Apart from his teachings, wonders and scientific discoveries, Pythagoras was also known for his wide-ranging journeys. Ancient authors alleged that he visited many countries and nations from Egypt to India, stayed with the Phoenicians and the Ethiopians and talked to the Persian Magi and Gallic Druids. However, he never went to the North. If, nevertheless, he was eventually associated with the northern inhabitants, it is only because they themselves came into close contact with him. The first of them was (...) Zalmoxis, a deity of a Thracian tribe, the Getae, who guaranteed them immortality after death. Having described a blood ritual that the Getae practised to become immortal, Herodotus relates a story he heard from the Hellespontine and Pontic Greeks. It goes that Zalmoxis was not adaimōnbut a former slave of Pythagoras on Samos and, having adopted the doctrine of immortality from him, he returned to Thrace and converted his tribesmen to it with a cunning trick. He invited the most prominent of them to a men's hall for entertainment and told them that neither he nor they or their descendants would die, but would live eternally. Then, having constructed a secret underground chamber, he suddenly disappeared from the eyes of the Getae and hid in his shelter for three full years, being lamented as dead. Then he showed himself again to the Getae, thus persuading them of the truth of his promises. (shrink)

Studying Plato's "unwritten doctrines" in the light of his discussion of limit and unlimited in his dialogue Philebus. The essay raises also the question whether there is too much "atomism" in the usual presentation of Plato's Forms as individual absolute entities, rather than as themselves derived from a more fundamental limit/unlimited ontology.

While the appeal of scientific materialism has been weakened by developments in theoretical physics, chemistry and biology, Pythagoreanism still attracts the allegiance of leading scientists and mathematicians. It is this doctrine that process philosophers must confront if they are to successfully defend their metaphysics. Peirce, Bergson and Whitehead were acutely aware of the challenge of Pythagoreanism, and attempted to circumvent it. The problem addressed by each of these thinkers was how to account for the success of mathematical physics if the (...) world consists of creative processes. In this paper I critically examine the nature of the challenge posed by Pythagoreanism to process philosophy and examine the efforts by process philosophers, particularly Whitehead, to overcome it, and offer some suggestions for advancing these efforts. (shrink)

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.

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.

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)

Reportedly ever since Pythagoras, but possibly much earlier, humans have been concerned about the way non human animals (henceforward “animals” for convenience) should be treated. By late antiquity all main traditions with regard to this issue had already been established and consolidated, and were only slightly modified during the centuries that followed. Until the nineteenth century philosophers tended to focus primarily on the ontological status of animals, to wit on whether – and to what degree – animals are actually (...) rational beings; accordingly they allowed – or denied – them some kind of moral standing. This modus operandi was for the first time seriously questioned by Jeremy Bentham, who put the issue on a different track. If the question, as Bentham suggested, is not if animals can think or speak, but if they can suffer1, then it seems plausible that moral agents ought to abstain from inflicting unnecessary suffering on animals; in other words, humans might have at least one – even limited – moral duty towards animals. And if this, in turn, is true, then animals should arguably be allowed the commensurate moral right, namely the right not to be inflicted unnecessary pain. Then, if animals possess this right, they could probably possess others, as well. This is how grosso modo the issue of animal rights became a pivotal part of the discussion concerning animal ethics. Bentham himself, of course, wouldn’t have gone that far; to him even the idea of human rights sounded like “simple… rhetorical nonsense upon stilts”.2 It was mostly due to his views, however, that the debate was moved from the way things actually are to the way things should ideally be – thus merging into what, in my view, should always have been: one primarily concerning ethics. (shrink)

