By scholarly consensus, extant fragments from, and testimony about, Aristotle’s lost dialogue Eudemus provide strong evidence for thinking that Aristotle at some point defended the human soul’s unqualified immortality (either in whole or in part). I reject this consensus and develop an alternative, deflationary, speculative, but textually supported proposal to explain why Aristotle might have written a dialogue featuring arguments for the soul’s unqualified immortality. Instead of defending unqualified immortality as a doctrine, I argue, the Eudemus was most (...) likely offering a dramatically engaging propaedeutic to the sort of philosophical inquiry about the soul and its prospects that Aristotle pursues more scientifically in the De anima and Parva naturalia. (shrink)

“Aristotle's successor as director of the Lyceum was Theophrastus, his friend and disciple; Eudemus, another of the Stagirite's important disciples should also be mentioned. Other philosophers belonging to the Peripatetic school were: Aristoxenus, Dikaiarchos, Phanias, Straton, Duris, Chamaeleon, Lycon, Hieronymus, Ariston, Critolaus, Phormio, Sotion, Hermippus, Satyrus and others. Straton even succeeded Theophrastus as director of the Lyceum but his name and those of the other Peripatetics of Aristotle's old school should not be considered in a history of logic as (...) they were mainly concerned with history and the natural sciences. Theophrastus rejoiced in an enormous prestige at this time and for long afterwards. Diogenes Laertius attributes a tremendous number of works to him. Of them a significant proportion are writings on logic: Analytica Priora (3 books); Analytica Posteriora (7 books); Analysis of Syllogisms (1 book); Summary of the Analytic s (1 book); Polemic on the Theory of Euristic Arguments. On Definition (1 book); The First Premises (18 books); The Sophisms (2 books); On the Solution of Syllogisms (1 book); Topics (2 books); On Artless Demonstrations (1 book); On Negation (1 book); On Intellect (1 book); Classifications (2 books); On Entymemes (1 book); On the Appreciation of Syllogism (1 book); On Lies and Truth (1 book); Argumentations (2 books); Theses (3 books); On Definition (2 books); On the Data of Problems (1 book); On the Liar (3 books); Preface to the Topics (1 book); On Arguments proper (1 book); Specifications on The Texts of Syllogisms (1 book). Eudemus also wrote some treatises on logic, concerning which some information has come down to us; Ammonius, in his Commentary On Aristotle's Categories attributes to him a writing on The Analytics -- 'Analitika', and another On Expressions -- Peri lexeos, in which he deals with the grammatical and logical functions of the sentence. The commentator David in Prolegomena to Isagoge by Porphiry also mentions these works.. (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)

In this paper, we examine a fundamental problem that appears in Greek philosophy: the paradoxes of self-reference of the type of “Third Man” that appears first in Plato’s 'Parmenides', and is further discussed in Aristotle and the Peripatetic commentators and Proclus. We show that the various versions are analysed using different language, reflecting different understandings by Plato and the Platonists, such as Proclus, on the one hand, and the Peripatetics (Aristotle, Alexander, Eudemus), on the other hand. We show that (...) the Peripatetic commentators do not focus on Plato’s solution but primarily on the formulation of the “Third Man” paradox. On the contrary, Proclus seems to be convinced that Plato suggests a sound solution to the paradox by defining the predicate of similarity (homogeneity) that demarcates two types of homogeneous entities – the eide and the participants in them in a way that their confusion would be inadmissible. We claim that Plato’s solution follows a sound line of reasoning that is formalisable in a language of Frege-Russell type; hence there exists a model in which Plato’s reasoning is valid. Furthermore, we notice that Plato’s definition of the second-order predicate of similarity is attained by resorting to first-order entities. In this sense, Plato’s definition is comparable to Eudoxus’ definition of ratio, which is also attained by resorting to first-order objects. Consequently, Plato seems to follow a logical practice established by the mathematicians of the 5th century, notably Eudoxus, in his solution to the paradox. (shrink)

ABSTRACT: This paper traces the evidence in Galen's Introduction to Logic (Institutio Logica) for a hypothetical syllogistic which predates Stoic propositional logic. It emerges that Galen is one of our main witnesses for such a theory, whose authors are most likely Theophrastus and Eudemus. A reconstruction of this theory is offered which - among other things - allows to solve some apparent textual difficulties in the Institutio Logica.

