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)

One of the hardest questions to answer for a (Neo)platonist is to what extent and how the changing and unreliable world of sense perception can itself be an object of scientific knowledge. My dissertation is a study of the answer given to that question by the Neoplatonist Proclus (Athens, 411-485) in his Commentary on Plato’s Timaeus. I present a new explanation of Proclus’ concept of nature and show that philosophy of nature consists of several related subdisciplines matching the ontological stratification (...) of nature. Moreover, I demonstrate that for Proclus philosophy of nature is a science, albeit a hypothetical one, which takes geometry as its methodological paradigm. I also offer an explanation of Proclus’ view of what is later called the mathematization of physics, i.e. the role of the substance of mathematics, as opposed to its method, in explaining the natural world. Finally, I discuss Proclus’ views of the discourse of philosophy of nature and its iconic character. (shrink)

The article tries to prove that the famous formula "epekeina tês ousias" has to be understood in the sense of being beyond being and not only in the sense of being beyond essence. We make hereby three points: first, since pure textual exegesis of 509b8–10 seems to lead to endless controversy, a formal proof for the metaontological interpretation could be helpful to settle the issue; we try to give such a proof. Second, we offer a corollary of the formal proof, (...) showing that not only self-predication of the form of the Good, but of any form is not possible, that is: no form of F has the form of F. Third, we apply Spinoza’s distinction between an ens imaginarium and a chimaera to Plato’s Idea of the Good. (shrink)

> καὶ πῶς τις ἀνάξει αὐτοὺς εἰς φῶς, ὥσπερ > > ἐξ Ἅιδου λέγονται δή τινες εἰς θεοὺς ἀνελθεῖν; > > Plato Republic 521c This study reconstructs Empedocles’ eschatology and cosmology, arguing that they presuppose one another. Part one surveys body and soul in Empedocles and argues that the transmigrating daimon is a long-lived compound made of the elements air and fire. Part two shows that Empedocles situates our current life in Hades, then considers the testimonies concerning different cosmic levels (...) in Empedocles and compares them with the afterlife schemes in Pindar’s Second Olympian Ode and Plato’s Phaedo myth. Part three offers a new edition of section d lines 5–10 of the Strasbourg papyrus of Empedocles that reinforces the connection between transmigration and different cosmic locations for souls. Part four reconstructs Empedocles’ cosmology, identifies three different levels or habitats of soul, and, more tentatively, suggests that Empedoclean “long-lived gods” are best understood as stars. (shrink)

Plato is commonly considered a metaphysical dualist conceiving of a world of Forms separate from the world of particulars in which we live. This paper explores the motivation for postulating that second world as opposed to making do with the one we have. The main objective is to demonstrate that and how everything, Forms and all, can instead fit into the same world. The approach is exploratory, as there can be no proof in the standard sense. The debate between explaining (...) Plato’s ontology with a single world and requiring a two-world model to make sense of the same thing is typically about scouring the Platonic corpus for evidence and turning to Aristotle for help where we need it. The aim here is to dig deeper than what either of them, or anyone else, has said or implied about the number or worlds, searching instead for any insight that might be gained from the way Forms are supposed to exist versus what we ourselves might understand by existence. Although the paper is, at its most basic level, about the existence of the Forms, the intention is not to prove that they exist, nor to evaluate the proofs and objections already on record, but to consider how they might exist and what follows if they do. Dialogue toward consensus on why we think the Forms exist, and why we think they do not, could perhaps provide a smoother “second sailing” in waters where we have been unable to agree whether they do and where they would if they did. (shrink)

The Platonic dialogues contain passages that seem to point in quite opposite directions on the question of the moral equality of women with men. Rep. V defends the view that sexual difference need not be relevant to a person’s capacity for philosophy and thus for virtue. Tim. 42a-c, however, makes incarnation in a female body a punishment for failure to master the challenges of embodiment. This paper examines the different ways in which two subsequent Platonists, Proclus (d. 485 CE) and (...) Theodore of Asine (d. c. 360 CE), dealt with this tension. (shrink)

