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13588 results in History of science and technology

Page 214 of 680

  • Chapter 2 - Philolaus

  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book:
    A History of Pythagoreanism
    Published online:
    05 May 2014
    Print publication:
    24 April 2014, pp 46-68

  • Summary

    This chapter examines Philolaus of Croton the philosopher in an attempt to understand his contributions to fifth-century thought. The phrase "having number" seems to have a set meaning in the Pythagorean tradition. From Anaximander on, philosophy was often understood as the study of nature, and the study of nature began with cosmogony and cosmology. Carl Huffman has done much to rehabilitate Philolaus astronomy as a viable theory in the context of fifth-century knowledge. The chapter attempts to add some support for Huffman's assessment. Philolaus' astronomical scheme is praised on the one hand for anticipating the heliocentric theory, and damned on the other for being based on a priori assumptions. Aristotle describes the development of Greek philosophy in terms of different views about the principles (archai) and causes (aitia) among the early philosophers, and about how many principles and causes there are and of what sort.

  • Chapter 13 - The Peripatetics on the Pythagoreans

  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book:
    A History of Pythagoreanism
    Published online:
    05 May 2014
    Print publication:
    24 April 2014, pp 274-295

  • Summary

    The Peripatetic view of Pythagoras mirrors the split in the tradition that was present in the earliest sources: Aristoxenus of Tarentum follow Empedocles in being overwhelmingly positive, whereas Dicaearchus and Hieronymus are heirs to Heraclitus' bitter critique. In terms of amount of material, the Peripatetics put greatest emphasis on the way of life of Pythagoras and later Pythagoreans. Theophrastus succeeded Aristotle as head of the Lyceum in 322 and remained until 287. He certainly referred to the Pythagoreans in his contribution to the Peripatetic survey of human knowledge, the Physical Opinions, which systematically collected early Greek views about the natural world. A text about the Pythagoreans in the later tradition can, with more or less plausibility, be traced back to Eudemus. Dicaearchus, writing at the same time as Theophrastus, Eudemus and Meno, focuses not on Pythagorean contributions to the sciences but rather on the life of Pythagoras himself.

  • Chapter 8 - The problem of Pythagorean mathematics

  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book:
    A History of Pythagoreanism
    Published online:
    05 May 2014
    Print publication:
    24 April 2014, pp 167-184

  • Summary

    This chapter considers the development of Greek mathematical culture as a whole, and turns specifically to Pythagorean mathematics. A significant part of the Greek creative achievement in pure mathematics may be assigned to two such networks: the one found in Proclus' summary of early Greek mathematics, standardly understood to derive from Eudemus' history of geometry, and the one constituted by Archimedes, his correspondents. Proclus list includes three names from the archaic era: Thales, Mamercus and Pythagoras. Archytas was a major mathematician as well as a "Pythagorean". Some people Aristotle identified as "Pythagoreans" engaged in the systematic analogy between mathematical terms (numerical and musical) and other, cultural and physical phenomena. Certain ideas, or even members, are shared between groups and so the history of culture becomes a network of networks. The group of south Italian "Pythagoreans" was interested in pursuing analogies based on mathematical concepts, especially those of music and number.

  • Chapter 21 - Pythagoras in the Early Renaissance

  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book:
    A History of Pythagoreanism
    Published online:
    05 May 2014
    Print publication:
    24 April 2014, pp 435-453

  • Summary

    The Renaissance story of Pythagoras and Pythagorean wisdom, its religious and its scientific aspects alike, is a complicated one. One of the arresting dimensions of early Renaissance Pythagoreanism is consequent on the rediscovery of certain ancient sources. From Marsilio Ficino's viewpoint, Pythagoras' musical and theological debts were unquestionably to Orpheus. Not only did Ficino confront the twin Pythagorean notions of metensomatosis and metempsychosis, but he was drawn into speculating about the cycle of lives and of deaths, deaths that are inter-lives as lives are inter-deaths. This chapter shows that Ficino specifically identified as Pythagorean in his Platonic Theology 4.1.14-16, one that focuses, on the mystery and the symbolism of 12. It can serve to introduce what the Renaissance saw as Pythagoras'mathematical, though to us it is his arithmological legacy. Iamblichus gives the fullest ancient listing of the Symbola in his Protreptic, but provides long list in On the Pythagorean Life.

  • Chapter 4 - Sixth-, fifth- and fourth-century Pythagoreans

  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book:
    A History of Pythagoreanism
    Published online:
    05 May 2014
    Print publication:
    24 April 2014, pp 88-111

  • Summary

    In the variety of the figures of the sixth-, fifth- and fourth-century Pythagoreans it is possible to perceive partly overlapping categories, but hardly any feature common to all of them. This chapter talks about a "family resemblance". This means that certain Pythagoreans had characteristics in common with some Pythagoreans, but not with others. Thus, Hippasus, Theodorus of Cyrene, Philolaus and Archytas shared an interest in mathematics; Democedes, Alcmaeon and Iccus were engaged in medicine; Alcmaeon, Hippo, Philolaus and Ecphantus wrote on natural philosophy; Milo, Astylus of Croton, Iccus and Dicon of Kaulonia were Olympic victors, whereas Milo, Democedes, Hippasus and Archytas were involved in politics. The Pythagorists of comedy and the real Pythagorizers launched the tradition of the existence (and then the coexistence) within Pythagoreanism of different groups, as a result of which two fictional categories of Pythagoreans appeared, the scientific mathematici and the religious acusmatici.