Mathematics is everywhere and yet its objects are nowhere. There may be five apples on the table but the number five itself is not to be found in, on, beside or anywhere near the apples. So if not in space and time, where are numbers and other mathematical objects such as perfect circles and functions? And how do we humans discover facts about them, be it Pythagoras’ Theorem or Fermat’s Last Theorem? The metaphysical question of what numbers are and (...) the epistemological question of how we know about them are central to the philosophy of mathematics. These and related philosophical questions are of particular interest because of mathematics’ unusual status. Mathematics is exceptional in that, on the one hand, it appears unhesitatingly true—no one doubts that 2 + 3 = 5—but on the other, as just noted, it is not about the physical world. This ambivalent status is what gives the philosophy of mathematics its special interest. The philosophy of mathematics is also one of the oldest academic fields, more or less coeval with philosophy itself. But contemporary philosophy of mathematics is rather different from its pre-twentieth-century antecedents, largely for three reasons. The first is that since the seventeenth century, mathematics has become integral to science. Science has over the past few centuries become increasingly mathematical, and indeed the fundamental science of nature, physics, is today recognised as a branch of applied mathematics. The second is that mathematics underwent a transformation in the course of nineteenth century: having started the century as a rather traditional-looking science of quantity it emerged a hundred years later a radically transformed abstract theory of structure. The final factor in the transformation of the philosophy of mathematics is the rise of modern logic. Developed by Frege, Cantor and others in the late nineteenth century, modern logic pervades contemporary mathematics, philosophy and computer science, and has had an immeasurable effect on the philosophy of mathematics. These volumes will collect the major works in this major field, with a focus on the last few decades. The anthology will include technical work, which interprets philosophically significant mathematical results or subfields of mathematics, as well as purely philosophical writing, aimed at those without advanced mathematics. The collection should be of interest to both philosophers and mathematicians, as well as to anyone who is susceptible to wondering what the main intellectual tool used in science, economics and finance, and indeed everyday life is ultimately about. (shrink)

This paper discusses continuity between ancient Pythagoreanism and the pseudo-Pythagorean writings, which began to appear after the end of the Pythagorean school ca. 350 BC. Relying on a combination of temporal, formal and substantial criteria, I divide Pseudopythagorica into three categories: 1) early Hellenistic writings ascribed to Pythagoras and his family members; 2) philosophical treatises written mostly, yet not exclusively, in pseudo-Doric from the turn of the first century BC under the names of real or fictional Pythagoreans; 3) writings (...) attributed to Pythagoras and his relatives that continued to appear in the late Hellenistic and Imperial periods. I will argue that all three categories of pseudepigrapha contain astonishingly little that is authentically Pythagorean. (shrink)

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and a (...) four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane - which obeys the Euclidean axioms in [Tarski and Givant, 1999] - and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagora’s theorem. We conclude with a Representation Theorem relating models of our system that satisfy second order continuity to the mathematical structure called ‘Minkowski spacetime’ in physics textbooks. (shrink)