We critically reconsider an old hypothesis of the role of the dekad in Pythagorean philosophy. Unlike Zhmud, we claim that: 1) the dekad did play a role in Philolaus’ astronomical system, and 2) Aristotle did not project Plato’s theory of the ten eidetic numbers onto the Pythagoreans. We claim that the dekad, as the τέλειος ἀριθμός, should be understood in Philolaus’ philosophy as completeness and the basis of counting in Greek – as in most other languages – in a decimal (...) system. Additionally, we argue that the number ten is not even a candidate for the τέλειος ἀριθμός in Plato’s philosophy. As a final result of our discussion, we compare and contrast Philolaus’, Plato’s, and Speusippus’ accounts of completeness in relation to numbers. (shrink)

At Metaphysics A 5 986a22-b2, Aristotle refers to a Pythagorean table, with two columns of paired opposites. I argue that 1) although Burkert and Zhmud have argued otherwise, there is sufficient textual evidence to indicate that the table, or one much like it, is indeed of Pythagorean origin; 2) research in structural anthropology indicates that the tables are a formalization of arrays of “symbolic classification” which express a pre-scientific world view with social and ethical implications, according to which the presence (...) of a principle on one column of the table will carry with it another principle within the same column; 3) a close analysis of Aristotle's arguments shows that he thought that the table expresses real causal relationships; and 4) Aristotle faults the table of opposites with positing its principles as having universal application and with not distinguishing between those principles that are causally prior and those that are posterior. Aristotle's account of scientific explanation and his own explanations that he developed in accordance with this account are in part the result of his critical encounter with this prescientific Pythagorean table. (shrink)

I present a systematic interpretation of the foundational purpose of constructions in ancient Greek geometry. I argue that Greek geometers were committed to an operationalist foundational program, according to which all of mathematics—including its entire ontology and epistemology—is based entirely on concrete physical constructions. On this reading, key foundational aspects of Greek geometry are analogous to core tenets of 20th-century operationalist/positivist/constructivist/intuitionist philosophy of science and mathematics. Operationalism provides coherent answers to a range of traditional philosophical problems regarding classical mathematics, such (...) as the epistemic warrant and generality of diagrammatic reasoning, superposition, and the relation between constructivism and proof by contradiction. Alleged logical flaws in Euclid can be interpreted as sound operationalist reasoning. Operationalism also provides a compelling philosophical motivation for the otherwise inexplicable Greek obsession with cube duplication, angle trisection, and circle quadrature. Operationalism makes coherent sense of numerous specific choices made in this tradition, and suggests new interpretations of several solutions to these problems. In particular, I argue that: Archytas’s cube duplication was originally a single-motion machine; Diocles’s cissoid was originally traced by a linkage device; Greek conic section theory was thoroughly constructive, based on the conic compass; in a few cases, string-based constructions of conic sections were used instead; pointwise constructions of curves were rejected in foundational contexts by Greek mathematicians, with good reason. Operationalism enables us to view the classical geometrical tradition as a more unified and philosophically aware enterprise than has hitherto been recognised. (shrink)

The discovery of incommensurability by the Pythagoreans is usually ascribed to geometric or arithmetic questions, but already Tannery stressed the hypothesis that it had a music-theoretical origin. In this paper, I try to show that such hypothesis is correct, and, in addition, I try to understand why it was almost completely ignored so far.

