Thesis (Ph. D.)--University of Pennsylvania, 1911. / "The Introductionis arithmeticae libri duo ... is the basis of the present essay"--P. 1. Includes bibliographical references (p. 1).

Thesis (Ph. D.)--University of Pennsylvania, 1911. / "The Introductionis arithmeticae libri duo ... is the basis of the present essay"--P. 1. Includes bibliographical references (p. 1).

In this work I reconstruct the physical and mental descriptions of perception in Aristotle. I propose to consider the thesis that αἴσθησις is a μεσότης (DA II 11) as a description of the physiological aspect of perception, meaning that perceiving is a physical act by which the sensory apparatus homeostatically counterbalances, and thence measures, the incoming affection produced by external perceptible objects. The proposal is based on a revision of the semantics of the word mesotês in Plato, Aristotle and later Greek mathematicians (mostly Nicomachus of Gerasa). I show how this interpretation fits the text, and how it solves problems that afflict the rival interpretations. I further develop a ‘non-dephysiologizing’ spiritualist reading of the additional description of perception as reception of forms without the matter (DA II 12). I show that Aristotle uses the expression ‘forms without matter’ to describe actually abstracted items in one’s mind rather than the way in which the form are received. In opposition to forms-in-matter, such items are causally powerless and metaphysically sterile: an F-without-matter somewhat determines the subject it is in (one’s mind content F) without qualifying or identifying it as an F-subject. Thus, we have a second ‘mental’ description of perception. Further parts of the thesis are devoted to settle interpretive questions raised by controversial statements about perception found in De Anima II 5 and III 2, and to discuss the question of how the mental and physiological descriptions of perception Aristotle offers are related. My conclusion is that Aristotle’s views combines a form of quasi-dualist vitalism about powers (the faculty of perception, and more generally the soul, are not just irreducible to matter, but also primitive and non-supervenient) which is nonetheless compatible with hylomorphism, and a form of epiphenomenalism (and thence the ‘bottom-up’ determination typical of modern supervenience) with regard to perceptual events (i.e., the activity of perceiving).

It has been said that Pythagoras discovered the perfect musical intervals by chance when he heard sounds of hammers striking an anvil at a nearby smithy. The sounds corresponded to the same intervals Pythagoras had been studying. He experimented with various instruments and apparatus to confirm what he heard. Math, and in particular, numbers are connected to music, he concluded. The discovery of musical intervals and the icon of the musical blacksmith have been familiar tropes in history, referenced in literary, musical, and visual arts. Countless authors since Antiquity have written about the story of the discovery, most often found in theoretical texts about music. However, modern scholarship has judged the narrative as a myth and a fabrication. Its refutation of the story is peculiar because modern scholarship has failed to disprove the nature of Pythagoras’s discovery with valid physical explanations. This report examines the structural elements of the story and traces its evolution since Antiquity to the early modern period to explain how an author interprets the narrative and why modern scholarship has deemed it a legend. The case studies of Nicomachus of Gerasa, Claudius Ptolemy, Boethius, and Marin Mersenne reveal not only how the story about Pythagoras’s discovery functions for each author, but also how the alterations in each version uncover an author’s views on music. / text

Auteur romain du 6ème siècle connu pour ses traductions en latin des textes en grec d’Aristote, Boèce a aussi rédigé une traduction-adaptation d’un texte de Nicomaque de Gérase sur l’arithmétique. La première partie de ce mémoire de maîtrise est consacrée à l’étude de Boèce en tant que passeur de savoir. Sa relation avec son père adoptif est mise en valeur afin de soutenir l’hypothèse selon laquelle Boèce aurait acquis sa connaissance du grec et son éducation tout en restant à Rome, sans avoir séjourné dans les écoles athéniennes ou alexandriennes. La deuxième partie porte sur le contenu mathématique du De institutione arithmetica. Après avoir montré comment le De arithmetica était relié à l’oeuvre de traduction par Boèce des philosophes grecs, le choix de l’Introduction à l’Arithmétique de Nicomaque comme point de départ du traité d’arithmétique de Boèce est étudié. Un catalogue raisonné des concepts mathématiques présentés est ensuite proposé, organisé autour des notions de quantité en soi et quantité relative qui conservent l’opposition entre le Même et l’Autre et rappellent l’opposition fondamentale entre Limité et Illimité, si chère aux pythagoriciens. Ce mémoire se termine par une analyse de la transmission du De institutione arithmetica et de son influence sur les mathématiques et l’enseignement du quadrivium au Moyen-Âge. / Roman author of the 6th century known for his Latin translations of Aristotle’s Greek texts, Boethius has also composed a translation-adaptation of a treatise on arithmetics written by Nicomachus of Gerasa. The first section of this master’s thesis focuses on characterizing Boethius as a intermediary, transferring Greek knowledge to the Latin West. His relationship with Symmachus is highlighted in order to argue that Boethius had been able to learn Greek and reach such a high level of learning in Rome, without the need to study in the Athenian or Alexandrian schools of his time. The mathematical content of the De institutione arithmetica is the main topic of the second section. After showing how the De arithmetica is related to Boethius’ magnum opus – the Latin translation of the Greek philosophers – the choice of Nicomachus of Gerasa’ Introduction to Arithmetics as the source of Boethius’ treaty on arithmetics is studied. Then, a catalogue raisonné of the mathematical concepts showcased is provided, organized around the notions of quantity constant of itself and relative quantity which retain the opposition between the Same and the Other and stems from the pythagoricians’ fondamental opposition between the Limited and the Unlimited. This masters’ thesis ends with an analysis of the medieval transmission of the De institutione arithmetica and of its influence on medieval mathematics and education through the quadrivium.