Pythagoreans

The Cosmological Circle from ancient geometry, with its right triangles, and the ratios of the Pythagorean Table are found to be harmonically related to the fundamental physical constants. After a brief history of harmonic mathematics, harmonic values are calculated for the speed of light constant, gravitational constant, Planck's constant, and the inverse fine-structure constant. We then calculate the harmonic of electron mass and proton mass, showing the related Pythagorean/Cosmological Circle harmonics; and speculate on geometry and symmetry.

Averiguando la esboza de Filolao, tomando cuenta del recurso acesorio que hizo verodImilmente a datos observacionales.

Mathematics appears to play an explanatory role in science. This, in turn, is thought to pave a way toward mathematical Platonism. A central challenge for mathematical Platonists, however, is to provide an account of how mathematical explanations work. I propose a property-based account: physical systems possess mathematical properties, which either guarantee the presence of other mathematical properties and, by extension, the physical states that possess them; or rule out other mathematical properties, and their associated physical states. I explain why Platonists (...) should accept that physical systems have mathematical properties, and why a property based account is better than existing accounts of mathematical explanation. I close by considering whether nominalists can accept the view I propose here. I argue that they cannot. (shrink)

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive evaluations are made by (...) a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker to evaluate the degrees of the truth, the indeterminacy and the falsity as PFVs to model the uncertainty in the evaluations. (shrink)

The well-known connection between the extant fragments of Philolaus and Plato’s Philebus is examined in its methodological aspect. By drawing on more texts, it is shown that Plato was aware of an explanatory scheme that can be attributed to Pythagoreanism. His attempt to modify it is also outlined, which sets the historical-philosophical perspective.

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

This chapter pursues an understanding of what Cicero thought 'Italic' philosophy to be, and proceeds to develop a broader account of how Cicero's version compares with the surviving textual evidence and testimonia from the Hellenistic period of the philosophy of the 'Italic' philosophers, including the Lucanians 'Ocellus', 'Eccelus', and 'Aresas/Aesara', and the Rudian Ennius. Special focus is placed on their theories of cosmology, psychology, and law. Collocation of 'Italic' with 'Pythagorean' philosophy of this era aids in building a more comprehensive (...) view of what Hellenistic Pythagoreanism may have looked like. Uploaded here is the pre-publication version; please email me for the printed version. (shrink)

This book presents a new account of Thales based on the idea that Acheloios, a deity equated with water in the ancient Greek world and found in Miletos during Thales’ life, was the most important cultic deity influencing the thinker, profoundly shaping his philosophical worldview. In doing so, it also weighs in on the metaphysical and epistemological dichotomy that seemingly underlies all academia—the antithesis of the methodological postulate of Marxian dialectical materialism vis-à-vis the Platonic idea of fundamentally real transcendental forms. (...) Unbeknownst to many scholars, there are various Neo-Marxian thinkers that position the origin of coinage as the pivotal technological development giving rise to impersonal “metaphysical cosmology,” suggesting that the value of money was more-or-less projected back onto the cosmos in the form of “ideal substances.” While the arguments are incredibly sophisticated and persuasive, their conclusions (either stated or implied) are rather difficult to swallow: the self is merely an illusion, abstract ideas of an ultimate source of value, like God or the Good, are totally delusional (as is the soul, and presumably any notion of inherent human dignity), and essentially everything is reducible to mankind’s enslavement to commodities and the notion of our own objectified labor, which is the true source of all value according to Marx. Not only is this an alarming belief that many scholars (consciously or unconsciously) have adopted, since essentially any action could be “justified,” it is also demonstrably false, since it rests on a misunderstanding of Thales and misconception of philosophy as such. -/- My work rectifies that misunderstanding. In an important sense, it is an attempt at redefining philosophy as a “love of wisdom,” which I argue was accurate even in the Presocratic setting, and it uses the influence of Acheloios on Thales to do so. Throughout its pages I explore the etymology and historical uses of the word ὔδωρ, examine the archaeological context of 7th to 6th century Miletos, consider various aquatic myths Thales encountered, and highlight a hitherto overlooked tradition stemming from Thales and influencing such thinkers as Pythagoras, Empedokles, and Hippo, which culminates in a completely new reading of Plato’s Phaedrus, a dialogue in which Plato responds to the exact type of thinking employed by the Neo-Marxians. It is there that we find Socrates and Phaedrus surrounded by the iconography of Acheloios and the nymphs, all while they lie reclined like river gods (the sinews of Acheloios) on the banks of the Ilisos. And it is in that dialogue that Plato defines philosophy as a love of wisdom—the beholding of a multiplicity of hermeneutical frameworks—and alludes to the fact that it began with the sacrifice of Acheloios, the initial philosophical maneuver which he attributes to Thales. The book ends with a threefold rejoinder to the Neo-Marxian school, corresponding to the λόγος, μῦθος, and ἔργον of Acheloios. It turns out that, (1) the λόγος of Acheloios contained the ideal preconditions conducive to an abstraction to a more refined philosophical worldview in which divine water operated as the One among the Many; (2) the μῦθος of Acheloios actually encouraged the application of the notion of sacrifice to Acheloios himself (thus revealing his essence as divine water); and, (3), the ἔργον of Acheloios, in which he kneels in assent to sacrifice, is found on a coin that was probably designed by Thales. In the final analysis, I suggest that the tradition of Acheloios is reflective of a greater philosophical truth, and that by following Thales’ lead, we transcend the Marxian hermeneutic of doubt and reorient ourselves toward the οὐσια ὄντως οὖσα. (shrink)

