The king therefore went down to the village, since the Wise Men's rule did not permit him to spend more than a day with them, but Iarchas said to the messenger, ‘Damis too we consider worthy of the secrets here, so tell him to come, while you look after the others in the village.’ When Damis had come, the Wise Men formed their usual circle and gave Apollonius permission to put questions. So he asked what they thought the (...) universe consisted of, to which they replied, ‘Elements.’ ‘Four, do you think?’ he said. ‘Not four’, said Iarchas, ‘but five.’ ‘What could a fifth one be’, said Apollonius, ‘besides water, air, earth, and fire?’ ‘Ether’, said Iarchas, ‘which we must consider to be the origin (γένεσιν) of the gods. All that breathes air is mortal, but what breathes ether is immortal and divine.’ Next Apollonius asked which of the elements came into existence first. ‘All came together’, said the other, ‘since a living being is not born one piece at a time.’ ‘Am I to consider the universe living?’, asked Apollonius. ‘Yes, if you reason correctly’, said Iarchas, ‘since itself it gives life to everything.’ ‘Should we then call it female’, asked Apollonius, ‘or of the contrary, male sex?’ ‘Of both’, was the answer, ‘since it has intercourse with itself, and performs both the mother's and the father's role with respect to generation. It feels a desire for itself more intense than that of any two other beings, and this joins and unites it, and there is nothing unreasonable about its coalescence. And just as the action of the hands and feet in a living creature comes from mobility and the intelligence (διὰ τὸν ἐκείνου νοῦν) that causes it, so also we must suppose that, because of the intelligence of the universe (κατὰ τὸν ἐκείνου ϕοιτᾷ νοῦν), its parts accommodate themselves to everything that undergoes birth and conception. For instance, the sufferings resulting from drought arise from the mind of the universe, when justice is banished from mankind and treated with dishonor. And this being guides itself not by one hand alone but by many unseen ones that it uses; though too large to be restrained, it moves obediently and tractably.’The doctrine contained in this extract – the only passage ofThe Life of Apollonius of Tyanatreating matters of ‘cosmogony’ – could be summarized in the six following propositions. First, the universe consists of five, not four elements, the fifth being the ether, the γένεσις θεῶν. Just as mortals breathe air, gods breathe ether. Secondly, there is no ‘primordial element’; all five came into being simultaneously. Thirdly, the universe is a living being. In the fourth place, the universe is both male and female at the same time. In the fifth place, as the universe is androgynous it feels desire (ἔρως) towards itself and it is this desire that makes it whole and united. And finally, the passion of the universe for itself is governed by Intelligence (ἐκείνου νοῦς). (shrink)

Epitome V (1621), and consisted of matching an element of area to an element of time, where each was mathematically determined. His treatment of the area depended solely on the geometry of Euclid's Elements, involving only straight-line and circle propositions – so we have to account for his deliberate avoidance of the sophisticated conic-geometry associated with Apollonius. We show also how his proof could have been made watertight according to modern standards, using methods that lay entirely within his (...) power. The greatest innovation, however, occurred in Kepler's fresh formulation of the measure of time. We trace this concept in relation to early astronomy and conclude that Kepler's treatment unexpectedly entailed the assumption that time varied nonuniformly; meanwhile, a geometrical measure provided the independent variable. Even more surprisingly, this approach turns out to be entirely sound when assessed in present-day terms. Kepler himself attributed the cause of the motion of a single planet around the Sun to a set of `physical' suppositions which represented his religious as well as his Copernican convictions; and we have pared to a minimum – down to four – the number he actually required to achieve this. In the Appendix we use modern mathematics to emphasize the simplicity, both geometrical and kinematical, that objectively characterizes the Sun-focused ellipse as an orbit. Meanwhile we highlight the subjective simplicity of Kepler's own techniques (most of them extremely traditional, some newly created). These two approaches complement each other to account for his success. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Two Sonnets DANIEL GALEF Thales to Thratta (spoken by “The Astrologer Who Fell into a Well”) All things are full of spirits. So said I, who plumbed the well of science, saw the sun made black and tracked its course across the sky, who, armed with muscle, wrote the river’s run. Where is my spirit? Thratta! I feel cold and wet. This well is deep. The world is wet (...) and cold. The world I knew was filled with gold and fire.... How quick the Olympic sun has set, how quick my words rewritten, and my land made palimpsest. The sea has left Miletus, the shore on which I walked and lectured—and the wise men who walked with me, whom I taught. The boundless sea, whose tides once rose to meet us has changed its shape, moved on. But I cannot. arion 27.2 fall 2019 Eudemus to Apollonius (spoken by the dedicatee of Apollonius of Perga’s first books of the Conic Sections) I write this note in the sand because I know the waves will wash it clean, and you won’t see it. Like the circles we traced here so long ago, our footprints fade from Pergamum. So be it. Your book was well-received. As was your son; his seems the echo of your dimming face. How did my thoughts, which like an hour-glass run, once hold the eternal laws of boundless space? The beach bends on forever. How might a man reckon every mote, each grit and grain? The universe of truths seems greater than could ever fit within the human brain— Yet love, which binds over such a greater span, all mortals its completeness can contain. 104 two sonnets... (shrink)

