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Bookends and reading rests Reading Accessories Bookmarks. On Aristoxenus as a source for Pythagoreanism see most recently Zhmud b and Huffman b, — There are also analyses of concepts important in ethics, such as desire and luck.
Aristotle, Plato and Pythagoreanism in the First Century BC
They might be expected to partially embody the views of his teacher Xenophilus. The standard scholarly view of this work, however, is that Aristoxenus plundered Platonic and Aristotelian ideas for the glory of the Pythagoreans Wehrli , 58 ff. There are serious difficulties with the standard view, however Huffman While the Precepts do have similarities to passages in Plato and Aristotle, they are at a very high level of generality and are shared with passages in other fifth and fourth century authors, such as Xenophon and Thucydides; it is the distinctively Platonic and Aristotelian features that are missing.
The Precepts are thus best regarded as what they appear on the surface to be, an account of Pythagorean ethics of the fourth century. The central outlook of the Precepts is a distrust of basic human nature and an emphasis on the necessity for supervision of all aspects of human life Fr. The emphasis on order in life is so marked that the status quo is preferred to what is right Fr. The Pythagoreans were particularly suspicious of bodily desire and analyzed the ways in which it could lead people astray Fr. There are strict limitations on sexual desire and the propagation of children Fr.
Despite the best efforts of humanity, however, many things are outside of human control, so the Pythagoreans examined the impact of luck on human life Fr. Aristoxenus is a source for the famous story of the two Pythagorean friends Damon and Phintias, which was set during the tyranny of Dionysius II in Syracuse — As a test of their friendship Dionysius falsely accused Phintias of plotting against him and sentenced him to death. Phintias asked time to set his affairs in order, and Dionysius was amazed when Damon took his place, while he did so. Phintias showed his equal devotion to his friend by showing up on time for his execution.
Dionysius cancelled the execution and asked to become a partner in their friendship but was refused Iamblichus, VP ; Porphyry, VP 59—60; Diodorus X 4. There are two other considerations. First, Aristoxenus cites Dionysius II himself as his source, whereas it is unclear what source Diodorus used. Second, it is far from clear that Aristoxenus would object to the Pythagoreans plotting against a tyrant.
Cleinias and Prorus are another pair of Pythagorean friends, whose story may have been told by Aristoxenus Iamblichus, VP , although they were not friends in the usual sense. Cleinias, who was from Tarentum, knew nothing of Prorus of Cyrene other than that he was a Pythagorean, who had lost his fortune in political turmoil. Nothing else is known of Prorus, although some pseudepigrapha were forged in his name Thesleff , It appears that Cleinias was a contemporary of Plato, since Aristoxenus reports that he and an otherwise unknown Pythagorean, Amyclas, persuaded Plato not to burn the books of Democritus, on the grounds that it would do no good, since they were already widely known Diogenes Laertius IX Cleinias was involved in several other anecdotes.
Like Archytas he supposedly refused to punish when angry VP and, when angered, calmed himself by playing the lyre Athenaeus XIV a. None of the Pythagoreans mentioned in the previous four paragraphs appear to have to have anything to do with the sciences or natural philosophy.
Since their Pythagoreanism consists exclusively in their way of life, they are best regarded as examples of the acusmatici. Many scholars have regarded Diodorus of Aspendus in Pamphylia southern Asia Minor , as an important example of what the Pythagorean acusmatici were like in the first half of the fourth century Burkert a, — Diodorus is primarily known through a group of citations preserved by Athenaeus IV c-f , which describe him as a vegetarian who was outfitted in an outlandish way, some features of which later became characteristic of the Cynics, e.
Diogenes Laertius VI Iamblichus, the other major source for Diodorus outside Athenaeus, also treats Diodorus with reserve, saying that he was accepted by the leader of the Pythagorean school at the time, one Aresas, because there were so few members of the school. He continues, perhaps again with disapproval, to report that Diodorus returned to Greece and spread abroad the Pythagorean oral teachings.
These sources clearly suggest that Diodorus was anything but a typical Pythagorean, even of the acusmatic variety. In support of this conclusion, he argues that the two earliest sources present Diodorus as a Pythagorean without any qualifications a, It is important to look carefully at those sources, however.
First, neither is a philosopher or a historian, who might be expected to give a careful presentation of Diodorus. The oldest is a lyre player named Stratonicus died BCE , who was famous for his witticisms, and the other, Archestratus fl. Such sources might be expected to accept typical stories that went around about Diodorus without any close analysis. In the case of our earliest source, Stratonicus, there is, moreover, once again evidence suggesting that Diodorus was not regarded as a typical Pythagorean.
Thus, rather than accusing the sources of bias against Diodorus, it seems better to accept their almost universal testimony that he was not a typical acusmatic but rather a marginal figure, who used Pythagoreanism in part to try to gain respectability for his own eccentric lifestyle. Pythagorizers, are ridiculed by writers of Greek comedy, such as Alexis, Antiphanes, Aristophon, and Cratinus the younger, in the middle and second half of the fourth century see Burkert a, , n. A number of these characteristics can be connected to the acusmata Arnott , , e. Epicharides and some other named figures may well be Athenians who are satirized by being assigned a Pythagorean life Athenaeus , Both Alexis Fr.
