Particularly, the paper focuses on the roles played in Origen's theory by the Academic categories of absolute and relative, the Middle-platonic and Philonian notion of the demiurgic agent and an original reframing of the Neopythagorean derivative system of causes. (shrink)

A general introduction by John Dillon, a Russian translation, annotations and indices by Eugene Afonasin. The first annotated Russian translation of the fragments by Neopythagorean philosopher Moderatus of Gades.

A general introduction by John Dillon. An annotated Russian translation of theIntroduction to Arithmetic and Manual of Harmonics by Neopythagorean philosopher Nicomachus of Gerasa, prepared by Andrej Schetnikov [Introduction], Timothy Myakin, and Ludmila Alexandrova [Manual]. These short treatises, important for the history of ancient mathematics and musical theory, is completely translated into Russian for the first time.

14o JOURNAL OF THE HISTORY OF PHILOSOPHY 34: X .JANUARY t996 method of reading the dialogues in an ascending order of philosophical importance need not be reflected completely or consistently in the tetralogical scheme. I pass over the account of Thrasyllus' logos-theory which Tarrant derives from an elusive section of Porphyry's commentary on Ptolemy's Harmonics in order to discuss the more important conclusions he draws in chapter 6, "The Neopythagorean Parmenides." By carefully sifting passages in Proclus' commentary on the (...) Parmenides and Simplicius' commentary on the Physics, Tarrant adds to our still incomplete picture of the development of a Neoplatonic ontology out of the hypotheses of Plato's Parmenides. E. R. Dodds made a brilliant case in this regard for Moderatus, the late first century A.D. Neopythagorean, but Tarrant finds even earlier evidence for it by ascrib- ing to Thrasyllus this quasi-Neoplatonic, fivefold ontology: transcendent One, one-being = the intelligibles, the third principle = the soul, physical particulars, matter. Epistle 2's "King of all" is drawn into Tarrant's net as an "esoteric" or symbolic emblem of the transcendent One. He argues plausibly that, since Thrasyllus was instrumental in getting this and other Epistles included in the standard edition of Platonic works, the connections he finds among the Parmenides, the Epistles, and pas- sages in the latter commentators are not facile and are worthy of.. (shrink)

This article proposes a reconstruction of the Sextan critique against the Pythagorean conception of number as principle of all existing things. Taking into consideration all the parallel passages concerning the presentation and the polemic about the Pythagorean doctrine, the present article proposes a division of the sceptical critique into two sections, the first one presenting the Pythagorean reasons to consider the numbers as principle existing apart from numbered things, and the second one presenting the arguments that Sextus himself built against (...) them. This paper will show that this structure is consistent with the sceptical method, which consists in pointing out the ἰσοσθένεια among different positions which leads to suspension of judgment. Regarding the Pythagorean doctrine that emerges from these passages, the present article discusses the way in which Sextus testified a juxtaposition between Pythagorean and Platonic doctrines, probably due to a Middle-Platonic or Neopythagorean elaboration, against which Sextus used Platonic concepts, adopting in original way arguments taken from the Parmenides and the Phaedo. Despite the ἐποχή about the nature of the number, this article will argue that Sextus did not avoid to use the number in practical daily life, in a way that is consistent with the sceptical practical criterion. (shrink)

In this project, I offer an extended treatment of Gabirol's metaphysical doctrine of universal hylomorphism . My thesis is that, for Gabirol , matter signifies the most sublime moment of the Neoplatonic Intellect, and, by extension, the pre-determinate, essential existence which each thing has in virtue of its subsistence in said Intellect. My reading thus identifies matter with a grade of pure Being. Drawing upon Latin, Hebrew and Arabic Fons Vitae materials, I develop and support this thesis in light of (...) three of Gabirol's most vexing remarks about matter, viz., that matter is 'per se existens,' descended directly from the First Essence, and like a Divine Throne. In the course of developing my thesis, I argue for strictly distinguishing between Gabirol's UH and other Augustinian forms of UH, for revising the accounts of Pines, Weisheipl, Brunner and Schlanger, for the relevance of Saadiah's Sefer Yez&dotbelow;irah commentary in a study of Gabirol, and for the conceptual identification of creation ex nihilo and emanation. I also provide the reader with a larger Neoplatonic context for considering the superiority of the material over the formal, as I additionally examine relevant notions of materiality in a variety of other textual traditions, including the writings of Plotinus, Proclus, and the Neopythagorean Nicomachus, as well as various Jewish and Islamic texts . ;I close with a 'meta' analysis of Gabirol's metaphysical project in which I suggest treating Gabirol's interest in universal hylomorphism---and any other bits of cosmo-ontology---in terms of said doctrine's ability to effect the reader's soul in certain ethically and epistemologically crucial ways. In this move, I suggest that the importance of Gabirol's philosophical metaphysics is not best gauged by considering what his metaphysical propositions denote, but instrumentally by considering the effect said propositions are intended to have on the reader. I develop this point by providing analyses of Neoplatonic dialectic, textual rhetoric, and the mechanics of imagination in Gabirol's Arabic Neoplatonic tradition. (shrink)