Η εύληπτη εκπαιδευτική προσέγγιση ότι «κληρονομιά είναι οτιδήποτε θέλεις “εσύ” να διατηρηθεί για τις επόμενες γενιές» κλονίζεται στην ερώτηση «όλα όσα μας παραδίδονται από τους προγόνους μας αποτελούν μια προς διαφύλαξη κληρονομιά, εφόσον “εσύ” το αποφασίσεις;». Εκφάνσεις «βαρβαρότητας» που διασώζονται σε προγενέστερες εθιμικές πρακτικές θα μπορούσαν άραγε να αποτελέσουν στοιχεία ΑΠΚ προς διαφύλαξη; Η παρούσα εργασία επιχειρεί μια πρώτη ανίχνευση του σύνθετου αυτού θέματος. Περιπτώσεις μελέτης από τον ελληνικό και διεθνή χώρο διερευνώνται με κριτήρια αξιολόγησης τα αναφερόμενα στη Σύμβαση για (...) τη Διαφύλαξη της ΑΠΚ (UNESCO, 2003). Βάσει αυτών δεν γίνονται αποδεκτές εθιμικές πρακτικές ΑΠΚ που αναζωπυρώνουν μνήμες βίαιων συγκρούσεων μεταξύ μελών κοινότητας/κοινοτήτων, αποκλείουν με βίαιο ή/και υποτιμητικό τρόπο μέλη εξαιτίας του φύλου, της ηλικίας, της επαγγελματικής ιδιότητας, ή του σεξουαλικού τους προσανατολισμού, καθώς και εθιμικές πρακτικές που περιλαμβάνουν κακομεταχείριση ή/και βασανισμό ζώων. Η εφαρμογή των παραπάνω στην πράξη παραμένει αχαρτογράφητο πεδίο. Απαραίτητες φάσεις μιας συστηματικής μελέτης αποτελούν α) η αναγνώριση και η ευαισθητοποίηση των τοπικών κοινωνιών και του ευρύτερου κοινωνικού συνόλου για τις αξίες της ΑΠΚ, β) η έρευνα, τεκμηρίωση και αξιολόγηση των επιμέρους στοιχείων της, γ) η υποστήριξη των διαδικασιών μεταβίβασής της στις νεότερες γενιές, μέσω της τυπικής και μη εκπαίδευσης, δ) η ανάδειξη της σημασίας της σε τοπική, περιφερειακή, εθνική ή/και παγκόσμια κλίμακα. Η ΑΠΚ μετεξελίσσεται και μεθερμηνεύεται διαρκώς μέσω σύνθετων κοινωνικών και πολιτισμικών διεργασιών. Απόπειρες εξαναγκασμένης «αναβίωσης» κάποιας «αυθεντικής» ή «γνήσιας» μορφής μιας έκφανσής της συχνά αποτυγχάνουν, ενώ παραμένουν μεθοδολογικά μετέωρες. Ο ρόλος της εκπαιδευτικής διαδικασίας στην ανάπτυξη σχετικών ηθικών αρχών και κριτικής σκέψης είναι κρίσιμης σημασίας. Λέξεις κλειδιά: άυλη πολιτιστική κληρονομιά, κοινότητες, αξίες, ηθικές αρχές, εκπαίδευση For educational purposes, we may claim that heritage is whatever each one of us individually or collectively wishes to preserve and pass on to the next generation. However, should violent or other disturbing forms of expression, preserved in customary practices, be safeguarded, if the whole or part of the ‘community’ decides to do so? The present paper attempts a first approach to this complex issue. Case studies from Greece and worldwide are investigated and appraised on the basis of the Convention for the Safeguarding of the ICH (UNESCO, 2003). According to the Convention criteria, customary practices that refresh memories of violent conflicts between members of the community/communities, or exclude members with an aggressive and pejorative way because of their gender, age, professional status or sexual orientation, as well as practices involving the ill-treatment and/or torture of animals do not deserve safeguarding. The implementation of the above criteria in practice, however, remains an uncharted area. A systematic study, therefore, should: (a) include initiation, recognition and awareness on the part of local communities and societies about the values of the ICH; (b) promote research, documentation and evaluation of heritage components; (c) support the transition to the younger generations through formal and non-formal educational events; (d) highlight its importance on the local, regional, national and international context. ICH is evolving and constantly interpreted through complex social and cultural processes. Any forced attempt to revive an ‘authentic’ or ‘genuine’ version of ICH cultural expression, besides appearing fake, is methodologically challenged. The role of education in developing ethical principles and a critical approach to heritage is undoubtedly crucial. Keywords: Intangible cultural heritage, communities, values, ethical principles, education. (shrink)

At Phaedo 86b7–c2 Simmias puts forward the theory that the soul is the attunement of bodily elements. Many scholars have claimed that this theory originates in the Pythagoreans, especially Philolaus. The claim is largely based on their reading of the Phaedo, since we have scarce doxographical evidence. In this paper I show that the dialogue in question does not constitute any evidence for the Pythagorean origin of Simmias’ attunement theory, and that it rather represents the theory as stemming from a (...) materialistic world view that had become widespread among people at that time. I also pursue the question how and why, then, the attunement theory was able to attract many people, by examining its relation to Socrates’ affinity argument. (shrink)