Given the fragmentary nature of the evidence, it is unclear whether these ascetic Pythagoreans who engage in argument are the same as the Pythagorists in the other comedies, who are characterized by their filth and eccentric appearance. Certainly the latter are more reminiscent of Diodorus of Aspendus, while the former might be closer to what we know of someone like Cleinias. The scholiast to the passage testifies to the continuing controversy about the Pythagorists by drawing a distinction between Pythagoreans who give every attention to their body and Pythagorists who are filthy although another scholion reports that others say the opposite, see Arnott , A passage in Iamblichus VP 80 similarly argues that the Pythagoreans were the true followers of Pythagoras, while the Pythagorists just emulated them.
In recent scholarship, the tendency has been to regard Diodorus and the Pythagorists as legitimate Pythagoreans of the acusmatic stamp, whose eccentricities are perhaps a little exaggerated in comedy. Many religious movements have a radical fringe, and there is little reason to think that Pythagoreanism should differ in this regard. In connection with his thesis that the acusmata were a literary phenomenon and that no one lived a life in accordance with them Zhmud argues that the Pythagorists of comedy are a creation of the comic stage and do not provide evidence for Pythagoreans living a life governed by acusmata Zhmud a, — It is true that many of the features of the Pythagorists are shared with Socrates as presented in the Clouds subtle arguments, plain food, filthy clothes.
Zhmud suggests that vegetarianism was added to this stock picture of the philosopher to give a Pythagorean color and that this vegetarianism was derived solely from the eccentric figure of Diodorus of Aspendus. However, as noted above there are more connections to the acusmata than just vegetarianism and it is hard to believe that the repeated jokes at the expense of those living a Pythagorean life had no correlate in reality other than Diodorus.
Perhaps the best way to evaluate the complicated evidence for fourth-century Pythagoreanism is to conclude that there were three main groups, each of which admitted some variation. They may have observed some mild dietary restrictions and may be similar to the figures satirized in The Men of Tarentum as eating a simple diet but still engaged in subtle arguments. There was probably a continuum of people in this category with some following more or different sets of the acusmata than others. Finally there are the Pythagorean hippies such as Diodorus and the Pythagorists, who ostentatiously live a life in accord with some of the acusmata , but who take such an extreme interpretation of them as to be regarded as eccentrics by most Pythagoreans.
These Pythagoreans are further identified as the pupils of Philolaus and Eurytus. Little more is known of Xenophilus beyond his living for more than years DK I — They are also shown to be pupils of Socrates, however, and it is unclear that their connection to Philolaus was any closer than their connection to Socrates. Echecrates might have been born around and thus be a young man at the dramatic date of the Phaedo.
This seems slender evidence upon which to be so critical of Aristoxenus. Virtually nothing is known of Lycon, and Aristocles 1st-2nd c. This would be compatible with a few individuals still claiming to be Pythagoreans after This is not inconsistent with the existence of a few isolated individuals, who still claim to be Pythagoreans.
Iamblichus In Nic. Kahn , 83 sees a hint of Pythagorean cult activity in the spurious Pythagorean Memoirs , which must date sometime before the first half of the first century BCE, when they are quoted by Alexander Polyhistor see section 4. A few other Pythagorean pseudepigrapha appear in the period see further below, sect.
Pythagoreanism is not completely dead between and see further below, sect. The names Timaeus of Locri and Ocellus of Lucania are famous as the authors of the two most influential Pythagorean pseudepigrapha see below, sect. In his catalogue of Pythagoreans, Iamblichus lists an Ocellus under Lucania and two men named Timaeus, neither under Locri. Some scholars have argued that Hicetas and Ecphantus, both of Syracuse, were not historical figures at all but rather characters in dialogues written by Heraclides of Pontus, a fourth-century member of the Academy. By a misunderstanding, they came to be treated as historical Pythagoreans in the doxographical tradition see Guthrie , ff.
This theory arose because both Hicetas and Ecphantus are said to have made the earth rotate on its axis, while the heavens remained fixed, in order to explain astronomical phenomena, and, in one report, Heraclides is paired with Ecphantus as having adopted this view Aetius III In addition Ecphantus is assigned a form of atomism DK I Theophrastus did accept the Academic glorification of Pythagoras see on Neopythagoreanism below, sect.
The testimonia for Hicetas are meager and contradictory DK I — He may also have followed Philolaus in positing a counter-earth, opposite the earth on the other side of a central fire, although, if he did, it is unclear how he would have explained why it and the central fire are not visible from the rotating earth.
A little more is known about Ecphantus DK I He too is said to have believed that the earth moved, not by changing its location as Philolaus proposed, in making the earth and counter-earth revolve around the central fire: see Section 4. Copernicus was inspired by these testimonia about Hicetas and Ecphantus, as well as those about Philolaus, to consider the motion of the earth see below, sect.
Ecphantus developed his own original form of atomism. He is best understood as reacting to and developing the views of Democritus. Democritus Frs. He differs from Democritus, however, in supposing that atoms are limited rather than unlimited in number and that there is just one cosmos rather than many.