Aristotle and Eudemus report a Speusippean argument to the effect that defining anything requires knowing everything. Scholars have failed to make sense of this argument. This paper argues that the main preoccupations to which the Puzzle is meant to respond are: (i) to ensure the co-extensiveness of the definition with the definiendum; (ii) to rule out a particular definitional mistake—underdivision. The implications of the Puzzle for Speusippus’ conception of knowledge are further explored.

Zurvanism was an ancient variant of Zoroastrianism. According to Zurvanism, the great powers of good and evil, Ahura Mazda and Angra Mainyu, were the sons of a greater god Zurvan, associated with time. According to Eudemus of Rhodes, some Persian thinkers, presumably Zurvanists, took there to be three great principles underlying the world: light, darkness, and greatest of all time (or perhaps, according to Eudemus, space). This paper explores what metaphysics might underlie these doctrines, and what contemporary options (...) we have for making sense of a metaphysics where time is the ultimate principle. Among the options explored is the option that despite appearance many of the entities of the concrete world are identical to stretches of time, or are somehow aspects of stretches of time; that they include times as parts, or are included in times as parts; that they are somehow properties of time; or hylomorphic compounds of which time is the matter; that the world is somehow a mixture of time, light, and dark; or that somehow the ends or teloi of everyday objects and processes are to be found among good, evil, and time. (shrink)

This book deals with some Peripatetic philosophers of the Hellenistic age who were direct and indirect pupils of Aristotle. The main focus of the book is Aristotle's school in the Hellenistic period, a subject not particularly explored by the scholars. Three main issues are addressed in the chapters of the book: the problem of knowledge, the question of time, and the doctrine of the soul. More specifically the topics addressed are: the problem of sense-perception and the method of multiple explanations (...) in the field of meteorology in Aristotle, Theophrastus and Epicurus, the epistemology of Strato, the notion of time in Eudemus and Strato, the conception of sleep in Clearchus, the doctrine of divination in Cratippus. Finally, the Appendix examines the probable influence of the physics of Strato on the medicine of Asclepiades of Bithynia. These themes are investigated by comparing the positions of the Peripatetics with Aristotle's philosophy, but above all by contextualising the doctrines of the Peripatetics within the broader framework of Hellenistic philosophies. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:New Light from Arabic Sources on Galen and the Fourth Figure of the Syllogism NICHOLAS RESCHER The Problem of the Origin of the Fourth Figure FLYING IN THE FACE of the long-standing tradition--going back in Europe to Renaissance times--which credits Galen of Pergamon with the origination of the fourth syllogistic figure, recent authorities have almost to a man evinced doubt about Galen's claim to this innovation. Heinrieh Scholz speaks (...) of "the Galenian syllogistic figure which has been attributed to him, probably wrongly." i j. W. Stakelum concludes his careful discussion of the matter with the categorical assertion that "Galen did not teach the fourth figure." ~ I. M. Bochenski--following Lukasiewicz (see below)--says that the fourth figure "was only ascribed to Galen by a misunderstanding." : William Kneale (also following Lukasiewicz) writes that "it is easy to see how misunderstanding.., by some Arabian philosopher... could have given rise to the tradition that Galen added a fourth figure to Aristotle's syllogistic theory." 4 The currently received account of the matter is that of Jan Lukasiewicz who, in his book on Aristotle's Syllogistic (1951; 2d ed., 1957), presents the known reports about Galen and the fourth figure as follows (I list them in the order in which they came to light) : 1) Several passages in Averroes' (d. 1198) Middle Commentary on Prior Analytics credit Galen with introducing a fourth figure (ad Anal. Pr. I, 5; I, 8; I, 23). These passages, known in Europe through a Renaissance Latin translation of a Hebrew version, provided the basis upon which Zabarella in his work, De Quarta Syllogismorum Figura (in his Opera [Leiden: 1587], pp. 41-53), popularized the "Galenian figure" in European logic. 2) In 1844 Minoides Mynas published in the Preface to his edition of Galen's EisagSg~ dialektik~ an anonymous Greek fragment (late, perhaps 6th century) which states that certain "later scholars" transformed the indirect moods of the first figure added by Theophrastus and Eudeffms into a new fourth figure, citing Galen as the originator of this doctrine.~ 1Abriss der Geschichte der Logik (Miinster: 1931), trans, into English by K. F. Leidecker, ConciseHistory of Logic (NewYork: 1961);p. 38ofthe Englishversion. "Why 'Galenian' Figure?" The New Scholasticism, XVI (1942),289-296. s Formale Logik (Miinchen-Freiburg:1956; 2nd. ed., 1962), trans, into English by Ivo Thomas, A History of Formal Logic (Notre Dame: 1961);p. 142of the Englishversion. Williamand Martha Kneale, The Developmentof Logic (Oxford: 1962),p. 184. Alsoprinted in Karl Kalbfieisch, ~ber Galen s Einleitung in die Logik, 2~. Supplementband der Jahrbi~cherfi~r klassische Philologie (Leipzig:1897), p. 707. This datum casts some 28 HISTORY OF PHILOSOPHY 3) A Greek fragment was found around 1858 by Karl Prantl in a logical work of the Byzantine scholar Ioannes Italus (llth century) which says that Galen taught the existence of a fourth figure, adding sarcastically that he (Galen) thought thus to appear cleverer than the older logical commentators (presumably Theophrastus and Eudemus are intended), but fell far short.6 4) In 1899 Maximilian Wallies published7 an anonymous Greek scholium (of perhaps the 6th or the 7th century) on Ammonins' commentary on Prior Analytics which states that Galen "says in his Apodictic that there are four figures, because he looks at the compound syllogisms consisting of four terms (i.e., with three premisses )" rather than the simple (three-term, two-premiss) syllogisms of Aristotle. (The scholiast goes on to explain at some length how such compound syllogisms can be sorted into four groups.) It is readily seen that, given these data, two possibilities stand before us: a) Galen did actually invent the traditional fourth figure. Reports (1)-(3) are correct, and the anonymous scholiast of (4) was put on the wrong track by the fact that Galen also said that compound syllogisms of four terms can be classed into four groups. b) Galen did not invent the traditional fourth figure. Only after his time when once the indirect moods of the first figure had--somehow--become systematized into a separate "figure," was this credited to Galen by a mistake along the lines described by the anonymous scholiast. Thus (4) alone is right, and (1)-(3) are mistaken. Which of... (shrink)