The Pythagorean women are a group of female philosophers who were followers of Pythagoras and are credited with authoring a series of letters and treatises. In both stages of the history of Pythagoreanism – namely, the fifth-century Pythagorean societies and the Hellenistic Pythagorean writings – the Pythagorean woman is viewed as an intellectual, a thinker, a teacher, and a philosopher. The purpose of this Element is to answer the question: what kind of philosopher is the Pythagorean woman? The traditional picture (...) of the Pythagorean female sage is that of an expert of the household. The author argues that the available evidence is more complex and conveys the idea of the Pythagorean woman as both an expert on the female sphere and a well-rounded thinker philosophising about the principles of the cosmos, human society, the immortality of the soul, numbers, and harmonics. (shrink)

Ancient Philosophy Today, Volume 4, Issue 2, Page 237-241, October, 2022.

For the first time, the reader can have a synoptic view of the reception of Pythagoras and Pythagoreanism in the Middle Ages and the Renaissance, East and West, in a multicultural perspective. All the major themes of Pythagoreanism are addressed, from mathematics, number philosophy and metaphysics to ethics and religious thought.

The article offers academic translation into Ukrainian of a number of works by Pythagorean woman philosophers, which reveal the problems of human nature and personality education. The focus is on such pseudo-epigraphs of ancient woman thinkers as two letters by Theano of Crotone, letters of Miya of Crotone and Melissa, as well as treatises by Fintys of Sparta "On a woman prudence", Aesara of Lucania "On human nature" and excerpts from Porphyry’s "Pythagorean music" which contain fragments of the works of (...) Ptolemais of Cyrene. The main themes of the above works and letters are the education of the individual in general, and women in particular. Accordingly, the basis of education should be an element of restraint and prudence in everything. If the child is brought up on this basis, he will be able to be strong and resilient during certain life situations. In the treatises of the Pythagorean women-philosophers it is noted that through the study of our own human nature we can understand the philosophical foundations of natural law and morality. Therefore, a woman should use in her life not fleeting emotions and reactions to a particular event, situation, but also be moderate and prudent. These texts are significant in the context of understanding gender issues in the Hellenistic era. Based on the translated works, we can say that, according to thinkers, a number of virtues are common to both sexes, moderation or abstinence are more common in women. At the same time, the limitation of the social role of women reflects an understanding of the nature of the female soul. Accordingly, the normative principle of harmony must be implemented in the context of the specific social roles allowed to women. At the same time, the availability of these texts indicates that philosophy is possible for both men and women, thus emphasizing the importance of involving the latter in knowledge and scientific knowledge. (shrink)

This paper attempts to demonstrate that the conviction about the harmony and order of the world was a fundamental metaphysical principle of the Pythagoreans. This harmony and order were primarily sought in the structures of arithmetics, yet following the discovery of incommensurable magnitudes (irrational numbers, as we now call them), the Pythagoreans began to see geometrical structure as a fundamental part of the world. On the example of the Pythagoreans’ metaphysics and science, the paper shows the mutual relations between metaphysics (...) and science. It demonstrates— on the one hand—the necessity of the first as a guide for the latter, and—on the other—how our scientific research can change its basic metaphysical principles when these are found to be inappropriate. The paper also tries to show the need for a realistic approach in our scientific research by means of the same example of the Pythagoreans, that is, the need to discern something which is below the surface appearance. (shrink)