As in Democritus, atoms differ in shape and size, but Ecphantus adds power dynamis as a third distinguishing factor. It is because of this divine power that the cosmos is spherical in shape. One testimony says that he was the first to make Pythagorean monads corporeal, thus differing from the fifth-century Pythagoreans described by Aristotle, who do not seem to have addressed the question of whether numbers were physical entities or not. It is difficult to be sure of the date of either Hicetas or Ecphantus.
There is an Ecphantus in the catalogue, but he is listed under Croton rather than Syracuse, so it cannot be certain whether he is the Ecphantus described in the doxography. There is currently a very wide range of opinions about the relationship of Plato to Pythagoreanism. Many scholars both ancient and modern have thought that Plato was very closely tied to Pythagoreanism.
He is the pupil of Archytas and the ninth successor to Pythagoras himself. If this were true then Plato would certainly be the most illustrious early Pythagorean after Pythagoras himself. Some modern scholars, while not going this far, have seen the connections between Plato and the Pythagoreans to be very close indeed. Thus, A. Guthrie in his famous history of ancient philosophy commented that Pythagorean and Platonic philosophy were so close that it is difficult to separate them , Recently it has been argued that Plato was so steeped in Pythagoreanism that he structured his dialogues by counting numbers of lines and placing important passages at points in the dialogue that correspond to important ratios in Pythagorean harmonic theory Kennedy, and There are, however, serious questions about the methodology used Gregory and it is a serious problem both that no one in the ancient world reports that Plato used such a practice and that the middle of the dialogue, which corresponds to the most concordant musical interval, the octave , does not usually contain the most philosophically important content.
Another approach sees Plato as engaged with and heavily influenced by Pythagorean ideas in passages where the Pythagoreans are not specifically mentioned in dialogues such as the Cratylus bd7 and Phaedo b10—c9 Horky The problem is that in contrast to the Philebus , where the connection to Philolaus is clear see below , the connections to the Pythagoreans in these passages are too indirect or general e.
In contrast to these attempts to connect Plato closely to Pythagoreanism, most recent Platonic scholars seem to think Pythagoreanism of little importance for Plato. In recent studies of the topic that lie somewhere between these extremes, one approach is to argue that there is clear Pythagorean influence on Plato but that its scope is much more limited than often assumed Huffman Plato explicitly mentions Pythagoras and the Pythagoreans only one time each in the dialogues and this provides prima facie evidence that Pythagorean influence was not extensive. It is often assumed that Plato owes his mathematical conception of the cosmos and his belief in the immortality and transmigration of the soul to Pythagoreanism Kahn , 3—4.
However, the role of Pythagoreanism in Greek mathematics has been overstated and while Plato had contacts with mathematicians who were Pythagoreans like Archytas, the most prominent mathematicians in the dialogues, Theodorus and Theaetetus, are not Pythagoreans. It is thus a serious mistake to assume that any mention of mathematics in Plato suggests Pythagorean influence.
The same is true of the immortality and transmigration of the soul in Plato, which are often assumed to be derived from Pythagoreanism. Some have also thought that Platonic myths and especially the myth at the end of the Phaedo draw heavily on Pythagoreanism Kingsley , 79— However, most of the contexts in which Plato mentions the immortality of the soul including the Platonic myths, suggest that he is thinking of mystery cults and the Orphics rather than the Pythagoreans Huffman , — On the other hand, in the Philebus 16ca Plato gives clear acknowledgement of the debt he owes to men before his time who posit limit and unlimited as basic principles.
However, most of the Timaeus is not derived from Pythagoreanism and some of it in fact conflicits with Pythagoreanism e. The same is true for Plato as a whole. Already in the Gorgias Plato argues that principles of order and correctness which are found in the cosmos and explain its goodness also govern human relations. Socrates here puts forth a much more definite conception of the good than in earlier dialogues.
His complaint that Callicles pays no attention to the role played by orderliness and self-control and neglects geometrical equality e6—a8 mirrors the emphasis on organization and calculation in contemporary Pythagorean texts such as Archytas Fr. Plato never abandons this Pythagorean conception of value and it can be traced through the Phaedo and Republic to late dialogues such as the Timaeus , where the cosmos is embued with principles of mathematical order, and Philebus , where the highest value is assigned to measure 66a.
The question is whether this emphasis on measure and order is uniquely Pythagorean in origin. Neopythagoreanism is characterized by the tendency to see Pythagoras as the central and original figure in the development of Greek philosophy, to whom, according to some authors e. Iamblichus, VP 1 , a divine revelation had been given. This revelation was often seen as having close affinities to the wisdom of earlier non-Greeks such as the Hebrews, the Magi and the Egyptians.
Because of the belief in the centrality of the philosophy of Pythagoras, later philosophy was regarded as simply an elaboration of the revelation expounded by Pythagoras; it thus became the fashion to father the views of later philosophers, particularly Plato, back onto Pythagoras. Neopythagoreans typically emphasize the role of number in the cosmos and treat the One and Indefinite Dyad as ultimate principles going back to Pythagoras, although these principles in fact originate with Plato. After a decline in interest in Pythagoreanism for a couple of centuries, Neopythagoreanism emerged again and developed further starting in the first century BCE and extending throughout the rest of antiquity and into the middle ages and Renaissance.
