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Switch to: References
Citations of:
Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King
New York: Cambridge University Press (2005)
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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 (...) |
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Interpreters of the Phaedo often cite the Pythagorean context of the dialogue as a source of influence on the demanding conception of philosophy defended therein. Sandra Peterson offers a striking account of that influence: the Pythagorean sympathies of Socrates's interlocutors lead him to defend a conception of philosophy that captures their commitments, but that he himself rejects. Call this the Strong Influence Thesis. Peterson defends SIT by attempting to demonstrate a mismatch between the conception of philosophy espoused by Socrates in (...) |
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Aristotle has traditionally been cast as the arch-enemy of all things mechanistic. Given the dichotomy long thought to exist between mechanistic and teleological schools of thought, there is a satisfying irony in discovering veins of apparently ‘mechanistic’ thought within the work of the definitive teleologist. Several waves of scholarship in the past century have argued, from different angles, for mechanistic interpretations of Aristotle’s natural philosophy. The present generation is no exception: in the last decade, Jean De Groot, Monte Johnson, and (...) |
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Discusses the importance of the early history of Greek mathematics to education and civic life through a study of the Parthenon and dialogues of Plato. |
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Archimedes’ Sand-Reckoner presents a system for naming extraordinarily large numbers, larger than the number of grains of sand that would fill the cosmos. Curiously, Archimedes addresses the treatise not to another specialist but to King Gelon II of Syracuse. While the treatise has thus been seen as evidence for the dynamics of patronage, difficulties in both Archimedes’ treatment of Gelon and his discussion of astronomical models make it fit incongruously within contemporary court and scientific contexts. This article offers a new (...) |
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In Archytas of Tarentum, Carl Huffman reconstructs Archytas’ theory of definition by linking definitions to the mathematical study of ratios and proportions. This paper considers whether and how Archytas used definitions and whether he possessed a theory of definition. Our evidence does not support the claim that Archytas has a theory of definition, and his approach to the science of harmonics suggests that he relied on analogies and proportions in the practice of inquiry. We understand sounds and other entities by (...) |
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This paper provides a definitive answer, based on considerations derived from first-order logic, to the question regarding the status of elementary geometry, whether elementary geometry can be reduced to algebra. The answer we arrive at is negative, and is based on a series of structural questions that can be asked only inside the geometric formal theory, as well as the consideration of reverse geometry, which is the art of finding minimal axiom systems strong enough to prove certain geometrical theorems, given (...) |
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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 (...) |
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What is a toy? As objects of play, toys seem to be inextricably bound up with mimesis: a child plays ‘make believe’, for example, with a doll or toy cart. But as I will show, Plato has a very different conception of toys from the modern one which tends to conceive of play as essentially mimetic. Toys do not derive their pleasure from being mimetic objects; rather, they are essentially pleasure objects and as such only incidentally mirror the objects of (...) |
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The volume contains 11 contributions of the best experts on the topics of fate, fortune and free will, in reference to Ancient Philosophy: Plato, Aristotle, Stoicism, Epicureanism, Plotinus. |
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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 (...) |
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Despite the fact that the theory of Forms is regarded as the hallmark of Plato’s philosophy, it has remained remarkably elusive, because it is more hinted at than explained in his dialogues. Given the uncertainty concerning the nature and extension of the Forms, this article makes no pretense to coming up with solutions to all problems that have occupied scholars since antiquity. It aims to elucidate only two aspects of that theory: the indication in certain dialogues that the Forms are (...) |
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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 (...) |
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Sense experience, naïvely conceived, is a way of knowing perceptible properties: the colors, sounds, smells, flavors, and textures in our perceptual environment. So conceived, ordinary experience presents the perceiver with the essential nature of a property like Sky Blue or Middle C, such that how the property appears in experience is identical to how it essentially is. In antiquity, as today, it was controversial whether sense experience could meet the conditions for knowledge implicit in this naïve conception. Aristotle was a (...) |
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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 (...) |
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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 (...) |
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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 (...) |
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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, (...) |
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