Perhaps the strangest controversy in the history of logic is that over the fourth figure of the syllogism. There was never any argument as to what syllogisms are valid, but merely as to how they should be arranged. Aristotle had divided syllogisms into figures according to whether the middle term was subject of one premiss and predicate of the other, or predicate of both premisses, or subject of both. Theophrastus and Eudemus subdivided the first figure into those moods in (...) which the middle term was subject of the major premiss and those moods in which the middle was predicate of the major premiss. The latter moods were termed indirect. Galen said they constituted a separate figure; and so the controversy started. It has continued to the present with many writers objecting to the fourth figure, generally on grounds that it does not represent a genuine process of thought, and even ascribing this objection to Aristotle. The issue has been joined by writers who believe that it does represent a genuine process of thought. (shrink)

Volume 13 in the RUSCH series continues work already begun on the School of Aristotle. Volume 9 featured Demetrius of Phalerum, Volume 10, Dicaearchus of Messana, Volume 11, Eudemus of Rhodes, and Volume 12, both Lyco of Troas and Hieronymus of Rhodes. Now Volume 13 turns our attention to Aristo of Iulis on Ceos, who was active in the last quarter of the third century BCE. Almost certainly he was Lyco's successor as head of the Peripatetic School. In antiquity, (...) Aristo was confused with the like-named Stoic philosopher from Chios, so that several works were claimed for both philosophers. Among these disputed works, those with Peripatetic antecedents, like Exhortations and Erotic Dissertations, are plausibly assigned to Aristo of Ceos. Other works attributed to the Peripatetic are Lyco, On Old Age, and Relieving Arrogance. Whether part of the last-named work or a separate treatise, Aristo's descriptions of persons exhibiting inconsiderateness, self-will, and other unattractive traits relate closely to the Characters of Theophrastus. In addition, Aristo wrote biographies of Heraclitus, Socrates, and Epicurus. We may be sure that he did the same for the leaders of the Peripatos, whose wills he seems to have preserved within the biographies. The volume gives pride of place to Peter Stork's new edition of the fragments of Aristo of Ceos. The edition includes a translation on facing pages. There are also notes on the Greek and Latin texts and substantive notes that accompany the translation. This edition will replace that of Fritz Wehrli, which was made over half a century ago and published without translation. (shrink)