During this entire period, it is the Neopythagorean construct of Pythagoras that dominates, a construct that has only limited contact with early Pythagoreanism; there is little interest in an historically accurate presentation of Pythagoras and his philosophy. In reading the following account of Neopythagoreanism, it may be helpful to refer to the Chronological Chart of Sources for Pythagoras , in the entry on Pythagoras. Some scholars reject this widely held view on the grounds that this fragment of Speusippus is spurious Zhmud a, —, who cites other scholars; Taran , ff.
Speusippus also wrote a book On Pythagorean Numbers Fr. We cannot be sure, however, either that the title goes back to Speusippus or that he assigned all ideas in it to the Pythagoreans. Aristotle twice cites agreement between Speusippus and the Pythagoreans Metaph. The evidence is not sufficient to conclude that Speusippus routinely assigned Platonic and Academic ideas to the Pythagoreans Taran , , but there is enough evidence to suggest that he did so in some cases.
He wrote a book entitled Things Pythagorean , the contents of which are unfortunately unknown Diogenes Laertius IV Several doctrines of Xenocrates are also assigned to Pythagoras in the doxographical tradition, e.https://senjouin-kikishiro.com/images/kodijen/2217.php
This suggests that Xenocrates, like Speusippus, may have assigned his own teachings back to Pythagoras or at least treated Pythagoras as his precursor in such as way that it was easy for others to do so Burkert a, 64—65; Dillon , —; Zhmud [a, 55 and —] disputes this interpretation. Yet another member of the early Academy, Heraclides of Pontus Gottschalk , in a series of influential dialogues, further developed the presentation of Pythagoras as the founder of philosophy.
Although some scholars have tried to find a kernel of truth in the story e. In the surveys of his predecessors in his extant works, Aristotle does not include Pythagoras himself and he evidently presented him in his lost special treatises on the Pythagoreans only as a wonder-worker and founder of a way of life. Eudemus assigns the Pythagoreans a number of important contributions to the sciences but does not give them the decisive or foundational role found in the Neopythagorean tradition. Neither assign to Pythagoras or the Pythagoreans the characteristics of Neopythagoreanism.
Aristoxenus is one of the most important and extensive sources for Pythagoreanism see 3. He presents Pythagoras and the Pythagoreans in a positive manner but avoids the hagiography and extravagant claims of the later Neopythagorean tradition. The standard view is that he tries to emphasize the rational as opposed to the religious side of Pythagoras e. He is supposed to have presented Pythagoras as the model of the practical life as opposed to the contemplative life Jaeger , ; Kahn , Thus, Aristoxenus and Dicaearchus were as divided in their interpretation of Pythagoras as were Heraclitus and Empedocles in earlier centuries.
The Peripatetic tradition as a whole is in strong contrast, then, with the Academy insofar as it emphasizes Pythagoreans rather than Pythagoras himself. When Pythagoras is mentioned, it is mostly in connection with the way of life, and interpretations range from positive to strongly satirical but in either case avoid the hagiography of the Neopythagorean tradition.
The standard view has thus been that the Academy was the origin of Neopythagoreanism with its glorification of Pythagoras and its tendency to assign mature Platonic views back to Pythagoras and the Pythagoreans. Aristotle and the Peripatetics on the other hand diminish the role of Pythagoras himself and, while noting connections between Plato and the Pythagoreans, carefully distinguish Pythagorean philosphy from Platonism. Zhmud has recently put forth a challenge to this view arguing the situation is almost the reverse: the Academy in general regards Pythagoras and Pythagoreans favorably but does not assign mature Platonic views to them, it is rather Aristotle who ties Plato closely to the Pythagoreans a, — Although the origins of Neopythagoreanism are thus found in the fourth century BCE, the figures more typically labeled Neopythagoreans belong to the upsurge in interest in Pythagoreanism that begins in the first century BCE and continues through the rest of antiquity.
Before turning to these Neopythagoreans, it is important to discuss another aspect of the later Pythagorean tradition, the Pythagorean pseudepigrapha. Many more writings forged in the name of Pythagoras and other Pythagoreans have survived than genuine writings. Most of the pseudepigrapha themselves only survive in excerpts quoted by anthologists such as John of Stobi, who created a collection of Greek texts for the edification of his son in early fifth century CE.
The modern edition of these Pythagorean pseudepigrapha by Thesleff runs to some pages. There is much uncertainly as to when, where, why and by whom these works were created. No one answer to these questions will fit all of the treatises. Most scholars e. Centrone argues convincingly that a central core of the pseudepigrapha were forged in the first centuries BCE and CE in Alexandria, because of their close connection to Eudorus and Philo, who worked in Alexandria in that period Centrone a.
For an overview of the Pythagorean pseudepigrapha see Centrone a and Moraux , — A number of motives probably led to the forgeries. The existence of avid collectors of Pythagorean books such as Juba, King of Mauretania see below , and the scarcity of authentic Pythagorean texts will have led to forgeries to sell for profit to the collectors.
Other short letters or treatises may have originated as exercises for students in the rhetorical schools e. The contents of the treatises suggest, however, that the primary motivation was to provide the Pythagorean texts to support the Neopythagorean position, first adumbrated in the early Academy, that Pythagoras was the source of all that is true in the Greek philosophical tradition.