  • Chapter 9 - Pythagorean harmonics

  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book:
    A History of Pythagoreanism
    Published online:
    05 May 2014
    Print publication:
    24 April 2014, pp 185-203

  • Summary

    Ptolemaaїs is the only Greek woman on record as a musical theorist. Most writings in Pythagorean harmonics after the fourth century BC were heavily influenced by Plato's Republic, with its rejection of empirical considerations and its insistence on the authority of reason, and especially by the cosmological and psychological implications of his musical construction of the World-Soul in the Timaeus. One of the Pythagorean approaches that Ptolemaїs describes seems nevertheless to preserve a pre-Platonic character, privileging reason over perception but still focused at least in part on the analysis of audible music; and so too do the Pythagoreans discussed by Ptolemy and Porphyry. The principle that a concord's ratio must be either multiple or epimoric has a significant consequence: the interval of an octave plus a fourth (which sense-perception, according to Aristoxenus, Ptolemy and many others, unquestionably recognizes as a concord) cannot really be concordant.

  • Chapter 11 - Aristotle on the “so-called Pythagoreans”: from lore to principles

  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book:
    A History of Pythagoreanism
    Published online:
    05 May 2014
    Print publication:
    24 April 2014, pp 227-249

  • Summary

    This chapter analyzes the most comprehensive account of the Pythagorean theory of principles in Aristotle's extant work: the first part of Metaphysics A5. It looks at the passage where Aristotle indicates what he considers to have been the intermediate steps, the additional premises, as it were, between the initial act of taking up the mathēmata and the fully fledged Pythagorean theory according to which the principles of the mathēmata are the principles of all things. The chapter deals with a piece of historiographical reasoning, which claims that some of the opinions attributable to the so-called Pythagoreans actually caused the coming-to-be of other opinions equally well attributable to them. The testimony provided by Alexander of Aphrodisias enables one to assess the function of the resemblances in Aristotle's historiographical reconstruction as outlined in Metaph. A5.

  • Chapter 16 - Pythagoreans in Rome and Asia Minor around the turn of the common era

  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book:
    A History of Pythagoreanism
    Published online:
    05 May 2014
    Print publication:
    24 April 2014, pp 341-359

  • Summary

    This chapter focuses on the city of Rome from the Late Republic up to and including the Julio-Claudian period, and on Asia Minor in the first and second centuries AD. It also discusses, in the case of Rome, both people to whom the label Pythagorean was applied and other members of the educated elite with an interest in Pythagoreanism. As for Asia Minor, two men who in the author's evidence are presented as not just following Pythagorean precepts, but as consciously modeling their public image after Pythagoras, are the center of attention: Apollonius of Tyana and Alexander of Abonouteichos. Both received biographical treatment, laudatory in the former case, defamatory in the latter. A treatment of Pythagoreanism at Rome during the Julio-Claudian period would be incomplete without mentioning the ongoing discussion about the subterranean basilica discovered in 1917 near the Porta Maggiore.

  • Chapter 20 - Pythagoras and Pythagoreanism in late antiquity and the Middle Ages

  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book:
    A History of Pythagoreanism
    Published online:
    05 May 2014
    Print publication:
    24 April 2014, pp 416-434

  • Summary

    This chapter surveys broad themes in the late ancient and medieval use of Pythagoras and the Pythagoreans beginning with a summary of Pythagoras' quadrivial legacy, followed by a resume of the music-theoretical heritage of Pythagoras musicus, and the natural philosophical heritage of Pythagoras physicus. Boethius begins the Fundamentals of Arithmetic with an account of philosophical knowledge from the standpoint of ontology. Fully in accord with what Proclus explicitly deems a Pythagorean classification of the mathematical sciences, Boethius divides the objects of mathematics into discrete quantity and continuous quantity. Cosmic music concerns the harmonic structures and periods of the celestial bodies, the delicate balance of the four elements, and the cyclical succession of the seasons. Undoubtedly the most important of Boethius "Pythagorean" legacies is his presentation of Pythagorean music theory in the Fundamentals of Music. There are two hints one lexical, the other contextual that Boethius intends sensus as sense perception.