A commentary on the Symposium as a challenge and a gift to Athens. I begin with a reflection on three dates: 416 bce, the date of Agathon’s victory party, c. 400, the approximate date of Apollodorus’ retelling of the party, and c. 375, the approximate date of the ‘publication’ of the dialogue, and I argue that Plato reminds his contemporary Athens both of its great poetic and legal and scientific traditions and of the historical fact that the way late fourth (...) century Athens appropriated them in some way led to the city’s demise at the turn of the century; thus the dialogue is Plato’s challenge to his contemporary Athens to recognize and overcome its flawed relation to its cultural resources. Heard in this way, the key moments are Aristophanes’ implied critique of Pausanias and Eryximachus and Socrates’ implied critique of Aristophanes and Agathon. Proceeding by a close reading, I argue that Plato exposes, for those moved to rise to his challenge, the failure of his great predecessors to conceive the divine in a way that, worthy of the height and otherness divinity requires, can provide substantive orientation for the burgeoning new reason that animates the city’s culture. (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 Vitruvian Man of Leonardo da Vinci is one of the most famous and most studied drawings over the world as well as one of the most reproduced ones, e.g. in coins, space suit patches, books and movies. The aim of the present work is to discuss the Vitruvian Man as a figurative representation of the Leonardo’s scientific method. Our analysis is based on scientific elements both present in the drawing and provided by Leonardo in his approach to this drawing. (...) Our thesis is that the square symbolizes the measurable physical world and that the man inscribed within the square refers to the physics measurement process based on the operational definition of quantities, including the measurement unit system and the quantities conversion factors. Therefore, the measurement process is fundamental for the Leonardo’s approach to the scientific knowledge, albeit, the drawing also suggests that this latter does not correspond with the true knowledge. The circle, which has a different center with respect to the square, symbolizes the truth, to which the man inscribed in the square yearns, without ever achieving it, the truth being reachable only by the man inscribed within the circle. (shrink)

Despite Diotima’s irresistible virtues and attractiveness across the millennia, she spells trouble for philosophy. It is not her fault that she has been misunderstood, nor is it Plato’s. Rather, I suspect, each era has made of Diotima what it desired her to be. Her malleability is related to the assumption that Plato invented her, that she is a mere literary fiction, licensing the imagination to do what it will. In the first part of my paper, I argue against three contemporary (...) ‘majority views’ about Diotima that I regard as false. The first is that we can be certain she is fictional;1 a second is that Diotima is our best evidence for Plato’s feminism; the third, that she is Plato’s mouthpiece for the higher mysteries in the Symposium. After I have set aside what I regard as false, I proceed in the second half of my paper to develop Diotima’s positive contribution to philosophical psychology, her naturalistic account of the psyche as mortal, unified, and developmental. Whether the view Plato assigns to her is one that he held I do not pretend to know; but it is a powerful, defensible, and coherent view that inspired positive aspects of Freudian psychology in the twentieth century. Freud’s insight, in fact, makes clear how erōs can be developed in relation to the bad as well as the good. (shrink)

The inclusion of De astrologia in the Lucianic corpus has been disputed for centuries since it appears to defend astrological practices that Lucian elsewhere undercuts. This paper argues for Lucian’s authorship by illustrating its masterful subversion of a captatio benevolentiae and subtle rejection of Stoic astrological practices. The narrator begins the text by blaming phony astrologers and their erroneous predictions for inciting others to “denounce the stars and hate astrology” (ἄστρων τε κατηγοροῦσιν καὶ αὐτὴν ἀστρολογίην μισέουσιν, 2). The narrator assures (...) readers that he, the knowledgeable astrologer, will correct for the “stupidity and laziness” (ἀμαθίῃ καὶ ῥαθυμίῃ, ibid.) that bring about false predictions. The narrator’s credibility quickly decays when he attempts to recast Orpheus, Bellerophon, Icarus, Daedalus, and a host of other mythological figures as Greek astrologers. Lucian’s audience would expect such far-fetched interpretations of myth from the stereotypical Stoic philosopher, a character lampooned elsewhere in the Lucianic corpus. (shrink)