The pseudepigrapha show the Pythagoreans anticipating the most characteristic ideas of Plato and Aristotle. Most of the treatises are composed in the Doric dialect spoken in Greek S. Italy but, apart from that concession to verisimilitude, there is little other attempt to make them appear to be archaic documents that anticipated Plato and Aristotle. In many cases, however, this glorification of Pythagoras may not have been the final goal. The ancient authority of Pythagoras was sometimes used to argue for a specific interpretation of Plato, often an interpretation that showed Plato as having anticipated and having responded to criticisms of Aristotle.
These pseudo-Pythagorean treatises are adopting the same strategy as Eudorus of Alexandria and thus may be more important for debates within later Platonism than for Pythagoreanism per se Bonazzi In those treatises Plato is presented as adopting a pair of principles, the one and the indefinite dyad, which are not obvious in the dialogues, but which Aristotle compares to the Pythagorean principles limit and unlimited e.
Aristotle can be read, although probably incorrectly, as virtually identifying Platonism and Pythagoreanism in these passages. Thus, Pythagorean enthusiasts may have felt emboldened by this reading of Aristotle to create the supposed original texts upon which Plato drew. The treatise of Timaeus of Locri is first mentioned by Nicomachus in the second century CE Handbook 11 and is thus commonly dated to the first century CE.
It is likely that in some cases letters were forged in order to authenticate these forged treatises. The thesis that the historical Pythagoras wrote a Sacred Discourse should be rejected Burkert a, There was also a spurious treatise on the magical properties of plants and the Golden Verses , which are discussed further below sect. On the spurious treatises assigned to Pythagoras see Centrone a, — Archytas appears to have been the most popular name in which to forge treatises.
There are also a series of pseudepigrapha on ethics by Archytas and other authors Centrone Philolaus, the third most famous Pythagorean after Pythagoras and Archytas, also turns up as the author of several spurious treatises, but a number of the forgeries were in the names of obscure or otherwise unknown Pythagoreans. Although there are indications that some ancient scholars had doubts about the authenticity of the pseudo-Pythagorean texts, for the most part they succeeded in their purpose all too well and were accepted as genuine texts on which Plato and Aristotle drew.
Although the pseudepigrapha are too varied to admit of one origin, Centrone has recently argued that a core group of pseudepigrapha do appear to be part of a single project a. They are written in Doric Greek the dialect used in southern Italy where the Pythagoreans flourished in order to give them the appearance of authenticity and share a common style. There are some twenty-five treatises belonging to this group and they include some of the most famous pseudepigrapha, including the work by ps. These treatises espouse the same basic system and seem designed to cover all the basic fields of knowledge.
The system is based on theory of principles in which God is the supreme entity above a pair of principles, one of which is limited and the other unlimited, and which are identified with Aristotelian form and matter. Starting from these principles a common system is then developed which applies to theology, cosmology, ethics, and politics. The connections to Eudorus and to Philo who also worked in Alexandria, very much suggest that this group of treatises was developed as a coherent project in Alexandria sometime in the first century BCE or the first century CE.
One important group of Pythagorean pseudepigrapha are those forged in the names of Pythagorean women. Although some work has been done on them there is still a pressing need for a comprehensive collection of these texts and a study of them in light of the most recent scholarship on Pythagoreanism. Pomeroy provides some useful commentary but has serious drawbacks see Centrone b and Brodersen Many of the texts are collected in Thesleff under the names Theano, Periktione, Melissa, Myia and Phintys and taken together occupy about 15 pages of text.
To Periktione are assigned two fragments from a treatise On the Harmony of a Woman. Two further fragments from On Wisdom are also assigned to her. These fragments show a strong similarity to fragments from a treatise with identical title by Archytas and are likely to have been assigned to Periktione by mistake. Two fragments from a work On the Temperance of a Woman are assigned to Phintys. For Theano, the most famous Pythagorean woman see 3. On Theano in the pseudepigraphal tradition see Huizenga , 96— Melissa and Myia are represented by one letter each. With few exceptions the works focus on female virtue, proper marital conduct, and practical issues such as how to choose a wet nurse and how to deal with slaves.
There is little that is specifically Pythagorean. Since the authors are pseudonymous it is impossible to be sure whether they were in fact written by women using female pseudonyms or men using female pseudonyms Huizenga , The letters of Melissa and Myia along with three letters of Theano are often found together in the manuscript tradition and may have come to be seen as offering a curriculum for the moral training of women Huizenga Due to the dearth of preserved writings by women from the ancient world some have been tempted to suppose that the writings are genuine works by the named authors.
However, as demonstrated above, Pythagorean pseudepigrapha were very widespread and more common than genuine Pythagorean works. In such a context the onus of proof is on someone who wants to show that a work is genuine. The content of the writings by Pythagorean women is simply too general to make a convincing case that a specific writing could only have been written by the supposed author rather than by a later forger. In fact, the writings by women fit the pattern of the rest of the pseudepigrapha very well. They are generally forged in the name of famous Pythagorean women, whose names give authority to the advice imparted Huizenga , How better could one impart force to advice to women than to assign that advice to women who belonged to the philosophical school that gave most prominence to women?
The pseudepigrapha written in the names of Pythagorean women probably mostly date to the first centuries BCE and CE like the other Pythagorean pseudepigrapha, but certainty is not possible. Thus the Notes date before the middle of the first century BCE probably towards the end of the third century BCE [Burkert a, 53] and are earlier than most pseudepigrapha.