It is not mere coincidence that several of Plato’s dialogues are set in gymnasia and palaistrai (wrestling schools), employ the gymnastic language of stripping, wrestling, tripping, even helping opponents to their feet, and imitate in argumentative form the athletic contests (agōnes) commonly associated with that place. The main explanation for this is, of course, historical. Sophists, orators, and intellectuals of all stripes, including the historical Socrates, really did frequent Athens’ gymnasia and palaistrai in search of ready audiences and potential students. (...) Perhaps they were following the example of Pythagoras, who may have been a boxing coach (gymnastēs) and was, in any case, associated with the extraordinary Olympic success of athletes from his adopted Croton—success so great it generated the saying that the last of the Crotonites was the first among all other Greeks. After his visit to Western Greece, Plato famously established his school in or adjacent to the Academy gymnasium in Athens, and he may have held the public office of Gymnasiarch there. In this essay, I would like to argue that there are also symbolic reasons for Plato setting some of his dialogues in gymnasia. These dialogues function as virtual gymnasia in which readers are coached by the character of Socrates toward an innovative ideal of aretē (virtue, excellence). (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 ancient Greeks already used to give ethnic names to their different scales, and observations on differences in music of the various nations always raised the interest of musicians and philosophers. Yet, it was only in the late nineteenth century that “comparative musicology” became an institutional science. An important role in this process was played by Carl Stumpf, a former pupil of Brentano’s who pioneered these researches in Berlin. Stumpf founded the Phonogrammarchiv to collect recordings of folk and extra-European music (...) and a dedicated journal, the Sammelbände für vergleichende Musikwissenschaft. Gifted in the field of science no less than in that of musicology, Stumpf developed an empirically-oriented approach to phenomenology, deeply divergent from Husserl’s and highly influential over the Berlin school of Gestalt psychology. A self-declared “outsider” among armchair philosophers, Stumpf experimentally investigated the perception of sounds and the origins of musical consonance. Developing the physiological studies of Ernst Weber on the sense of touch, Stumpf discovered that two sensations of tone, given at the same time, tend to mix in a certain degree. Musical consonance – he claimed – lays in this level of “tonal fusion”, not in the allegedly “natural” series of the harmonic partials of a vibrating chord, as suggested by the naturalists of all times from Pythagoras to Stumpf’s great contemporary Hermann Helmholtz. Accordingly, no musical system can claim for preponderance over the others: Stumpf’s researches in comparative musicology served to corroborate his theses on “tonal fusion” and the psychological foundations of consonance. Although Stumpf later revised and finally abandoned this theory, its permanent value lays in its opposition to dominant naturalistic approaches. The commitment for comparative musicology at the Berlin School is then no concession to a positivistic fashion for exoticism. The fundamentally Eurocentric stance of naturalistic theories of music is also fiercely contrasted by Stumpf’s pupil Erich Hornbostel, who suggests that music ought to be considered as culture, rather than as nature, and focuses attention on the eventually melting human cultures. The Berlin school flourished until the Nazis forced most of its exponents to emigration and, for tragically obvious reasons, heavily discouraged researches on these topics. (shrink)

The term “Presocratics” refers to a group of Greek thinkers who lived not later than Socrates and who were not decisively influenced by him. They are often referred to as the first philosophers as they represent the dawn of human speculation in the West. The essay examines the fragments of major Presocratics - Thales, Anaximander, Anaximenes, Heraclitus, Pythagoras, Parmenides, Empidocles and Anaxagoras, which contain their views and arguments as reported by subsequent authors. Although these fragments are incomplete and are (...) based on secondary quotations, it is possible to sift through them and develop coherent and logical interpretations that approximate the original idea and intentions of these philosophers. The aim of this essay is to shed light on the philosophical meaning and significance of the concept of Arche (ἀρχή) – an untranslatable Greek word that connotes origin, principle, first in the series, or source, which constitutes the central thread of speculation among the Presocratics and their most influential contribution to the history of Western thought. (shrink)

I contend that “philosophos” is meant to carry the connotation of a Pythagorean: Euenus is a native from Paros which had a strong Pythagorean community down to the end of the fifth century. Moreover, “philosophos” was used to refer to the Pythagoreans, as can be seen from the story related by Cicero from Heraclides Ponticus (Tusc. Disp. V, iii, 7-8; cp. DL, 1.12; 8.8). I argue (against Burkert) that even if this story is part of the lore surrounding Pythagoras (...) and, hence, without historical value as for Pythagoras, it may still be used as evidence for the use of “philosophos” among latter-day Pythagoreans. (shrink)

This paper aims to synthesize two equally impressive systems of thought: Indian philosophy in the East and Presocratic philosophy in the West, which are separated not only by space and time but by our prejudices. It attempts to show the universality of philosophy by exploring the parallelisms and similarities, clarifying contrasts, and highlighting the common themes that are emphasized and de-emphasized in them. The study does not intend to give a complete account of the early Greek and Hindu thoughts. The (...) discussion of Hindu philosophy focuses on the Upanishads, the main source of Hinduism. We will use for our primary source the following texts which majority of Indologists consider as the most authoritative: Aiteriya, Kaushitaki, Taittiriya, Chandogya, Brihadharanyaka, Katha, Mandukya, Maitriyani, Svetasvatara, Isa, and Kena. On the side of Presocratic philosophy are included such major thinkers as Thales, Anaximander, Anaximenes, Heraclitus, Pythagoras, Parmenides, Anaxagoras, and Empidocles. (shrink)