The solution attributed to Archytas for the problem of doubling the cube is a landmark of the pre-Euclidean mathematics. This paper offers textual arguments for a new reading of the text of Archytas’ solution for doubling the cube, and an approach to the solution which fits closely with the new reading. The paper also reviews modern attempts to explain the text, which are as complicated as the original, and its connections with some xvi-century mathematical results, without any documented relation to (...) Archytas’ doubling the cube. (shrink)

This paper explores the role the Panhellenic centers played in facilitating the circulation of wisdom in ancient Greece. It argues that there are substantial thematic overlaps among practitioners of wisdom , who are typically understood as belonging to different categories . By focusing on the presence of σοφοί at the Panhellenic centers in general, and Delphi in particular, we can acquire a more accurate picture of the particular expertise they possessed, and of the range of meanings the Greeks attributed to (...) the word σοφία. This approach seeks to challenge the conventional categories of modern scholarship and to offer a broader and more inclusive interpretive framework in its stead. One such thematic overlap is the way in which many σοφοί are described as exerting an almost uncanny, yet highly conventional ability to attract listeners and enchant them with their verbal performances. There is plenty of material to support the view that σοφοό, through tapping into the repository of σοφία that Delphi constituted and by aligning themselves with its authority, were seen as themselves being a conduit for a similar type of charismatic speech. (shrink)

This book sets high standards for itself. Regrettably it fails to meet them: apart from a few displays of thorough and competent research, it is generally based on substandard scholarship.

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)

RESUMEN Este artículo pretende comprender la filosofía de Platón como un ejercicio esencialmente político. Esto implica, sin embargo, distinguir cómo se ejerce esta filosofía política, su sentido y alcance. Muchos estudiosos han atribuido a Platón el proyecto político que Sócrates desarrolla en la República. Sin embargo, el símil de la caverna da cuenta de la imposibilidad o, al menos, de la interna problematicidad de tal proyecto, por lo cual se sugiere que no es en el diálogo República donde se encontraría (...) la auténtica filosofía política de Platón, sino en los denominados diálogos aporéticos. En estos diálogos no se habla sobre una posible ciudad, sino que se ejercita de manera viva una política desarrollada por la dialéctica terapéutica de Sócrates, cuya tarea es desvelar la virtud mediante el desenmascaramiento de los rostros de la ciudad. ABSTRACT The following paper contends that Plato's philosophy is essentially a political activity. This imply, however, to distinguish how this political philosophy carries out, its meaning and scope. Many scholars have attributed to Plato the political project, which Socrates develops in the dialogue Republic. Nevertheless, the simile of the cave reveals the impossibility of such a project or, at least, the serious problems that lie behind it. So, I suggest, that is not in the dialogue Republic where it finds Plato's authentic political philosophy, but in the so-called aporetic dialogues. In these dialogues it does not discuss about a possible city, but it exercises in a lively way a politics builted by Socrates' dialectic therapy, whose task is unveiling the virtue through the unmasking the faces of the city. (shrink)

Drawing on recent scholarship and delving systematically into Iamblichean texts, these ten papers establish Iamblichus as the great innovator of Neoplatonic philosophy who broadened its appeal for future generations of philosophers.

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

David Hernández Castro ABSTRACT: Scholars have generally analysed Empedocles’ criticism of sacrifices through a Pythagorean interpretation context. However, Empedocles’ doctrinal affiliation with this school is problematic and also not needed to explain his rejection of the ‘unspeakable slaughter of bulls.’ His position is consistent with the wisdom tradition that emanated from the Sanctuary of Apollo ….