It is tempting to suppose that some early material may be preserved amidst later material, but the text is such an amalgam that it is in practice impossible to identify securely any early material Burkert , 26; Laks , The Notes are well organized and present a complete if compressed philosophy organized around the concept of purity Laks Starting from basic principles the Platonic monad and dyad they give an account of the world, living beings, and the soul ending with moral precepts some of the Pythagorean acusmata. Kahn thought that the treatise reflected a Pythagorean community that was active in the Hellenistic period , 83 but Long is more likely to be right that its learned eclecticism suggests that it is a scholarly creation Long , — There are several different strands in Neopythagoreanism.
One strand focuses on Pythagoras as a master metaphysician. The first Neopythagorean in this sense is Eudorus of Alexandria, who was active in the middle and later part of the first century BCE. He evidently presented his own innovations as the work of the Pythagoreans Dillon , According to Eudorus, the Pythagoreans posited a single supreme principle, known as the one and the supreme god, which is the cause of all things. Below this first principle are a second one, which is also called the monad, and the indefinite dyad. The system of principles described by Eudorus also appears in the pseudo-Pythagorean writings e.
A generation after Eudorus, another Alexandrian, the Jewish thinker Philo, used a Pythagorean theory of principles, which is similar to that found in Eudorus, and Pythagorean number symbolism in order to give a philosophical interpretation of the Old Testament Kahn , 99—; Dillon , — For Philo Pythagoras and his travels to the east evidently played a crucial role in the transmission of philosophy to the Greeks Dillon Philo like Eudorus has close connections to the Pythagorean pseudepigrapha Centrone Moderatus of Gades modern Cadiz in Spain , who was active in the first century CE, shows similarities to Eudorus in his treatment of Pythagorean principles.
Plutarch explicitly labels him a Pythagorean and presents his follower, Lucius, as living a life in accord with the Pythagorean taboos, known as symbola or acusmata Table Talk b. It is thus tempting to assume that Moderatus too lived a Pythagorean life Dillon , His philosophy is only preserved in reports of other thinkers, and it is often difficult to distinguish what belongs to Moderatus from what belongs to the source.
He wrote a comprehensive eleven volume work entitled Lectures on Pythagoreanism from which Porphyry quotes in sections 48—53 of his Life of Pythagoras. In this passage, Moderatus argues that the Pythagoreans used numbers as a way to provide clear teaching about bodiless forms and first principles, which cannot be expressed in words. In this system there are three ones: the first one which is above being, a second one which is identified with the forms and which is accompanied by intelligible matter i.
Moderatus was a militant Neopythagorean, who explicitly charges that Plato, Aristotle and members of the early academy claimed as their own the most fruitful aspects of Pythagorean philosophy with only small changes, leaving for the Pythagoreans only those doctrines that were superficial, trivial and such as to bring discredit on the school Porphyry, VP These trivial doctrines have been thought to be the various taboos preserved in the symbola , but, since his follower Lucius is explicitly said to follow the symbola , it seems unlikely that Moderatus was critical of them.
The charge of plagiarism might suggest that Moderatus was familiar with the pseudo-Pythagorean treatises, which appear to have been forged in part to show that Pythagoras had anticipated the main ideas of Plato and Aristotle see Kahn , It is with Numenius see Dillon , — and Kahn , —, and the entry on Numenius , especially section 2 , who flourished ca.
The third century Platonist, Longinus, to a degree describes Plotinus himself as a Neopythagorean, saying that Plotinus developed the exegesis of Pythagorean and Platonic first principles more clearly than his predecessors, who are identified as Numenius, his follower Cronius, Moderatus and Thrasyllus, all Neopythagoreans Porphyry, Life of Plotinus Numenius is regularly described as a Pythagorean by the sources that cite his fragments such as Eusebius e.
Des Places. He presents himself as returning to the teaching of Plato and the early Academy. That teaching is in turn presented as deriving from Pythagoras. Strikingly, Numenius presents Socrates too as a Pythagorean, who worshipped the three Pythagorean gods recognized by Numenius see below.
Thus Plato derived his Pythagoreanism both from direct contact with Pythagoreans and also from Socrates Karamanolis , — For Numenius a true philosopher adheres to the teaching of his master, and he wrote a polemical treatise, directed particularly at the skeptical New Academy, with the title On the Revolution of the Academics against Plato Fr. Numenius presents the Pythagorean philosophy to which Plato adhered as ultimately based on a still earlier philosophy, which can be found in Eastern thinkers such as the Magi, Brahmans, Egyptian priests and the Hebrews Fr.
Matter in its disorganized state is identified with the indefinite dyad. Numenius argues that for Pythagoras the dyad was a principle independent of the monad; later thinkers, who tried to derive the dyad from the monad he does not name names but Eudorus, Moderatus and the Pythagorean system described by Alexander Polyhistor fit the description , were thus departing from the original teaching. Since it is in motion, disorganized matter must have a soul, so that the world and the things in it have two souls, one evil derived from matter and one good derived from reason.
Numenius avoids complete dualism in that reason does have ultimate dominion over matter, thus making the world as good as possible, given the existence of the recalcitrant matter.