The latest book of Reviel Netz presents a highly erudite analysis of the style of Hellenistic mathematics. Besides the Introduction and Conclusion the book is composed of four chapters. Before turning to more general remarks I would like first to outline the contents of the book.The Introduction starts with the presentation of Archimedes’ Spiral lines. In a condensed form, the author outlines his approach and calls attention to the stylistic peculiarities of that work. Most of the themes discussed in more (...) detail in the following chapters, such as the analysis of the narrative structure of the treatise, its working with surprise, the exposition of the rhetorical devices, the discussion of technical tools, and the breaking of genre-boundaries emerge here side by side in a single treatise.The first chapter, called The carnival of calculation, starts with another work of Archimedes, the Stomachion, for which Netz offers a new interpretation as a treatise in geometrical combinatorics. Then he turns to Archimedes’ On the measurement of the circle, where, in a detailed analysis of the calculations made by Archimedes, Netz presents a pattern that he identifies in several other works of Hellenistic mathematics, a pattern he calls ‘asymptotic calculation’. It consists in a combination of strict geometric arguments with calculations of proportions, some precise, some only approximate, which together with rather arbitrary simplifications lead to a result that is achieved after an abrupt and unexpected halt. Netz shows that, according to the surviving testimonies, a similar pattern can be found in many Hellenistic authors, such as Aristarchus, Hipparchus, and Apollonius of Perga. "[I]n many Hellenistic mathematical works we see calculations that give rise to values that are big and unwieldy, or else are only asymptotically found. Such calculations end up not with the satisfaction of having simplified … ". (shrink)

The Greek astronomer and geometrician Apollonius of Perga produced pioneering written work on conic sections in which he demonstrated mathematically the generation of curves and their fundamental properties. His innovative terminology gave us the terms 'ellipse', 'hyperbola' and 'parabola'. The Danish scholar Johan Ludvig Heiberg, a professor of classical philology at the University of Copenhagen, prepared important editions of works by Euclid, Archimedes and Ptolemy, among others. Published between 1891 and 1893, this two-volume work contains the definitive Greek text (...) of the first four books of Apollonius' treatise together with a facing-page Latin translation. Volume 2 contains the fourth book in addition to other Greek fragments and ancient commentaries, notably that of Eutocius, as well as the editor's Latin prolegomena comparing the various manuscript sources. (shrink)

The Argonautica is the dramatic story of Jason's quest for the Golden Fleece and his relations with the dangerous Colchian princess, Medea. The only extant Greek epic poem to bridge the gap between Homer and late antiquity, it is a major product of the brilliant world of the Ptolemaic court at Alexandria, written by Apollonius of Rhodes in the 3rd century BC. Apollonius explores many of the fundamental aspects of life in a highly original way: love, deceit, heroism, (...) human ignorance of the diven, the limits of science. This volume offers the first scholarly translation into English prose for many years, combining readability with accuracy and an attention to detail that will appeal to readers both with and without Greek. `Based on a deep understanding of the text, this translation, with informative notes and an excellent introduction, will bring Apollonius to the audience he deserves....' ABOUT THE SERIES: For over 100 years Oxford World's Classics has made available the widest range of literature from around the globe. Each affordable volume reflects Oxford's commitment to scholarship, providing the most accurate text plus a wealth of other valuable features, including expert introductions by leading authorities, helpful notes to clarify the text, up-to-date bibliographies for further study, and much more. (shrink)