RESUMEN El siguiente artículo tiene como objetivo destacar el carácter polifónico del pensamiento platónico y poner en cuestión el sentido de la autoría de Platón. Suponer, a partir de obstinados prejuicios modernos, que Platón, tal como cualquier escritor moderno, habría expuesto su propia doctrina, es ignorar la importancia de la forma dramática de su pensamiento. El testimonio de la variedad de interlocutores y de puntos de vista que se suceden en los diferentes diálogos, nos invita a prestar atención a la (...) compleja trama del pensamiento platónico, cuya variedad de funciones corresponde a los límites y al alcance del discurso de quienes en un determinado momento y situación cooperan en el diálogo. ABSTRACT The following paper aims to highlight the polyphonic character of Platonic thought and to question the meaning of Plato's authorship. To assume, from obstinate modern prejudices, that Plato, like any modern writer, would have exposed his own doctrine, is to ignore the importance of the dramatic form of his thought. The testimony of the variety of interlocutors and points of view that take place in the different dialogues, invites us to pay attention to the complex plot of Platonic thought, whose variety of functions corresponds to the limits and scope of the discourse of those who, in a given moment and situation, cooperate in the dialogue. (shrink)

The present paper argues that the early Pythagoreans contributed significantly to the development of ancient hermeneutics. The article builds on the assumption that even if the thinkers did not deal with allegoresis directly, the very manner of articulating their thought was, nevertheless, quite conducive to the growth of allegorical interpretation. Thus, at least indirectly, Pythagoreanism must have played an important role in the development of allegoresis. The paper identifies two crucial aspects of Pythagorean influence on the allegorical tradition. Firstly, the (...) Pythagoreans made a very specific use of the poetry of Homer and Hesiod as well as of the traditional mythology in general. Secondly, the teachings of Pythagoras were expressed in terms of various ambiguous symbols that required special exegesis. Both these factors must have contributed considerably to the development of allegoresis: the idiosyncratic use of conventional mythology, on the one hand, and the enigmatic nature of the Pythagorean symbols, on the other, must have provoked extensive search for the latent meaning of the “messages” in question. (shrink)

The development of philosophical ideas throughout history has sometimes been assisted by the use of handcrafted instruments. Some paradigmatic cases, such as the invention of the telescope or the microscope, show that many philosophical approaches have been the result of the intervention of such instruments. The aim of this article is to show the determining role that stringed musical instruments with frets had in the crisis and generation of philosophical paradigms. In fact, just as the observations of the moon with (...) the telescope broke more than a thousand years of Aristotelian hegemony, the fretted string instruments, predecessors of the guitar, played a central role in the collapse of one of the most influential approaches in the history of Philosophy: Pythagorism. We focus on the fundamental hallmarks of Pythagorism and on how, during the 16th century and from the fretted string instruments, the mathematical-musical notion of equal temperament emerged, which from the middle of the 19th century will be established as the prevailing philosophical-musical paradigm of the West. (shrink)

Sometime between 1589 and 1591, a momentous discovery was announced in Florence; or, at least, a discovery thought to be momentous by its promoter: "The true form of the octave is the octuple [ratio 8:1] and not the duple [2:1]".1 Thus taken out of context, we might be forgiven if we failed either to share the author's enthusiasm or to recognize the importance of his finding. But the fact remains that, sadly, nobody else did either: not only did his contemporaries (...) decline to adopt this dramatic solution to the problem of the musical consonances,2 but even those who may take an almost perverse interest at times in the forgotten or the misbegotten—among others, historians of... (shrink)

Heraclitus is generally recognised as the first of the Greek thinkers to develop a psychology, but the understanding of his psychology is held back by the assumptions that his soul is a life-principle and is ‘comprehensive’ of the various faculties we regard as psychological. The fragment that best displays the revolutionary character of Heraclitus’ soul doctrine, from a properly psychological viewpoint, is B 85. I offer an extended analysis of this fragment in order to bear out the claims, firstly, that (...) psyche or ‘soul’ for Heraclitus is the intelligence alone, divine in origin, and secondly that thumos (primarily as the seat of desire) is a better candidate for his biological life-principle, whose exigencies are at odds with those of soul. I also offer some reflections on why, despite Heraclitus’ multifaceted influence on fifth-century thought, and despite the coherence of his psychology, this ‘revolution’ never quite took hold. (shrink)

Allusions to a cosmogony contained in a Vedic hymn present striking analogies to a cosmogony attributed to the Pythagoreans by Aristotle, Simplicius and Stobaeus. The aim of the paper is to evaluate the extent to which they are similar and to which their differences respond to different cultural premises.