The monad, which is opposed to the indefinite dyad, is just one of three gods for Numenius Fr. The first god is equated with the good, is simple, at rest and associates only with itself. The second god is the demiurge, who by organizing matter divides himself so that a third god arises, who is either identified with the organized cosmos or its animating principle, the world soul Dillon , — Numenius is famous for the striking images by means of which he elucidated his philosophy, such as the comparison of the helmsman, who steers his ship by looking at the heavens, to the demiurge, who steers matter by looking to the first god Fr.
It is hard to know which way the influence went Dillon , Hippolytus spends considerable time describing Pythagoreanism, since he regards it as the primary source for gnostic heresy see Mansfeld for this and what follows. He regards Platonism and Pythagoreanism as the same philosophy, which ultimately derives from Egypt. Empedocles is regarded as a Pythagorean and is quoted, sometimes without attribution, as evidence for Pythagorean views.
According to Hippolytus the Monad and the Dyad are the two Pythagorean principles, although the Dyad is derived from the Monad. The Pythagoreans recognize two worlds, the intelligible, which has the Monad as its principle, and the sensible, whose principle is the tetraktys , the first four numbers, which correspond to the point, line, surface and solid. The tetraktys contains the decad, since the sum of 1, 2, 3 and 4 is 10, and this is embodied in the ten Aristotelian categories, which describe the sensible world.
The pseudo-Archytan treatise, The Whole System of Categories , had already claimed this Aristotelian doctrine for the Pythagoreans see 4. Nicomachus of Gerasa modern Jerash in Jordan was probably active a little before Numenius, in the first half of the second century CE. Unlike Neopythagoreans such as Eudorus, Moderatus and Numenius, whose works only survive in fragments, two complete works of Nicomachus survive, Introduction to Arithmetic and Handbook of Music.
More than anyone else in antiquity he was responsible for popularizing supposed Pythagorean achievements in mathematics and the sciences. In the next century, Iamblichus took this chapter over virtually verbatim and without acknowledgement in his On the Pythagorean Life Chapter 26 and it was repeated in many later authors.
The harmonic theory presented by Nicomachus in the Handbook is not original and is, in fact, somewhat retrograde.
Pythagoreanism (Stanford Encyclopedia of Philosophy)
It is tied to the diatonic scale used by Plato in the Timaeus 35bb , which was previously used by the Pythagorean Philolaus in the fifth-century Fr. The Handbook was influential because it put forth an accessible version of Pythagorean harmonics Barker , — Nicomachus provided a more detailed treatment of Pythagorean harmonics in his lost Introduction to Music.
Again Nicomachus was not an original or particularly talented mathematician, but this popularizing textbook was widely influential. Most importantly, Boethius 5th-6th CE provides what is virtually a translation of it in his De Institutione Arithmetica , which became the standard work on arithmetic in the middle ages. In the Introduction to Arithmetic , Nicomachus assigns to Pythagoras the Platonic division between the intelligible and sensible world, quoting the Timaeus as if it were a Pythagorean text I 2.
He also assigns Aristotelian ideas to Pythagoras, in particular a doctrine of immaterial attributes with similarities to the Aristotelian categories I 1. Nicomachus divides reality into two forms, magnitude and multitude. Wisdom is then knowledge of these two forms, which are studied by the four sciences, which will later be known as the quadrivium : arithmetic, music, geometry and astronomy. He quotes a genuine fragment of Archytas Fr.
Nicomachus presents arithmetic as the most important of the four, because it existed in the mind of the creating god the demiurge as the plan which he followed in ordering the cosmos I 4 , so that numbers thus appear to have replaced the Platonic forms as the model of creation on forms and numbers in Nicomachus see Helmig Nicomachus apparently presents the monad as the first principle and demiurge, which then generates the dyad, but much is unclear Dillon , — The Theology of Arithmetic may have been most influential in its attempt to set up an equivalence between the pagan gods and the numbers in the decad, which was picked up later by Iamblichus and Proclus Kahn , Nicomachus also wrote a Life of Pythagoras , which has not survived but which Porphyry e.
Although Plotinus was clearly influenced by Neopythagorean speculation on first principles see above , he was not a Neopythagorean himself, in that he did not assign Pythagoras a privileged place in the history of Greek philosophy. Plotinus treats Pythagoras as just one among many predecessors, complains of the obscurities of his thought and labels Plato and not Pythagoras as divine Enneads IV 8. The earliest extant Life of Pythagoras is that of Diogenes Laertius, who was active ca. Unlike his successors Porphyry and Iamblichus see below Diogenes had no philosophical affiliation and hence no philosophical axe to grind in presenting the life of Pythagoras.
Indeed, it is striking that his life shows little influence from the Neopythagorean authors discussed above. Diogenes draws on a wide variety of important sources, some going back to the fourth century and others deriving from the Hellenistic period. This material is put together in a very loose, sometimes undetectable, organizational structure.
He shows particular interest in the Pythagorean way of life and quotes a large number of Pythagorean symbola for some of which his source was Aristotle VIII 34— For more on this treatise see the section on Pythagorean pseudepigrapha above 4. However, other parts of his life present Pythagoras in a quite postive light so that it is hard to determine precisely what attitude Diogenes took towards Pythagoras Laks , — It was originally part of his now lost Philosophical History.