A ‘pious pessimism’ pervaded much of archaic Greek poetry: ‘It is for the gods to know and men merely to opine’ was the prevailing sentiment. However, in the late 6th century a set of independent-minded individuals began to move away from the older pessimism to embrace a more optimistic and secular outlook. In various ways they maintained that mere mortals could, if they were prepared to undertake the appropriate inquiries, achieve a clear and sure understanding of the entire cosmos. Heraclitus (...) and Parmenides offered the most detailed lines of investigation, but both Pythagoras and Empedocles presented themselves as savants able and willing to impart their wisdom to all those prepared to listen to and embrace their teachings. Among the most important elements in this transition were the concepts of phusis or the essential nature of a th’ing, and the logos or rational account in which that nature could be formulated. -/- . (shrink)

Philosophical problems arise in every sphere of the science. Philosophers should be able to recognize an issue and give a reasonable response. Medicine is an especial sphere, where one can discover many philosophical questions about the nature of human health and diseases, limits of scientific methodology, etc. Since ancient times, philosophers have been engaged in medicine. Pythagoras, Empedocles, Democritus, Aristotle, Avicenna, René Descartes were famous in both areas: philosophy and medicine. Nowadays, links between these spheres in their strong meaning (...) are reflected in three types: philosophy for medicine, philosophy in medicine and philosophy of medicine. (shrink)

This textbook has been written to discuss the fundamental problems of Greek Philosophy. There has been many philosophical Problems which Greek philosophers has discussed and examined with rational approach. The philosophical problems which we have mentioned in this book are: Greek Rationalism, Greek Naturalism, Greek Idealism, Greeks on human mind, Number theory and Greek Metaphysics. We have defined some significant issues like Greek atomism, Nihilism, Solipsism, Dogmatism, Sophism and Pluralism. Philosophy is the subject which studies the fundamental Problems of the (...) world. The problems which Philosophy studies are reality, existence, mind, thought, language, essence, experience, perception, knowledge, God, and so on. This book ‘Problems of Greek Philosophy’ is divided into six chapters while first Chapter ‘Introduction to western Philosophy’ deals with overall discussion and argumentation of western philosophy and also some valuable introductory information on Greek Philosophy. Second Chapter ‘Greeks on Nature’ attempts to discuss the lonian classification and examination of natural elements like water, air, Aperion, fire and reality. This chapter deals with the ultimate constituents of the natural stuff. Third chapter ‘Greek Rationalism’ deals with the role of reason in explanation of the world. Greek rationalists have used reason as the fundamental constituent of the universe. Fourth chapter ‘Number theory and Greek Metaphysics’ deals with the contribution of great mathematicians like Pythagoras and Zeno to the world. This chapter has highlighted the philosophy of number and metaphysics. Fifth Chapter ‘Greek Idealism’ highlights the philosophy of Greek idealists; Protagoras, Socrates and Plato. Sixth Chapter ‘Mind in Greek Philosophy’ deals with the concept of mind and thought in Greek philosophy. This section examines the contribution of Anaxagoras and Empedocles. (shrink)