The concept of number is the troublemaker in the history of Platonism. It separated the followers of Plato and Aristotle into two camps for generations. For Plotinus, however, the concept becomes the peacemaker, which reconciles the camps. The importance of this reconciliation is central to Plotinus’ philosophical system because it not only uses Aristotle to defend Plato from Aristotle himself, but establishes Plotinus’ concept of number as the fundamental link between the number theories of the Neopythagoreans and the later Neoplatonists.This (...) book demonstrates that the subject of number should be considered among the most important concepts for understanding Plotinus’ philosophy and therefore deserves greater scholarly attention than it has received. Plotinus adopts and adapts Platonic and Neopythagorean cosmology to place number in the foundation of the intelligible realm and the construction of the universe. Throughout the Enneads and especially in Ennead VI.6, he systematically peels off the layers of mathematical and quantitative perception from the concept of number to reveal that real intelligible number is the primary activity of substance, which orders the unfolding of the universe from its absolute source into a finite multiplicity. (shrink)

This chapter traces the historical and philosophical background of the concept of number from the Presocratics’ understanding of One and Many through Plato’s concepts of Limit and Unlimited, and Aristotle’s debate on the nature of number with Speusippus and Xenocrates, to the Neopythagoreans and Plotinus. Next, it examines the main difficulties with the concept of number in Plotinus: the unsystematic presentation of the concept in the Enneads, the lack of scholarly interest, and the brevity of Plotinus’ treatment of the subject. (...) At the end, this examination focuses on the presentation of the concept in Ennead VI.6, the treatise On Numbers. From a bird’s-eye view, the subject of multiplicity begins and ends the thematic composition of the treatise. As multiplicity unfolds from the One and enfolds to the One, so does the composition of the treatise unfold and enfold in nesting circles, moving away from and yet turning toward their center. The concentric composition of VI.6 conveys non-discursively the higher ontological presence of number in the intelligible realm and iconically sketches the spherical figure of the universe. (shrink)

This chapter analyzes Plotinus’ refutation of the Aristotle’s criticism of Plato’s view of number in the Parmenides. By rejecting any quantitative value of number in the intelligible realm, Plotinus specifically focuses on Aristotle’s inability to understand the Monad and the Indefinite Dyad as the principles of creation and order of the intelligible. The chapter shows that Plotinus not only follows the steps of his Platonic and Neopythagorean predecessors in defence of Plato’s position, but cleverly uses Aristotle’s own ideas in (...) arguing that number in the intelligible is activity and a property of primary substance. The result is an original and ontologically elaborate theory of substantial number which offers a new and more successful defence of Plato’s “true numbers” against Aristotle’s criticism and explains the relationship between substantial non-quantitative number and monadic quantitative number as that between intelligible paradigm and its material copy. (shrink)