Continuing interest in Pythagoras in later centuries led the Life of Pythagoras to be preserved separately and it is the only large section of the Philosophical History to survive. In the Life of Pythagoras Porphyry does not structure his information according to any overarching theme but instead sets out the information derived from other sources in a simple and orderly way with the minimum of editorial intervention. Since these sources come from the first and second centuries CE, Porphyry basically provides us with the picture of Pythagoras common in Middle Platonism.
This Pythagoras is the prototype of the sage of old who was active as a teacher and tied to religious mystery. Porphyry provides little criticism of his sources and, although his life has a neutral factual tone, in contrast to Diogenes Laertius in his Life of Pythagoras , he includes no negative reports about Pythagoras.
It would appear, however, that Pythagoras was not made the source of all Greek philosophy, but was rather presented as one of a number of sages both Greek and non-Greek e. This philosophy is, in fact, Platonic in origin as it relies on the Platonic distinction between the intelligible and sensible realms; Porphyry unhistorically assigns it back to these earlier thinkers, including Pythagoras. Porphyry himself lived an ascetic life that was probably largely inspired by Pythagoreanism Macris , — Iamblichus wrote a work in ten books entitled On Pythagoreanism.
Book One, On the Pythagorean Life , has biographical aspects but is primarily a detailed description of and a protreptic for the Pythagorean way of life. Porphyry, indeed, had written a treatise Against the Christians , now lost. Matthew 1. Iamblichus, on the other hand, advocates a return to the philosophy that inspired Plato, Pythagoreanism. Pythagorean philosophy is portrayed by Iamblichus as a gift of the gods, which cannot be comprehended without their aid; Pythagoras himself was sent down to men to provide that aid VP 1. It is also true that the remaining books of On Pythgoreanism use a variety of sources.
Book Three, On General Mathematical Science , deals with the general value of mathematics in aiding our comprehension of the intelligible realm and is followed by a series of books on the specific sciences.
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Books V-VII then dealt with arithmetic in physics, ethics and theology respectively and were followed by treatments of the other three sciences in the quadrivium: On Pythagorean Geometry , On Pythagorean Music and On Pythagorean Astronomy. Iamblichus was particularly interested in Pythagorean numerology and his section on arithmetic in theology is probably reflected in the anonymous treatise which has survived under the title Theologoumena Arithmeticae and which has sometimes been ascribed to Iamblichus himself. It appears that here again Iamblichus relied heavily on Nicomachus, this time on his Theology of Arithmetic.
It is possible that Iamblichus used the ten Books of On Pythagoreanism as the basic text in his school, but we know that he went beyond these books to the study of Aristotelian logic and the Platonic dialogues, particularly the Timaeus and Parmenides Kahn , — Nonetheless, it was because of Iamblichus that Pythagoreanism in the form of numerology and mathematics in general was emphasized by later Neoplatonists such as Syrianus fl. Proclus is reported to have dreamed that he was the reincarnation of Nicomachus Marinus, Life of Proclus This strand is closely connected to the striking interest in and prominence of Pythagoreanism in Roman literature during the first century BCE and first century CE.
In De Finibus V 2 , he presents himself as the excited tourist, who, upon his arrival in Metapontum in S. Italy and even before going to his lodgings, sought out the site where Pythagoras was supposed to have died. Brutus freed Rome from the tyranny of the kings and founded the Republic; there is a clear implication that Pythagorean ideas, which reached Rome from southern Italy, had an influence on the early Roman Republic. Cicero goes on to assert explicitly that many Roman usages were derived from the Pythagoreans, although he does not give specifics.
According to Cicero, it was admiration for Pythagoras that led Romans to suppose, without noticing the chronological impossibility, that the wisest of the early Roman kings, Numa, who was supposed to have ruled from — BCE, had been a pupil of Pythagoras. In addition to references to Pythagoras himself, Cicero refers to the Pythagorean Archytas some eleven times, in particular emphasizing his high moral character, as revealed in his refusal to punish in anger and his suspicion of bodily pleasure Rep.
XII 39— VI 9 , which owes even more to Plato. This flourishing of Pythagoreanism in Roman literature of the golden age has its roots in one of the earliest Roman literary figures, Ennius — BCE , who, in his poem Annales , adopts the Pythagorean doctrine of metempsychosis, in presenting himself as the reincarnation of Homer, although he does not mention Pythagoras by name in the surviving fragments.
Roman nationalism also played a role in the emphasis on Pythagoreanism at Rome. Since Pythagoras did his work in Italy and Aristotle even referred to Pythagoreanism in some places as the philosophy of the Italians e. In BCE during the war with the Samnites, Apollo ordered the Romans to erect one statue of the wisest and another of the bravest of the Greeks; their choice for the former was Pythagoras and for the latter Alcibiades. Pliny, who reports the story Nat. This Roman attempt to forge a connection with Pythagoras can also be seen in the report of Plutarch Aem. Thus we are told that Varro —27 BCE was buried according to the Pythagorean fashion in myrtle, olive and black poplar leaves Pliny, Nat.
XXXV It is Nigidius Figulus, praetor in 58, who died in exile in 45, however, who is usually identified as the figure who was responsible for reviving Pythagorean practices.