  • Chapter 1 - Pythagoras

  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book:
    A History of Pythagoreanism
    Published online:
    05 May 2014
    Print publication:
    24 April 2014, pp 24-45

  • Summary

    The evidence for Pythagoras in Aristotle's lost work on the Pythagoreans is problematic, and what he has to say about him in the extant treatises amounts to very little. This chapter discusses the issues by going back some fifty years, to 1962, which happens to be the date of two highly influential books by supremely distinguished scholars. Plato has one important reference to Pythagoras, namely to the point that he taught his followers a way of life which later Pythagoreans continued to pursue. Pythagoras was certainly a historical figure and no mere legend, unlike Orpheus, Musaeus, Abaris and others. Certainly there is some convergence on the point that his teaching on the soul was exceptional, with most of our early sources suggesting that he taught a doctrine of metempsychosis. It is only in the Hellenistic period that Pythagoras' reputation as a mathematician, harmonic theorist and cosmologist takes off.

  • Chapter 15 - The pseudo-Pythagorean writings

  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book:
    A History of Pythagoreanism
    Published online:
    05 May 2014
    Print publication:
    24 April 2014, pp 315-340

  • Summary

    The content of the pseudo-Pythagorean writings results from a blending of Platonic and Aristotelian doctrines, which is typical of Platonism, beginning in the first century BC. Platonic doctrines are mediated by the academic tradition, which shapes the basic orientation of the treatises towards systematization and classification. Pythagoreanism became inextricably entwined with Platonism and came to exercise a far wider influence than its actual standing should have permitted. The theory of principles plays a fundamental role in all spheres of knowledge, but its very formulation contains innovative elements, which make the pseudo-Pythagorean system more than simply a repetition of early Academic doctrines. The Aristotelian doctrines are integrated within a Platonizing system: Aristotle's hylomorphism is thus interpreted in the light of the doctrine of Ideas, identified with Aristotelian Forms, and traced back to the two fundamental principles. The same reduction of Aristotelian notions to two principles occurs in cosmology, ethics and politics.

  • Chapter 17 - Diogenes Laertius’ Life of Pythagoras

    • By André Laks, Universidad Panamericana and Université de Paris-Sorbonne
  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book:
    A History of Pythagoreanism
    Published online:
    05 May 2014
    Print publication:
    24 April 2014, pp 360-380

  • Summary

    This chapter reviews the content of Book 8 of Lives and Opinions of Eminent Philosophers and explains its place within Diogenes Laertius' work. It discusses some specific features of Diogenes' picture of Pythagoras. If one wants to detect an overall interest in Diogenes' Life of Pythagoras, they must certainly locate it in the Pythagorean mode of life as reflected in the long lists of religious and ethical precepts. The chapter gives an analysis of the extended report about Diogenes' doctrines which plays a central function in the overall construction of the book. The report excerpted by Alexander Polyhistor and copied by Diogenes is itself a sample of pseudo-Pythagorean literature. The chapter addresses the problem of Diogenes' attitude towards Pythagoras. The Pythagorean Notes would be a testimony of an eclectic Pythagoreanism and also of an eclectic Pythagoreanism.

  • Chapter 3 - Archytas

  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book:
    A History of Pythagoreanism
    Published online:
    05 May 2014
    Print publication:
    24 April 2014, pp 69-87

  • Summary

    Archytas, a citizen of Tarentum on the Adriatic coast of southern Italy, and a contemporary of Plato, is a significant figure in the history of ancient Greek science. Carl Huffman offers a restrained account of Archytas so far as his work on music and in geometry is concerned. Diogenes Laertius includes an account of Archytas in the Pythagorean Book 8 of his Lives. The chapter discusses the main substance of Diogenes' biographical account. In commenting on Aristotle's Categories the sixth-century-AD Neoplatonist Simplicius quotes extensively from earlier authorities, included among them Archytas. The "Archytean writings" sounds like an abbreviated reference to the Extracts; and if that work demonstrated similarities between Plato's dialogue and passages from Archytas, the Timaeus' account of the receptacle and the movements to which it is subject would be a natural candidate for treatment.

  • Chapter 18 - Porphyry's Life of Pythagoras

  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book:
    A History of Pythagoreanism
    Published online:
    05 May 2014
    Print publication:
    24 April 2014, pp 381-398

  • Summary

    For centuries, Porphyry's Life of Pythagoras (Vita Pythagorae (VP)) and Iamblichus' On the Pythagorean Way of Life have conveyed idealized pictures of Pythagoras that continued to be canonic down to the nineteenth century. Before examining the VP this chapter looks at the History of Philosophy (HP) as a whole in order to find out how Pythagoras' biography fitted into this ambitious work. One of the aspects of the HP that immediately catches the attention is its essentially antiquarian, scholarly, and at the same time compilatory and derivative character. Porphyry probably organized his material in roughly chronological order by individual philosophers, i.e., neither by schools of thought nor by philosophical themes or questions. The chapter concludes that reading Porphyry's VP gives access to the state of Pythagoreanism in the first centuries AD and to its views of Pythagoras and the Pythagorean tradition.

Page 214 of 680