This paper critically examines the use of the name 'Pseudo-Archytas' to refer to two aspects of the reception of Archytas of Tarentum in antiquity: the 'author-inflection' and the 'authority-inflection'. In order to make progress on our understanding of authority and authorship within the Pythagorean tradition, it attempts to reconstruct Porphyry's views on the importance of Archytas as guarantor of Pythagorean authenticity in the former's lost work On the History of the Philosophers by considering a fragment preserved in Arabic by Ibn (...) Abī Uṣaybi‘a. The article finally argues that a range of problems attend our use of the term 'pseudo-Archytas', which is not fit for purpose when considering the evidence regarding authorship and authority in the Pythagorean tradition. It recommends a more critical approach to the notion of authenticity within the Pythagorean tradition and suggests a new term, 'Archytism', as a more useful point of reference. (shrink)

The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis of the world in a Pythagorean manner. Hilbert arithmetic unifies the foundations of mathematics (Peano arithmetic and set theory), foundations of physics (quantum mechanics and information), and philosophical transcendentalism (Husserl’s phenomenology) into a formal theory and mathematical structure literally following Husserl’s tracе of “philosophy as a rigorous science”. In the pathway to that objective, Hilbert arithmetic identifies by itself information related to finite sets and series and quantum (...) information referring to infinite one as both appearing in three “hypostases”: correspondingly, mathematical, physical and ontological, each of which is able to generate a relevant science and area of cognition. Scientific transcendentalism is a falsifiable counterpart of philosophical transcendentalism. The underlying concept of the totality can be interpreted accordingly also mathematically, as consistent completeness, and physically, as the universe defined not empirically or experimentally, but as that ultimate wholeness containing its externality into itself. (shrink)

To eliminate racist prejudices, it is necessary to identify the root cause of racism. American slavery preceded racism, and it was closely associated with genocide. Accordingly, we seek the unique cause of the unique event of genocide + slavery. This was initially justified by religious prejudice, rather than colour prejudice. This religious justification was weakened when many Blacks converted to Christianity, after the trans-Atlantic slave trade. The curse of Kam, using quick visual cues to characterize Blacks as inferior Christians, was (...) inadequate. Hence, the church fell back on an ancient trick of using false history as secular justification for Christian superiority. This trick had resulted in a false history of science during the Crusades when scientific knowledge in translated Arabic texts was indiscriminately attributed to the early Greeks, without evidence. This false history enabled belief in religious superiority to mutate into a secular belief in White superiority. After colonialism, and the Aryan race conjecture, the belief in White superiority further mutated into a belief in Western civilizational superiority, openly propagated today by colonial education. Hence, to eliminate racist prejudice, it is necessary to engage simultaneously with the allied prejudices about Christian/White/Western superiority, based on the same false history of science. (shrink)

Previously we saw that racist prejudice is supported by false history. The false history of the Greek origins of mathematics is reinforced by a bad philosophy of mathematics. There is no evidence for the existence of Euclid. The “Euclid” book does not contain a single axiomatic proof, as was exposed over a century ago. Such was never the intention of the actual author. The book was brazenly reinterpreted, since axiomatic proof was a church political requirement, and used in church rational (...) theology adopted during the Crusades, as a counter to Islamic rational theology. Deductive proofs are MORE fallible than inductive or empirical proofs. Even a validly proved mathematical theorem, such as the “Pythagorean” theorem, is invalid knowledge in the real world. There is no concept of approximate truth in formal mathematics. Nevertheless, the myth of “superior” axiomatic proofs in the “Euclid” book continues to be reiterated by Western historians, and colonial education teaches axiomatic mathematics. Actually, superior practical value comes from the two “Pythagorean” calculations well known toIndian/Egyptian tradition, but unknown to Greeks. The advantage of related decolonized courses in mathematics has been pedagogically demonstrated. But understanding and political will are needed to change colonial/church education. (shrink)