In the "Doxographi Graeci" the preferred short heading of Aët. 2.31 (Greek text below, p. 28) is 'On Distances', though ps.Plutarch has a long heading. This chapter is about the distances of the sun and moon from each other and from the earth (lemmas 1 to 3, in both ps.Plutarch and Stobaeus), and of the real or apparent shape of the heaven relative to its distance from the earth (lemmas 4 and 5, Stobaeus only). Parallels from Ioann. Lydus and Theodoret (...) for what is in ps.Plutarch are given by Diels in apparatu. To the best of my knowledge it has not been noticed that a version of ps.Plutarch's text is preserved in a scholium on the "Almagest", which constitutes our earliest evidence for the text. The correctness of Diels' reconstruction is questionable. Though certainty, naturally, is beyond our reach it is quite possible that these two sets of lemmas represent two distinct Aëtian (or proto-Aëtian) chapters. These may have been coalesced by Stobaeus (or Aëtius), while ps.Plutarch abridged the second (or the two final lemmas) away. These considerations necessitate an inquiry into the parallels that are available, including material from an introduction to Aratus. The vexing question of short versus long(er) chapter headings is also relevant in this context. Furthermore, the contrasting views regarding cosmic distances are not only a feature of the Placita literature with a distant origin in Aristotle, but also, apparently, of the commentary literature on Plato's "Timaeus". Arguably in a passage in Plutarch's "De facie" these two traditions intersect. Finally, a case can be made out for Eudemus not Theophrastus as an intermediary source of Presocratic astronomical data in the Placita. (shrink)

"This volume offers a new translation of the Neoplatonist philosopher Simplicius' commentary on the chapters concerning place and time in Aristotle's Physics, Book Four. Written after the closing of the Athenian Neoplatonist school in A.D. 529, the commentary clarifies the structure and meaning of Aristotle's arguments and provides a rich account of 800 years of interpretation." "Surprisingly, in the first five chapters of Book Four Aristotle shows place as two-dimensional: one's place is the two-dimensional inner surface of one's surroundings. He (...) also suggests that the upward motion of air and fire and the downward motion of earth and water are partly explained by the natural places to which they tend. Place thus has power (dunamis) of its own. In his last five chapters, Aristotle argues that if time did not entail change its passage would be undetectable, and that time, by definition countable, requires the existence of conscious beings to do the counting. Among the many relevant views that Simplicius records are those of Galen, who attacks this claim, and of Eudemus, who rebuts the Pythagorean theory that history will repeat itself exactly. J. O. Urmson's translation serves as a companion to his earlier translation of the Corollaries on Place and Time, in which Simplicius sets forth his own views as distinct from those of Aristotle." "A major sourcebook for the interpretation of Aristotle, this volume will be welcomed by scholars and students in the fields of classics, ancient philosophy, ancient history, and medieval studies."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved. (shrink)

El objetivo de este trabajo es discutir la interpretación tradicional según la cual los razonamientos de Zenón de Elea en contra de la multiplicidad constituyen una defensa de la tesis monista. Intentaré demostrar que las objeciones zenonianas a la multiplicidad suponen una critica previa a la existencia de "lo uno". Por este motivo, Zenón no es monista ni pluralista, sino, más bien, un crítico de las perspectivas metafísicas que consideran al ser en términos numéricos, i. e. como uno o como (...) múltiple. Para ello me concentraré en el análisis de la interpretación que Aristóteles desarrolla sobre la filosofía de Zenón, considerando algunos pasajes de Física, Refutaciones sofísticas y, fundamentalmente, Metafísica, III. 4. 1001b7-13. También incluiré algunos testimonios del comentario a la Física de Simplicio, en los que se discuten las interpretaciones de Eudemo de Rodas y Alejandro de Afrodisia, que ratifican el punto de vista aristotélico sobre la filosofía de Zenón. The aim of this paper is to discuss the traditional interpretation according to which the arguments of Zeno of Elea against multiplicity constitute a defense of monism. I will try to prove that Zeno's objections on plurality suppose a previous critique to the existence of the one. Therefore Zeno is neither a monist nor a pluralist but a philosopher who criticizes metaphysical theories that consider being in numerical terms, i. e. as many or as one. I will focus on the analysis of the interpretation of Zeno's philosophy developed by Aristotle. I will consider some passages from Physics, Sophistical Refutations and mainly Metaphysics III. 4. 1001b7-13. I will also include some testimonies from Simplicius' commentary on Aristotle's Physics, where he discusses the interpretations of Eudemus of Rhodes and Alexander of Aphrodisias that support the Aristotelian point of view on Zeno's philosophy. (shrink)

ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Content: 1. Pre-Aristotelian Logic 1.1 Syntax and Semantics 1.2 Argument Patterns and Valid Inference 2. Aristotle 2.1 Dialectics 2.2 Sub-sentential Classifications 2.3 Syntax and Semantics of Sentences 2.4 Non-modal Syllogistic 2.5 Modal Logic 3. The early Peripatetics: Theophrastus and Eudemus 3.1 Improvements and Modifications of Aristotle's Logic 3.2 Prosleptic Syllogisms 3.3 (...) Forerunners of Modus Ponens and Modus Tollens 3.4 Wholly Hypothetical Syllogisms 4. Diodorus Cronus and Philo the Logician 5. The Stoics 5.1 Logical Achievements Besides Propositional Logic 5.2 Syntax and Semantics of Complex Propositions 5.3 Arguments 5.4 Stoic Syllogistic 5.5 Logical Paradoxes 6. Epicurus and the Epicureans 7. Later Antiquity. (shrink)

In Plato’s Parmenides 132a-133b, the widely known Third Man Paradox is stated, which has special interest for the history of logical reasoning. It is important for philosophers because it is often thought to be a devastating argument to Plato’s theory of Forms. Some philosophers have even viewed Aristotle’s theory of predication and the categories as inspired by reflection on it [Owen 1966]. For the historians of logic it is attractive, because of the phenomenon of self-reference that involves. Bocheński denies any (...) possibility of correct logical reasoning before Aristotle. In particular, he flatly declares of Plato that “correct logic we find none in his work” [1951, 15]. In this line, many papers have been written that call attention to the violation of a metalogical principle – the type rules – because of the Third Man Paradox. The problem of interpretation of the paradox raised many discussions, since the 50’s, and the literature devoted to this topic is today enormous. Nevertheless, many points in Plato’s reasoning remain obscure. Hitherto, it is commonly believed that the paradox was simply stated by Plato in his "Parmenides", but not actually solved. Even more, it is believed that it is hardly possible for Plato to have suggested a solution, because he confused the categories of substance and attribute. B. Russell has also argued that Plato violates in his arguments the restrictions imposed on language by the theory of logical types. This view is encouraged by the linguistic difficulties, which Plato has faced in his attempt to formulate an ontology of abstract entities, i.e. that in Greek language abstract and concrete terms are formally indistinguishable [Kneales 1984]. In this paper, we analyse the logical structure of the argument in an attempt to give a systematic consistent reconstruction of the text appealing to methods and concepts of modern logic and semantics. Already in 1954 G. Vlastos had noted in his seminal paper “The ‘Third Man’ Argument in the Parmenides” that “if any progress … is to be made at this juncture it must come from some advance in understanding the logical structure of the Argument”. Accordingly, our analysis is primarily focused on the line of logical reasoning, rather than the metaphysical underpinnings and philosophical implications of the paradox for Plato’s theory of Forms. We divide the Platonic text into three parts, presenting apparent thematic coherence: a) Formulation of the Third Man Paradox (132a-132b). The central issue of this part is a step-like generation of Forms that can continue ad infinitum. b) Discussion of the paradoxical situation (132b-c), by passing to the use of terminology echoing Eleatic philosophy. The concept of “thought” and the underlying semantics of Eleatic origin are central in this passage. c) Solution of the paradox (132d-133a). In our view, this part contains not only a resemblance regress, as most interpretators con-sider, but also the solution of the paradox by the introduction of a sound definition of the concept of “similarity”. We should note that the name ‘Third Man Paradox’ never occurs in Plato, who, strictly speaking, formulates a ‘Third Large Paradox’. The name ‘Third Man Paradox’ appears in the works of Aristotle and the commentators of the Peripatetic tradition. Later commentators have identified Aristotle’s Third Man with Plato’s Third Large Argument. In our paper, we also examine other testimonies about the Third Man Paradox found in the works of commentators in order to illuminate the logical structure of the argument. Although the vocabulary used in these versions is different, they do not affect its logical structure, but rather reveal different understandings by the ancient authors. These testimonies are divided into two main categories: those met in Neo-Platonic authors, notably in Proclus’ "Commentary on Plato’s Parmenides", and the versions of the Third Man Paradox found in texts of the Peripatetic tradition (Eudemus, Aristotle, Alexander). From our discussion, it becomes clear that the approaches to the paradox by the various scholars of antiquity are different, depending also on their participation in the one or the other campus of philosophical thought. We show that the Peripatetic authors are aware of the source of the paradox. However, the first scholar of antiquity who explicitly ascribes a solution to Plato seems to be Proclus. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Two Sonnets DANIEL GALEF Thales to Thratta (spoken by “The Astrologer Who Fell into a Well”) All things are full of spirits. So said I, who plumbed the well of science, saw the sun made black and tracked its course across the sky, who, armed with muscle, wrote the river’s run. Where is my spirit? Thratta! I feel cold and wet. This well is deep. The world is wet (...) and cold. The world I knew was filled with gold and fire.... How quick the Olympic sun has set, how quick my words rewritten, and my land made palimpsest. The sea has left Miletus, the shore on which I walked and lectured—and the wise men who walked with me, whom I taught. The boundless sea, whose tides once rose to meet us has changed its shape, moved on. But I cannot. arion 27.2 fall 2019 Eudemus to Apollonius (spoken by the dedicatee of Apollonius of Perga’s first books of the Conic Sections) I write this note in the sand because I know the waves will wash it clean, and you won’t see it. Like the circles we traced here so long ago, our footprints fade from Pergamum. So be it. Your book was well-received. As was your son; his seems the echo of your dimming face. How did my thoughts, which like an hour-glass run, once hold the eternal laws of boundless space? The beach bends on forever. How might a man reckon every mote, each grit and grain? The universe of truths seems greater than could ever fit within the human brain— Yet love, which binds over such a greater span, all mortals its completeness can contain. 104 two sonnets... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Aristotle on the Etruscan Robbers:A Core Text of "Aristotelian Dualism"Abraham P. Bos (bio)1. A Non-Platonic Dualism in Aristotle's Lost WorksThe Soul of a Mortal on Earth is not "At Home," says Aristotle in his dialogue Eudemus. The story about the mantic dream of the expatriate Eudemus and his expectation that he "will return home"1 is well known. It makes clear that, in Aristotle's view, the death of (...) the human individual should be interpreted as the soul's "return to its homeland."2 This is strongly suggested by "the revelation of Silenus" which Plutarch (first century CE) passes down in a literal quotation from the Eudemus.3 It contains the theme of human life on earth as a punishment (timôria). The motif of human life as a punishment is central to two texts by Iamblichus (250-325 CE) and Augustine (354-430 CE), which are usually connected with Aristotle's Protrepticus.4 I want to examine these texts in more detail here. My intention in the following exposition is to propose a non-Platonistic explanation of these texts. In my opinion they have wrongly been read as testimonies of a "Platonistic" phase in Aristotle. The existence of such a phase in Aristotle's development has never been proved. Besides, the interpretation of these texts suffered from the fact that [End Page 289] Aristotle's De anima had also been explained in an unhistorical way since Alexander of Aphrodisias in the third century CE.2. Revising the Modern View of AristotleWe have to make a different assessment of Aristotle's contribution to the discussion on the soul compared with what was current until recently. For after W. Jaeger5 and F. Nuyens6, modern scholars became inclined to leave Aristotle's dialogues out of consideration, because they regarded them as "Platonizing." But a fundamental correction is necessary on this point.7 Jaeger led modern Aristotle studies in a wrong direction by assuming a sharp distinction between Aristotle's lost dialogue Eudemus and his surviving treatise De anima. Although nowadays Jaeger's theory for many scholars is something of a dead horse, nevertheless a real alternative has not been proposed. We still have to get rid of the consequences of the Jaegerian paradigm and develop a unitary interpretation of Aristotle's entire oeuvre. Even more consistently than O. Gigon has already done,8 we should assume that Aristotle's lost works and his surviving biological writings and De anima did not propose two (or more) different psychological theories but one and the same. Because this one Aristotelian psychology was a non-Platonistic but nevertheless dualistic psychology, we have much more reason than could be recognized in the past to assume Aristotelian influence on this discussion.On one essential issue Aristotle disagreed with his teacher Plato: the soul,9 more particularly the indissoluble bond of the soul with a body. Aristotle radically and [End Page 290] consistently argued for the distinction between nous and psychè.10 For Aristotle the nous-in-act is always wholly incorporeal. But he considered it characteristic of the soul that it cannot carry out its functions "without body."11However, the crucial question is: what body does Aristotle mean when he says that the soul cannot perform its specific activities "without body"? Jaeger and Nuyens were wholly convinced that Aristotle was referring to the visible, external body of a human being, animal, or plant. Hence they saw a yawning gap between Aristotle's views in De anima and his position in the dialogue the Eudemus. In the Eudemus Aristotle had clearly argued that the soul can perform its own functions very well, indeed better, without the galling and oppressive visible body.12 But in De anima II 1, in his famous definition of "the soul," Aristotle says that the soul is inextricably bound up with a "sôma physikon organikon."13 Jaeger and Nuyens, following an almost unanimous tradition since Alexander of Aphrodisias in the third century CE, interpreted this sentence in the sense that the soul is the formal principle or entelechy of an "organic body" or a "natural body equipped with organs," i.e., the visible body... (shrink)