The Greek astronomer and geometrician Apollonius of Perga produced pioneering written work on conic sections in which he demonstrated mathematically the generation of curves and their fundamental properties. His innovative terminology gave us the terms 'ellipse', 'hyperbola' and 'parabola'. The Danish scholar Johan Ludvig Heiberg, a professor of classical philology at the University of Copenhagen, prepared important editions of works by Euclid, Archimedes and Ptolemy, among others. Published between 1891 and 1893, this two-volume work contains the definitive Greek text (...) of the first four books of Apollonius' treatise together with a facing-page Latin translation. Volume 1 contains the first three books, with the editor's introductory matter in Latin. (shrink)

The Greek astronomer and geometrician Apollonius of Perga produced pioneering written work on conic sections in which he demonstrated mathematically the generation of curves and their fundamental properties. His innovative terminology gave us the terms 'ellipse', 'hyperbola' and 'parabola'. The Danish scholar Johan Ludvig Heiberg, a professor of classical philology at the University of Copenhagen, prepared important editions of works by Euclid, Archimedes and Ptolemy, among others. Published between 1891 and 1893, this two-volume work contains the definitive Greek text (...) of the first four books of Apollonius' treatise together with a facing-page Latin translation. Volume 1 contains the first three books, with the editor's Latin introductory matter. Volume 2 contains the fourth book in addition to other Greek fragments and ancient commentaries, notably that of Eutocius. (shrink)

Revision of the author's thesis--Oxford University, 1977. Bibliography: p.[142]-144.

Chapter INTRODUCTION: OTTO NEURATH, THE VIENNA CIRCLE AND THE PROTOCOL SENTENCE DEBATE Everybody familiar with contemporary analytical philosophy is likely ...

The tendency to attribute foundationalist ambitions to the Vienna Circle has long obscured our view of its attempted revolution in philosophy. The present paper makes the case for a consistently epistemologically anti-foundationalist interpretation of all three of the Circle's main protagonists: Schlick, Carnap, and Neurath. Corresponding to the intellectual fault lines within the Circle, two ways of going about the radical reorientation of the pursuit of philosophy will then be distinguished and the contemporary potential of Carnap's and (...) Neurath's project explored. (shrink)

Discussions of the relation between pragmatism and logical empiricism tend to focus on the period when the logical empiricists found themselves in exile, mostly in the United States, and then attempt to gauge the actual extent of their convergence. My concern lies with the period before that and the question whether pragmatism had an earlier influence on the development of logical empiricism, especially on the thought of the former members of the “first” Vienna Circle. I argue for a substantially (...) qualified affirmative answer. (shrink)

Apollonius Dyscolus’ use of ambiguity in grammatical problem-solving has in recent years had the benefit of two scholarly studies. David Blank, in the course of his analysis of the Syntax as a whole , has described the broad functions which Apollonius assigns to ambiguity. Jean Lallot's 1988 paper, ‘Apollonius Dyscole et l'ambigüité linguistique: problemes et solutions’, is devoted exclusively to the treatment of linguistic ambiguity in Apollonius’ work. Yet it is to be feared that the flood (...) of light thrown by these scholars on what had been an unregarded corner of ancient grammar has shown up rather more than Apollonius would have cared to admit, both about the nature, and about the prospects for success, of the enterprise on which he was engaged. At the same time, certain structural features of ancient grammar, at least of the ancient grammar which Apollonius himself constructed, have come into sharper focus: features clear enough with the benefit of hindsight, but glimpsed, it appears, all too dimly by Apollonius himslf. It is now worryingly clear not only that ambiguity was ambiguous for Apollonius, but also that the ambiguity of ambiguity represented a genuine threat to the coherence and value of his work. In this paper I set out to justify both these claims. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This article makes two claims. The first is that Archimedes’ On Floating Bodies included a punning reference, in its key diagrammatic figure AΠΟΛ: the precise purpose of the pun may not be recovered by us, but even so it remains a powerful example of the playful in Archimedes’ writing. The second is that Apollonius could have been Archimedes’ younger contemporary. The outcome could be that we find Archimedes addressing a playful, hidden message to Apollonius, providing us with a (...) unique insight into the communication of Greek mathematics. (shrink)