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

The article reveals in detail the understanding of raising children in the context of two pseudo-epigraphic letters of Pythagorean wonan thinkers – Theano and Myia of Crotone. Based on these letters, it was found that pedagogical issues were important in general for the whole Pythagorean tradition. In fact, we can say that this early Greek philosophical school was the first to systematically and comprehensively approach the problem of upbringing and education in ancient society. It is hypothesized that this topic is (...) not accidentally in the center of attention of these philosophers, because their authority was the greatest among all other representatives of this philosophical school. The author’s position is proved that Theano of Crotone letter to Eubule focuses on moderation in education, which is aimed at avoiding luxury, fulfilling all children’s whims, comfort. This is the purpose of hardening in difficult circumstances in order to withstand with dignity all the potential difficulties of adult life. Accordingly, if you do not raise a child in certain restrictions, then, according to Theano, it may well be unprepared for certain trials that may occur. The thesis is substantiated that the key task of upbringing and education, according to Myia of Crotone letter, is moderation, prudence and balance, which is based on both archaic elements and Hellenistic plots, which testifies to the skill of writing this letter. It is revealed that the Pythagorean principles of education, according to both philosophers, have no gender difference. This is because both girls and boys, if they grow up in luxury, comfort and do not know the limitations, can potentially become dangerous both for themselves and for society as a whole. It is emphasized that according to the style of writing, these letters are not so much moral and ethical as paraenetic epistolary genre, ie they act as advice on the upbringing and education of the younger generation. Because of this, these letters are such sources of ancient culture, which are one of the few that are devoted to the philosophical understanding of upbringing and education. (shrink)

Archytas of Tarentum, a contemporary and associate of Plato, was a famous Pythagorean, mathematician, and statesman of Tarentum. Although his works are lost and most of the fragments attributed to him were composed in later eras, they nevertheless contain valuable information about his thought. In particular, the fragments of On Law and Justice are likely based on a work by the early Peripatetic biographer Aristoxenus of Tarentum. The fragments touch on key themes of early Greek ethics, including: written and unwritten (...) laws; freedom and self-sufficiency; moderation of the emotions and cultivation of virtues; equality and the competence of the majority to participate in government; criticism of “rule by an individual”; a theory of the ideal “mixed constitution”; distributive and corrective justice and punishment, and of the rule of law. The fragments also contain one of the only positive accounts of democracy in ancient Greek philosophy. (shrink)

This paper traces how the dualism of body and soul, cosmic and human, is bridged in philosophical and religious traditions through appeal to the notion of ‘breath’ (πνεῦμα). It pursues this project by way of a genealogy of pneumatic cosmology and anthropology, covering a wide range of sources, including the Pythagoreans of the fifth century BCE (in particular, Philolaus of Croton); the Stoics of the third and second centuries BCE (especially Posidonius); the Jews writing in Hellenistic Alexandria in the first (...) century BCE (Philo); and the Christians of the first century CE (the gospel writers and Paul). Starting from the early Pythagoreans, ‘breath’ and ‘breathing’ function to draw analogies between cosmogony and anthropogony – a notion ultimately rejected by Plato in the Timaeus and Aristotle in his cosmological works, but taken up by the Posidonius (perhaps following the early Stoa) and expanded into a rich and challenging corporeal metaphysics. Similarly, the Post-Hellenistic philosopher and biblical exegete Philo of Alexandria, who was deeply influenced by both Platonist and Stoic physics, approaches the cosmogony and anthropogony described in Genesis (1:1–3 and 1:7) through Platonist-Stoic philosophy, in his attempt to provide a philosophically rigorous explanation for why Moses employed certain terms or phrases when writing his book of creation. Finally, the chapter sees a determined shift in the direction of rejecting pneumatic cosmology for a revised pneumatic anthropogony in the writings of the New Testament: by appeal to the ‘Holy Spirit’ or ‘Holy Breath’ (πνεῦμα ἅγιον), early Christians effectively adapted the Stoic metaphysics of ‘breath’, with its notions of divine intelligence and bonding, to the prophetic and ecclesiastical project of building a Christian community conceived of as the ‘body of Christ’. Hence, the spiritual cosmogony of the Pythagoreans, Stoics, and Philo is effectively subordinated to the spiritual anthropogony that facilitates the construction of the Christian kosmopolis, only fully realised in the form of New Jerusalem, the ‘bride’ which, in tandem with the Holy Spirit, calls to the anointed. At the end of the Christian worldview, the kosmos of Greek philosophy is supplanted by the pneumatic kosmopolis. (shrink)

How did the ancient Greeks and Romans conceptualise order? This book answers that question by analysing the formative concept of kosmos in ancient literature, philosophy, science, art, and religion. This concept encouraged the Greeks and Romans to develop theories to explain core aspects of human life, including nature, beauty, society, politics, the individual, and what lies beyond human experience. Hence, Greek kosmos, and its Latin correlate mundus, are subjects of profound reflection by a wide range of important ancient figures, including (...) philosophers, poets and playwrights, intellectuals, and religious exegetes. By revealing kosmos in its many ancient manifestations, this book asks us to rethink our own sense of 'order', and to reflect on our place within a broader cosmic history. (shrink)