This article deals with the complex relation between providence and descent in Neoplatonism, with particular reference to Proclus and especially his Commentary on the First Alcibiades. At least according to this work, descent is only a species of providence, because there can be providence without any descent. Whereas the gods provide for our cosmos without descending to it, a large group of souls provide for our cosmos by descending to it. The former kind of providence is better than the latter, (...) even if it is necessary that souls descend in order to give existence to the beautiful cosmos. The following study deals with providence as descent, looking at it from two angles. In the first section I show that Proclus designates this form of providence in two rather surprising ways. One term he uses for it, which will be well known to readers of Plotinus, is τόλµα —this despite the word’s negative connotations due to its Neopythagorean and Gnostic origin. A second name for descended providence is ἐπιστροφή. Again, this may be surprising, since we usually expect this term to express the ‘turning back’ of a lower effect to its cause. In Proclus, the word ἐπιστροφή too can have negative connotations, but he also uses it in a positive way when applying it to providence. In the second part of the paper, I explain how Socrates’ providence for Alcibiades can be undefiled, even if Socrates necessarily descends as he offers providential guidance. Proclus’ comparison of Socrates with Hercules, who went to the Underworld in order to save Theseus, serves as a positive illustration of Socrates’ divinelike providence, and marks the deficiency of Socrates compared to the transcendent and undefiled providence of Neoplatonic divinities. (shrink)

Our purpose on the present occasion is to evaluate some ideas the biographers of late antiquity held about the origins of European thought. Speaking about this period we are no longer dealing with the question of transferring of the archaic practices: these practices are indeed long dead. What we encounter can be better defined as the import of ideas. Equally important is a study of the changing attitudes of our authors: rather than passive witnesses, they became active participants of this (...) import. The process is truly fascinating and we hope that the following examples, mostly from Hippolytus, will elucidate this. The best, almost a paradigmatic example is Pythagoras, who in late antiquity had many faces. His biography is an interesting instance of general change of attitude to ancient wisdom, typical for the source utilized by Hippolytus. Looking at a number of peculiar features of Hippolytus’ report which, we hope, will help us to see why the image of Pythagoras and his philosophy, formed by Hippolytus, is somewhat untypical for the period. We will see that Hippolytus’ biographic report, however garbled, shows no signs of so-called ‘Neopythagorean’ biographic development. Admittedly, the later authors frequently combine their sources to make them suitable to their needs, polemical or apologetic. Do we still have a reason to believe that these stories, however doubtful from the historical point of view, may contain the germs of truth? (shrink)

Romanticism fabricated a poet of vast oracular powers largely from superstitious notions and suspicious philosophies which the Renaissance had gathered up somewhat by chance with the rational part of the Graeco-Roman legacy. The model was surely an imposture and, historically considered, a scandal. Seer, sage, prophet, mage—the pretensions varied, but all were titles to transcendent disclosure in times increasingly committed, at least officially, to a unified scientific view. That the poet could be confirmed to any degree in this anachronistic role (...) was probably owing to the circumstance that the general cultural reflex following the Enlightenment reawakened widespread interest in those dark and excluded passages of the human spirit which mystics and seers were thought to frequent. Poets who pretended to voyance benefited from the muffled but persistent rumor of profound mysteries accessible to the high priests of Kabbala and the Corpus Hermeticum, to Illuminists, Rosicrucians, and Neopythagoreans. Western Europe had never ceased to acknowledge, even in such unlikely periods as the later Middle Ages, the aboriginal priestly and prophetic functions of the poet; but romanticism contrived—out of occultism and neoplatonism, antirationalism and anticlassicism—such a warrant for unabashed oracular saying as Antiquity had scarcely imagined. While perhaps none of the romantic was actually prepared to grant the poet his ancient powers in full measure, few seemed inclined to diminish the stature of the heroic abstraction, who symbolically contested the claims of naturalism and positivism. (shrink)