The dualism of emic and etic plays a crucial role in the emergence of three culturally informed approaches of psychology: cross-cultural psychology , cultural psychology and indigenous psychologies , a distinction largely accepted nowadays. Similarities and/or differences between these positions are usually discussed either on the level of phenomena or theory. In this paper, however, the discussion takes place on a meta-theoretical or epistemological level, which is also emerging elsewhere. In following several earlier papers of the author, first, four perspectives (...) are distinguished that underlie present day psychology. Second, these are used as a framework for linking them to the three “camps”. This analysis will show that these perspectives are characterized by different underlying worldviews, interests as well as methodical preferences. Third, it is claimed that this level of discussion is quite fruitful for the ongoing discourse on the three camps, but also helps one to understand, why the duality between emic and etic approaches is—implicitly or explicitly—at the core of these discussions, because their relevance turns out to differ in the three camps. In that sense, the emic/etic duality is used here as a “litmus test” to exemplify these deeper differences between the camps, thereby highlighting them. Fourth, in order to overcome not only the dilemma between the unique and general in psychology, but also to clarify the relation between the individual and culture it is proposed that psychology should take human action as its unit of analysis, thereby connecting historically to the early beginnings of psychology at the end of the 19th century. It will be argued that a culture inclusive action theory may overcome this tension and may help to integrate western and other indigenous psychologies, and hence it could be advantageous to integrate CP and IPs as well. This is possible because the proposed theory hopefully provides a universal framework for psychological concepts, yet allows for their culture specific expression. (shrink)

This work brings in both the original German and English translation of over one hundred short essays in philosophical logic and the philosophy of mind of historical importance to understanding Wittgenstein's philosophical thought and development in the 1930's. Transcribed from the papers of Friedrich Waismann and dating from 1932-35, the majority are highly important dictations by Wittgenstein to Waismann, but also includes texts of redrafted material by Waismann closely based on the dictations. Many of these texts become the ultimate sources (...) of material on philosophy of language that constitutes the bulk of Waismann's book Logic, Sprache, Philosophy. The transcriptions throw light on the development of Wittgenstein's thought in this period and some of the topics are not covered in any of the existing publications of his writings, in particular his detailed attention to causal theories of meaning. They also contain texts covering psychological concepts such as expecting, intending and experience; these have no counterparts in Waismann's publications. (shrink)

Both within and among churches that have traditionally held to just war teaching, various formulas in the last fifty years have allowed for the recognition that Christian pacifism is a respectable tradition alongside just war. It is not obvious, however, how historic peace churches can officially reciprocate with the same kind of ecumenical generosity by recognizing the legitimacy of the just war tradition. To do so, after all, would seem to require giving up their very claim to the confessional status (...) of nonviolence, thus undermining their very identities as historic peace churches. Glen Stassen's well-accepted exegesis of Jesus's Sermon on the Mount opens up an unexpected path out of this impasse. If he is right that the sermon is organized around a consistent succession of triads in which Jesus first named "traditional righteousness,'' then diagnosed a "vicious cycle," then presented a "transforming initiative" for escaping that cycle, then the relationship between just war and pacifism can be reconceived in entirely fresh ways. (shrink)

My final aim in this paper is to show that Descartes is not guilty, as is so often maintained, of circular argumentation in the Meditations. But first it is important to uncover and remove certain tenacious misconceptions and confusions concerning what goes on in the Meditations which lend credence to the charge of circular argumentation. In this connection Mr. Harry Frankfurt's recent article, “Memory and the Cartesian Circle,” is peculiarly instructive; for it presents not only a completely untenable defence (...) of Descartes but one that, implicitly at least, rests on the very misconceptions that give substance to the notion of a Cartesian Circle. With the intention, then, of clearing the ground for the construction of my own defence of Descartes, I shall spend the first part of this paper examining Frankfurt's central thesis, the errors contained in it, and their sources. This thesis is contained in his statement, which I shall henceforth designate by the letter “J,” “Descartes did not attempt to justify present clear and distinct perceptions.”. (shrink)