When did kosmos come to mean *the* kosmos, in the sense of ‘world-order’? I venture a new answer by examining later evidence often underutilised or dismissed by scholars. Two late doxographical accounts in which Pythagoras is said to be first to call the heavens kosmos (in the anonymous Life of Pythagoras and the fragments of Favorinus) exhibit heurematographical tendencies that place their claims in a dialectic with the early Peripatetics about the first discoverers of the mathematical structure of the universe. (...) Likewise, Xenophon and Plato refer to ‘wise men’ who nominate kosmos as the object of scientific inquiry into nature as a whole and the cosmic ‘communion’ (koinônia) between all living beings, respectively. Again, later testimonies help in identifying the anonymous ‘wise men’ by associating them with the Pythagoreans and, especially, Empedocles. As Horky argues, not only is Empedocles the earliest surviving source to use kosmos to refer to a harmonic ‘world-order’ and to illustrate cosmic ‘communities’ between oppositional pairs, but also his cosmology realises the mutual correspondence of these aspects in the cycle of love and strife. Thus, if later figures posited Pythagoras as the first to refer to the universal ‘world-order’ as the kosmos, they did so because they believed Empedocles to have been a Pythagorean natural scientist, whose combined focus on cosmology and ethics exemplified a distinctively Pythagorean approach to philosophy. (shrink)

The Pythagorean Precepts by Aristotle's pupil, Aristoxenus of Tarentum, present the principles of the Pythagorean way of life that Plato praised in the Republic. They are our best guide to what it meant to be a Pythagorean in the time of Plato and Aristotle. The Precepts have been neglected in modern scholarship and this is the first full edition and translation of and commentary on all the surviving fragments. The introduction provides an accessible overview of the ethical system of the (...) Precepts and their place not only in the Pythagorean tradition but also in the history of Greek ethics as a whole. The Pythagoreans thought that human beings were by nature insolent and excessive and that they could only be saved from themselves if they followed a strictly structured way of life. The Precepts govern every aspect of life: e.g. procreation, abortion, child rearing, friendship, religion, desire and even diet. (shrink)

Journal Name: Apeiron Issue: Ahead of print.

According to Dicaearchus, metempsychosis was the best known among Pythagoras’ teachings. In this paper, I investigate two features of Pythagorean metempsychosis: its non-retributive character and its epistemological value. I argue that the Pythagoreans did not conceive of reincarnation as a punishment for the wicked and a reward for the virtuous, but rather as a way to gain experience, knowledge and therefore wisdom. This reading enables us to throw light on the puzzling list of Pythagoras’ past lives, which includes Aethalides son (...) of Hermes, Euphorbus the warrior, Pyrrhus the fisherman and even Alco the harlot. (shrink)

Quel est le secret de Pythagore? On pourrait avancer que, par défi nition, s'il y a secret, il est caché et n’est pas dévoilable, ou ne sera pas dévoilé. Le vrai secret est celui dont on ne soupçonne même pas l’existence. On peut toutefois approcher tangentiellement le coeur du pythagorisme à partir d’un idéal qui a traversé les âges.

Mathematician. Philosopher. World traveler. Pythagoras was an intelligent and curious scholar and teacher. While he¿s best-known for the Pythagorean theorem, he shared ideas about numbers, animals, and many other areas of knowledge with his students. Since none of his writings were left behind, it¿s not always easy for historians to know what¿s true about Pythagoras and what may be legendary. What does seem apparent is that he was a vegetarian but not a trendy dresser. Some people saw him as godlike. (...) Others felt he made false claims about things. No matter what, Pythagoras¿s curiosity and willingness to grapple with complex issues have helped further the knowledge of mathematics and philosophy for thousands of years. (shrink)

It is argued that mathematics is unreasonably effective in fundamental physics, that this is genuinely mysterious, and that it is best explained by a version of Pythagorean metaphysics. It is shown how this can be reconciled with the fact that mathematics is not always effective in real world applications. The thesis is that physical structure approaches isomorphism with a highly symmetric mathematical structure at very high energy levels, such as would have existed in the early universe. As the universe cooled, (...) its underlying symmetry was broken in a sequence of stages. At each stage, more forces and particles were differentiated, leading to the complexity of the observed world. Remnant structure makes mathematics effective in some real world applications, but not all. (shrink)