This publication is the translation of the first fragment of F. W. J Schelling's Presentation of Philosophical Empiricism accompanied by the analytical translator's preface. In his treatise, Schelling assesses the history of modern philosophy. Namely, he treats it as history of experiments, the goal of which was in the search for the primary fact in the world. In Schelling's opinion, this fact is in the growing over-weight of the subjective over the objective. Only his philosophy of nature was able to (...) find this fact. However, it is not genuine fact but only pure fact, because it does not content in itself any ground for the over-weighting of the subjective over the objective. For resolve this problem, Schelling starts to use the concepts formed by Ancient philosophers, namely by Pythagoras and Plato. The concepts of the limitless and the limit are belonging to the series of the mentioned concepts. Accordantly, Schelling associates the notion of the objective with the one of the limitless being and the notion of the subjective with the one of the limit or limiting instance. His inquiry into the correlation between the limitless being and the limit, i.e. between the objective and the subjective leads him to the declaration of the existence of the free efficient cause, which determinates their interplay and the rise of that-what-should-be from that-what-should-not-be. Since the limitless is the objective and the limit is the subjective in accordance with Schelling, such efficient cause is also the cause of the progressive over-weighting of the subjective over the objective as well. It can explain the fact, which the Schelling's philosophy of nature has only found but not explained. The in his preface, the translator puts the question of the possibility as well as of a relevance of the Schelling's late philosophy to the phenomenological thought. In this context, he emphasizes few moments, by which the later Schelling' philosophy could be of interests for phenomenologists, namely the following ones: the concept of philosophical empiricism itself, the Schelling's division between the pure fact and the genuine fact, his treatment of history of philosophy as history of experiments. Moreover, he speaks about main difficulties connected with the translation of Schelling's text into Russian and gives a German-Russian glossary for utility of Russian readers. The translator gives also the commentaries by Arthur Drews, who reedited the Schelling's treatise in 1902, in their Russian translation. (shrink)

The article "Philosophy is the unborn child of science: in search of a universal commonly used language" explores the problem of creating a universal philosophical language that includes not only the language of classification concepts of natural language that define people's reasoning thinking, but also the language of comparative concepts, which is the basis their mind and wisdom. At the same time, the author divides comparative concepts into two parts, the first of which is determined by particular concepts – concepts (...) of practical mind peculiar to natural and exact sciences, while the second part is determined by extremely general concepts – categories of pure mind, which were supposed to become the beginnings of philosophy as a verifiable rigorous science. Along with the majority of thinking people, the author sees that as a cumulative rigorous science, philosophy has not taken place, and therefore considers it an unborn child of science. In this regard, he analyzes various philosophical traditions and comes to the conclusion that "everything is known in comparison." Therefore, the basis of a language that would facilitate effective communication between different philosophical directions, as well as between natural and humanitarian disciplines, can only be the language of comparative concepts. As a result of using the four types of opposition identified by Aristotle as the principles of philosophy: "contradictory", "correlated", "opposite", "deprivation and possession", the author built a philosophical Matrix from which he approaches the creation of such a universal language. At the same time, the Matrix includes other more complex comparative concepts than those of Aristotle – concepts of pure mind found by the author in the teachings of outstanding thinkers of the past: Lao Tzu, Pythagoras, Heraclitus and K. Marx, but today misunderstood or forgotten. The comparative concepts returned from oblivion, in the author's opinion, represent a valuable contribution to many areas of philosophy and linguistics, and can be useful for philosophers, psychologists, educators, linguists and anyone interested in the problem of language in philosophy and their undeniable role in the development of mind and wisdom. (shrink)

The symbolism of nature as a book in which one reads is of ancient origin. This study focuses on the question of its mathematical and theological language in the biblical context and on the background of changes in natural philosophy, especially in the Renaissance period. The biblical context is associated with the paradigm shift in the Renaissance period, because all the researched authors addressed the questions of meaning and methods of research of nature in connection with the hermeneutics of biblical (...) texts. The change in attitude towards the method and results of nature research is connected with two concepts of the relationship of mathematics to the real world. As this world is considered to be created by God, the relationship of mathematics and matter is linked to the question of God's relationship to mathematics. In relation to nature, it was initially significantly limited to geometry, largely under the influence of Euclid and Pythagoras. In the Renaissance period, the preconditions for analytical geometry and infinitesimal calculus were already being created. Thanks to them, Newton was able to build a new physics that combined ancient and medieval approaches to astronomy and terrestrial nature, originally diametrically different, into one whole. (shrink)