Pour parler de la chute ou de la déclinaison de l’Âme dans le cadre des récits cosmogoniques gnostiques, Plotin a recours, en sus du terme νεῦσις, au substantif σφάλμα, comme s’il s’agissait d’un synonyme de νεῦσις. L’enquête que nous avons menée montre le bien-fondé de cet usage, puisque le terme σφάλμα est, de fait, utilisé par les hérésiologues pour décrire, dans un langage hérité du néo-pythagorisme et donc rythmé par le nombre, la chute de Sophia, laquelle incarne le douzième éon (...) de la Dodécade en même temps que le trentième et dernier éon de l’ensemble du Plérôme. Rapporté à la métaphysique pythagoricienne dont il relève, le récit gnostique perd toute apparence d’arbitraire et révèle enfin sa véritable structure, commandée de bout en bout par le nombre. Il est raisonnable de penser que l’arithmologie rivale du traité 34 de Plotin est là pour y couper court. When speaking of the fall or decline of the Soul within the context of the Gnostic cosmogonic narratives, Plotinus, in addition to the term νεῦσις, resorts to the substantive σφάλμα, as if it were a synonym of νεῦσις. The following investigation demonstrates the validity of this usage, as the term σφάλμα is, in fact, used by the heresiologists to describe, in a language inherited from Neopythagoreanism, and therefore structured by number, the fall of Sophia, which embodies both the twelfth aeon of the Dodecade as well as the thirtieth and final aeon of the entire Pleroma. Related back to the Pythagorean metaphysics whence it is stems, the Gnostic narrative loses any appearance of arbitrariness and finally reveals its true structure, ordered from start to finish by number. It is reasonable to think that the rival arithmology of Plotinus’ Treatise 34 was created in order to undermine this very narrative. (shrink)

In chapters twenty and twenty-one of his Life of Plotinus Porphyry identifies Thrasyllus as the first of four Neopythagorean forerunners of Plotinus, the others being Moderatus, Cronius, and Numenius. That means that Thrasyllus was recognized by Porphyry as the earliest representative of one of the strands of the Plotinian philosophical synthesis. More widely--and Tarrant is concerned with the wider theme throughout his book--we must learn to recognize Thrasyllus as one of those to whom we must look if we are (...) to understand more of the shift in the last century B.C. and the first century of the Christian era from the empiricism and anti-transcendentalism of Hellenistic philosophy, with its predominantly epistemological emphases, to the restored theories of transcendentalist Platonism which dominated the final centuries of ancient thought. (shrink)

14o JOURNAL OF THE HISTORY OF PHILOSOPHY 34: X.JANUARY t996 method of reading the dialogues in an ascending order of philosophical importance need not be reflected completely or consistently in the tetralogical scheme. I pass over the account of Thrasyllus' logos-theory which Tarrant derives from an elusive section of Porphyry's commentary on Ptolemy's Harmonics in order to discuss the more important conclusions he draws in chapter 6, "The Neopythagorean Parmenides." By carefully sifting passages in Proclus' commentary on the Parmenides (...) and Simplicius' commentary on the Physics, Tarrant adds to our still incomplete picture of the development of a Neoplatonic ontology out of the hypotheses of Plato's Parmenides. E. R. Dodds made a brilliant case in this regard for Moderatus, the late first century A.D. Neopythagorean, but Tarrant finds even earlier evidence for it by ascrib- ing to Thrasyllus this quasi-Neoplatonic, fivefold ontology: transcendent One, one-being = the intelligibles, the third principle = the soul, physical particulars, matter. Epistle 2's "King of all" is drawn into Tarrant's net as an "esoteric" or symbolic emblem of the transcendent One. He argues plausibly that, since Thrasyllus was instrumental in getting this and other Epistles included in the standard edition of Platonic works, the connections he finds among the Parmenides, the Epistles, and pas- sages in the latter commentators are not facile and are worthy of... (shrink)

Dominic O'Meara has produced a scholarly and sympathetic account of a most enigmatic subject, namely, the role of mathematics in late Greek Platonic thought. O'Meara traces the path of mathematical philosophy from the Neopythagoreanism of the second and third centuries A.D. through that master of Athenian Neoplatonism, Proclus. Without this study few would recognize the paradigmatic role that mathematics played in Platonic thinkers throughout this period, for mathematics became the model for many forms of philosophical inquiry--not only theology and physics, (...) but even ethics. (shrink)

Historically, the fallacies have been neglected as objects of systematic study. Yet, since Hamblin's famous criticism of the state of fallacy theory, a substantial literature has been produced. A large portion of this literature is the work of Douglas Walton and John Woods. This paper will deal directly with the criticism of that work which has been advanced by van Eemeren and Grootendorst, particularly the complaints found in their writings of 1992, concerning the disunification of the fallacies and the exemplaristic (...) approach of Woods and Walton's theories. It proposes a unification of the theories of Woods and Walton with that of van Eemeren and Grootendorst, and suggests that such a unification could be advantageous to both theories, and highly interesting for fallacy theory in general. (shrink)