In this paper I argue that we can better understand Plato’s Phaedo, if we don’t concentrate solely on the hints of Pythagoreanism among the characters and their doctrines, as though that were the principal key to the dialogue’s dialec- tical targets. I suggest that the dialogue is intended to make us think of the meta-physics of at least one other Presocratic predecessor, besides any Pythagorean influence (which may be much less than has been thought). Not least among the thinkers of (...) whom we are reminded is Heraclitus. In the Phaedo, Plato invites us to explore the limitations of these earlier metaphysical views, and to consider how far they can or cannot make space for the capacity of the soul to direct the body, to make decisions, to grasp eternal truths and potentially to survive in perpetuity beyond the decay of the body. (shrink)

Pythagoras von Samos (ca. 570-510 v.Chr.) war in den antiken Uberlieferungen nicht nur als Naturphilosoph, sondern auch als religioser Experte und Wundertater bekannt. Diesen Wundererzahlungen rund um Pythagoras widmet sich Stephan Scharinger in der vorliegenden Studie. Basis seiner Uberlegungen sind Analyse und Auswertung des einschlagigen Quellenmaterials, beginnend mit den altesten schriftlichen Quellen, die in die Lebenszeit des Pythagoras zuruckreichen, bis hin zu den Pythagorasviten der romischen Kaiserzeit. Darauf aufbauend und mithilfe der historischen Kontextualisierung des Pythagoras (Pythagoreismus und Orphik, Pythagoras und (...) die "Sieben Weisen", Schamanismus) klassifiziert Scharinger die pythagoreischen Wundertaten in Abhangigkeit von der griechisch-romischen Umwelt (ethnische Religionen, altindische und alttestamentarisch-fruhkirchliche Vorstellungen). Die Wundertraditionen in den pythagoreischen Uberlieferungen werden schliesslich in einem zweifachen Vergleich beleuchtet. Der "interne" Vergleich zeigt Parallelen und Unterschiede zwischen den Wunderberichten bei Diogenes Laertios, Porphyrios von Tyros und Iamblichos von Chalkis auf, wahrend der "externe" Vergleich die pythagoreischen Wundertaten mit den Berichten rund um andere Wundertater der antiken Mittelmeerwelt in einen grosseren Zusammenhang stellt. Uberlegungen zum religionshistorischen Umfeld, zur Diskussion um Pythagoras als theios aner sowie zur Klassifikation der Wundertaten als "magische" oder "religiose" Wunder runden die Arbeit ab. (shrink)

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

This paper examines the methodology used by Kepler to discover a quantitative law of refraction. The aim is to argue that this methodology follows a heuristic method based on the following two Pythagorean principles: (1) sameness is made known by sameness, and (2) harmony arises from establishing a limit to what is unlimited. We will analyse some of the author's proposed analogies to find the aforementioned law and argue that the investigation's heuristic pursues such principles.

Pythagoras’s number doctrine had a great effect on the development of science. Number – the key to the highest reality, and such approach allowed Pythagoras to transform mathematics from craft into science, which continues implementation of its project of “digitization of being”. Pythagoras's project underwent considerable transformation, but it only means that the plan in knowledge is often far from result.

The article deals with the doctrines of Orpheus and Pythagoras about the immortality of the soul in the context of the birth of philosophy in ancient Greece. Orpheus demonstrated the closeness of heavenly (divine) and earthly (human) worlds, and Pythagoras mathematically proved their fundamental identity. Greek philosophy was “an investment in the afterlife future”, being the product of the mystical (Orpheus) and rationalist (Pythagoras) theology.

The paper examines the definitions of the concept ›philosophy‹ resp. ›the philosopher‹ in Florentine renaissance Platonism, namely Marsilio Ficino and his scholar Francesco di Zanobi Cattani da Diacceto. Following Socrates and Pythagoras, Ficino distinguishes between mundane philosophy and divine sapientia. In contrast to his teacher, Diacceto's Aristotelism rejects the Pythagoreanism and connects philosophy with sapientia. In order to show how the differences between Ficino and Diacceto emerge, three more contemporaries are taken into consideration: Christoforo Landino, Angelo Poliziano and Giovanni Pico (...) della Mirandola. As a result of this examination, it can be said that the definition of ›philosophy‹ in Florentine renaissance Platonism tends either to Pythagoreism or to Aristotelism or to both. Closely connected with the debate on philosophy are topics and maxims such as meditatio mortis, theologia negativa, docta ignorantia, scio ne scio, nosce te ipsum, ne quid nimis et al. (shrink)