Plato's philosophy is in line with the pre-Socratics, sophists and artistic traditions that underlie Greek education, in a new framework, defined by dialectics and the theory of Ideas. For Plato, knowledge is an activity of the soul, affected by sensible objects, and by internal processes. Platonism has its origins in Plato's philosophy, although it is not to be confused with it. According to Platonism, there are abstract objects (a notion different from that of modern philosophy that exists in another realm (...) distinct from both the external sensible world and the internal world of consciousness, and is the opposite of nominalism). An essential distinction for Plato in his philosophy is the theory of Forms, the distinction between perceptible but unintelligible reality (science) and imperceptible but intelligible reality (mathematics) Geometry was Plato's main motivation, and this shows the influence of Pythagoras. Forms are perfect archetypes whose real objects are imperfect copies. -/- DOI: 10.13140/RG.2.2.21536.05121. (shrink)

Suhrawardi created a revolution in the field of Iranian and Islamic thought by compiling the Illuminated Philosophy. The philosophy of Suhrawardi, which includes the collection of works and philosophical and mystical thoughts of Suhrawardi, is well presented in his book Hikma al-Ishraq. Unlike Farabi, Suhrawardi did not write an independent work about Utopia, but he spoke about the ideal ruler and the right to rule. Moreover, in his allegorical works, more than anything else, he pointed out moral points that can (...) lead the people of a society to salvation. Suhrawardi's philosophy is based on the originality of light, which shows that he had an opinion on the philosophers of Ancient Iran. In addition, Suhrawardi has repeatedly referred to Khosrvanion and Ancient Persian Scholars such as Zoroaster and Key Khosro and, for example, considered Key Khosro's government to be a desirable government in terms of politics and government. Another pillar of Suhrawardi's thought is the Quran and Islamic traditions, and therefore, his opinion about the government and ruler is consistent with Islamic teachings. In addition, he considered himself indebted to the divine philosophers of Greece such as Pythagoras and Plato and other divine scholars of the world such as Hermes, and he also took many of the opinions of his predecessor philosophers such as Farabi and Avicenna; Therefore, it can be assumed that he agrees with Farabi in many respects about utopia and its governing characteristics and conditions. (shrink)

This paper aims to show that the idea of a female friendship in Ancient Greece and Rome is possible, even in terms of an “ideal” friendship, i.e. form of a friendship ancient philosophers aspired to. The author of this paper will elucidate the position of women in Greece and Rome and points out that various women actively participated in the work of the philosophical schools and women’s societies. In accordance with the philosophical ideals, “ideal,” “perfect” or “genuine” friends could only (...) be those who possess or at least strive for moral virtue (ἀρετή), while education (παιδεία) was seen as a precondition for acquiring moral virtue. Having in mind that various women met that precondition, it is emphasized that the ideal friendship could be ascribed not only to virtuous men but also to virtuous women. Thus, educated women could potentially be both, “ideal” and “ordinary” friends. (shrink)

The quest to understand the natural and the mathematical as well as philosophical principles of dynamics of life forms are ancient in the human history of science. In ancient times, Pythagoras and Plato, and later, Copernicus and Galileo, correctly observed that the grand book of nature is written in the language of mathematics. Platonism, Aristotelian logism, neo-realism, monadism of Leibniz, Hegelian idealism and others have made efforts to understand reasons of existence of life forms in nature and the underlying (...) principles through the lenses of philosophy and mathematics. In this paper, an approach is made to treat the similar question about nature and existential life forms in view of mathematical philosophy. The approach follows constructivism to formulate an abstract model to understand existential life forms in nature and its dynamics by selectively combining the elements of various schools of thoughts. The formalisms of predicate logic, probabilistic inference and homotopy theory of algebraic topology are employed to construct a structure in local time-scale horizon and in cosmological time-scale horizon. It aims to resolve the relative and apparent conflicts present in various thoughts in the process, and it has made an effort to establish a logically coherent interpretation. (shrink)