The philosophical practices undertaken in Plato's Academy remain, in the words of Cherniss, a 'riddle'. Yet surviving accounts of the views of the first two scholarchs of Plato's Academy after his death, Speusippus and Xenocrates, reveal a sophisticated engagement with their teacher's ideas concerning the pursuit of knowledge and the ends of philosophy. Speusippus and Xenocrates transform Plato's views on epistemology and happiness, and thereby help to lay the groundwork for the transformation of philosophy in the Hellenistic era.

This book treats so‐called Greek mathematics, developed in the Greek‐speaking world between about 600 b.c. and 600 a.d. It consists of four parts: early Greek mathematics, Hellenistic mathematics, Graeco‐Roman mathematics, and late ancient mathematics. Each part is divided into two chapters, “The Evidence” and “The Questions.”This separation of evidence and questions is significant. Serafina Cuomo has refused to follow the familiar method of weaving an apparently seamless history of Greek mathematics out of fragmentary and heterogeneous documents and conjectures about them. (...) The chapters of questions, where she points to issues that remain open, are very suggestive. For example, most important documents about the early development of Greek mathematics derive from a single lost work, the History of Geometry by Eudemus. Cuomo dares to cast doubt on its authenticity. Though her reservations seem extreme, we should remember that no document is neutral: Eudemus's history is a compilation, which involved choices, and the fragments we have now are the result of selection, partly intentional, partly by chance.Another merit of this book is that it considers a wide range of activity as mathematics. Practical mathematics—such as land surveying and accounting, with their sociopolitical importance—is emphasized.Cuomo's chief claim is that the standard historiography that associates the development of Greek mathematics with Plato's philosophy is only the version promulgated by Proclus; other descriptions are also possible. In fact, Pappus, Iamblichus, and others had their own versions. This claim is reasonable and contributes to a better understanding of Greek mathematics and the authors of late antiquity.In her citations, the author tries to let the text speak for itself, allowing as much as a full page to a passage or a proposition, and she refrains from using modern symbolism to explain mathematical content. Though this attitude is admirable, its cost is not negligible. Readers expecting to acquire a basic knowledge of Greek mathematics may find themselves at a loss when faced with highly technical propositions presented without elucidation.What this compact book does not include should also be mentioned. In contrast to her enthusiasm for the social and political dimensions of ancient mathematics, the author seems somewhat indifferent to its technical and theoretical aspects. Archimedes and Apollonius command only 16 pages—less than 7 percent of the text—whereas T. L. Heath dedicated 150 pages of his 1,000‐page history to them . Though documents showing the importance of land surveying are frequently quoted, little is said about the practice and the technical development of this art. The technical details of Ptolemy's works are practically dismissed—but should he not have an especially important role in alternative versions of the history of ancient mathematics because of his ingenious reconciliation of rigorous theory and the limitations imposed by reality in fields like astronomy and geography?The scantiness of the technical ingredients makes Ancient Mathematics more a history of discourses about mathematics than a history of mathematics—though this is to some extent inevitable given the character of late ancient mathematics, as Cuomo correctly emphasizes. The plan of the series to which this book belongs may be too modest to accommodate the author's ambition. Another problem attributable to the publisher is that the notes appear at the end of each chapter, so checking the references is annoying. Short references could be put in parentheses, and footnotes would be more convenient for longer notes. (shrink)