A model is proposed for interpreting the course of Western Science’s conception of mathematics from the time of the ancient Greeks to the present day. According to this model, philosophy of science, in general, has traced a horseshoe-shaped curve through time. The ‘horseshoe’ emerges with Pythagoras and other Greek scientists and has curved ‘back’—but not quite back—towards modern trends in philosophy of science, as for example espoused by Bas van Fraassen. Two features of a horseshoe are pertinent to this (...) metaphor: (1) The horseshoe’s semicircular shape models the emergence of science from monism towards dualism, and its modern return towards unity. (2) The logical ‘horseshoe’ operator (“if…then”) makes possible the logical rule ‘modus ponens’--so central to Western science’s deductive approach (which is reaching its limits). Descartes fits approximately at the turning point of the curve. ‘Where might the curve go next?’ is posed to the reader. (shrink)

This paper seeks to explore the way Giovanni Pico della Mirandola treated the Orphics and the Pythagoreans in his Conclusiones nongentae, his early and most ambitious work, so that he formulates his own philosophy. I do not intend to present and analyze the sum of Pico’s references to Orphics and Pythagoreans, since such an attempt is beyond the scope of this paper. Rather, I aim to highlight certain Pico’s aphorisms that allow readers to understand and evaluate his syncretic method and (...) his goals. In addition, I attempt to trace Pico’s sources and evaluate his proper knowledge, understanding and treatment of the Orphics and the Pythagoreans. Pico resorts to the Orphics and the Pythagoreans because he wants to give a practical and applied dimension to his philosophy. He attempted the revival of the original wisdom that underlies the traditions he combined. He was not a fan of the Aristotelian θεωρίης ἢνεκεν. Philosophy does not aim at proper knowledge, but is the key for the manipulation of the cosmos, physically and metaphysically speaking. Pico probably thinks of himself as the modern Orpheus: he does not intend to reveal the paths which cross the sensible and the intelligible, but he aspires to tread them. (shrink)

This article presents the proposal of the principle of sound and light from mathematics and physics, as the origin of nature and the universe, using the Cartesian plane, together with the triadic plane of potential manifestation and complex organisation, starting from the contributions of four pre-Socratic philosophers, Pythagoras of Ephesus, Parmenides of Elea, Heraclitus of Samos and Democritus of Abdera, thus identifying essential principles of the origin of these, to conclude with the most important demonstrations of this theory, which (...) allow its articulation with current science. (shrink)

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

Shahāb ad-Dīn" Yahya ibn Habash ibn Amirak as-Suhrawardī, (also Shaikh al-Ishraq, Shaikh al-Maqtul) was founder of the illuminationist school (Ar. Hikmat al-ishraq; Pers. falsafaye ešrāqi ). Derived from “illumination,” a conventional translation of the Arabic term ishraq (lit. radiance, shining of the rising sun), “illuminationism” refers to the doctrine of the Ishraqiyyun, a school of philosophical and mystical thought of various Graeco-Oriental roots whose principles were propounded as an ancient “science of lights” (‘ilm al-anwar) . He chose this title to (...) distinguish his philosophical theory from mashshaī's philosophy; and he is one of the first philosophers to elaborate on an old tradition. His approach Adopted from Zoroastrian and Platonic ideas. In fact, he associates his science of lights principally with the names of Plato, Hermes, Empedokles, Pythagoras, and the ‘Oriental principle concerning light and darkness’ of the sages of ancient Iran. (shrink)

Plato drew on the philosophical work of some of his predecessors, especially Socrates, but also Parmenides, Heraclitus, and Pythagoras, to develop his own philosophy, which explores most important fields, including metaphysics, ethics, aesthetics, and politics. With his professor Socrates and his student Aristotle, he laid the foundations of Western philosophical thought. Plato is considered one of the most important and influential philosophers in human history, being one of the founders of Western religion and spirituality. The philosophy he developed, known (...) as Platonism, is based on the theory of Forms known by pure reason as a solution to the problem of universals. Plato's philosophy is in line with the pre-Socratics, sophists and artistic traditions that underlie Greek education, in a new framework, defined by dialectics and the theory of Ideas. For Plato, knowledge is an activity of the soul, affected by sensible objects, and by internal processes. In The Republic of Plato, the highest form is considered to be the Form of Good, the source of all other Forms that could be known by reason. The central theme of the book is justice, argued with the help of several Platonic theories, including the allegorical myth of the cave, the doctrine of ideas, dialectics, the theory of the soul, and the design of an ideal city. His dialectic is a type of knowledge, with an ontological and metaphysical role, which is reached by confronting several positions to overcome opinion (doxa), a shift from the world of appearances (or "sensible") to intellectual knowledge (or " intelligible ”) to the first principles. Plato's educational model (paidèia) differentiates the level of education according to the students' skills. According to Socratic principles, in order to do justice, one must know what is good, and this is best known to the philosopher. Plato detailed this concept, highlighting the distinction between the philosopher (who seeks the principles of truth without claiming to possess it) and the sophist (who lets himself be guided by opinion as the only valid parameter of knowledge). -/- CONTENTS -/- Plato - Biography - Travels - Socrates - Academy - Plato's work - - Classifications of works - - - Chronological - - - Tetralogy - - - Trilogies - - - Lexical grouping Plato's philosophy - Soul - The function of the myth - Ideas - Theory of Forms - Ontology - Epistemology - Ethics - Politics - The philosophical state - Art - Unwritten doctrines: One and the Dyad The Republic - Characters - Summary - Topics - - Justice and righteousness (Book I) - - The Ideal State (Books II-III) - - The city-soul analogy. Harmony of the parties (Books IV-V) - - Form Theory (Metaphor of the Line and the Myth of the Cave, Books VI-VII) - - Family and State (Books VIII-IX) - - Myth of Er (Book X) Dialectics Education Philosopher-king Bibliography -/- DOI 10.13140/RG.2.2.29990.19520 . (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)

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)

In this book the author presented the history of the Greek philosophy that extends from the six century BC till the six century AC. He divided the book into three main stages: Philosophy before Socrates: It extended from 6th century BC to mid 5th century BC. This stage began with Thales and his school of Physics; Heraclitus; Pythagoras school; Eleaties School; then Empedocles and Anaxagoras; Democritus and Sophists school. The themes of philosophical contemplation were nature, universe and man. Socratic (...) Method was represented by Socrates, Plato and Aristotle as all of them paid much concern to establishing philosophical systems especially Plato and Aristotle. They both presented solutions to the problems raised by philosophers before the time of Socrates. As for Socrates, he was the real founder of Ethics science and approach. The third stage is Hellenistic philosophy which is in its turn divided into two stages. The first is represented by Stoicism school, The Epicureanism School, and Skepticism. The second was represented in the modern Pythagorean and Platonic schools. The researcher focused on two aspects which the Greek philosophy. The first one is the large number of philosophers and philosophical schools in comparison with Islamic, Christian, modern and contemporary philosophies. The second is the diversity and change amongst the philosophers of Greece whether they belong to the same philosophical school or to independent schools in addition to the miracle of the Greek philosophy as mentioned by Aristotle who said that it was created from nothing as well as the opinions by the researcher in this concern. (shrink)

A work on the philosophy of mathematics (2017) -/- ‘Number’, such a simple idea, and yet it fascinated and absorbed the greatest proportion of human geniuses over centuries, not to mention the likes of Pythagoras, Euclid, Newton, Leibniz, Descartes and countless maths giants like Euler, Gauss and Hilbert, etc.. Einstein thought of pure maths as the poetry of logical ideas, the exactitude of which, although independent of experience, strangely seems to benefit the study of the objects of reality. And, (...) interestingly as well as surprisingly we are nowhere near any clear understandings of numbers despite discoveries of many productive usages of numbers. This is - rightly or wrongly - a humble attempt to approach the subject from an angle hitherto unthought-of. (shrink)