Diss.--Philosophie--Nashville, Tenn., 1981. / Contient quelques exemples musicaux. Bibliogr. p. 436-445.

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Descartes' Meditations on First Philosophy is often hailed as one of the great classics of western philosophy. First-time readers of the Meditations are often struck by Descartes' clear and accessible writing style. Within recent scholarship (e.g., most notably, Amelie Osksenberg Rorty's collection of Essays on Descartes' Meditations [1986]), much attention has been focused toward examining the philosophical import of Descartes' literary techniques. In particular, discussions have centered upon whether there is a significant relationship between the literary format of Descartes' "Metaphysical Meditations" with that of religious devotional exercises, also known as meditations, that were prevalent during the early part of the seventeenth century. Although commentators are fairly equally divided on whether the stylistic devices employed by Descartes are philosophically important, there is general agreement that Descartes' text, at the very least, exemplifies the features of religious meditation. Building upon the efforts of previous scholarship, the focus of this present study is to provide a philosophically plausible and historically accurate account of how Descartes' Meditations are meditational. Much of our attention will be directed toward examining the different styles and techniques of religious meditation. In particular, we will examine the relevance of Marin Mersenne's recently rediscovered treatise L'usage de la raison (1623). This work exhibits features of an Augustinian style of religious meditation and it is a text which can be easily connected to Descartes. / Master of Arts

Cette thèse doctorale prétend contribuer, premièrement, à soumettre à discussioncette interprétation dominante de la pensée philosophique et scientifique du PèreMinime Marin Mersenne (1588-1648), étant portée et structurée par la question duscepticisme, et deuxièmement, à mettre en avant la manière dont cette philosophieincarne l’esprit de la révolution scientifique du XVIIe siècle par sa capacité de se mettreen question dans sa recherche insatiable de la vérité; une recherche accompagnée d’unsouci de conservation de l’ordre politique et religieux. L’hypothèse principale de notretravail consiste à affirmer une profonde transformation dans la conception de la musique: transformation qui mène d’une science quadriviale et subalterne aux mathématiques,exigeant la soumission au jugement de la raison dans la pratique, à une science physiqueet mathématique, dont la recherche se fonde sur de nombreuses expériences,reconnaissant l’individualité de l’expérience esthétique, la liberté de l’imagination descompositeurs et le caractère ineffable du sublime musical. Il s’agit d’une transformationqui n’est pas exempte de difficultés, car elle ne conduit pas simplement à affirmerl’existence de deux périodes dans la pensée de Mersenne. En effet, il exprime ses doutessur la pertinence de l’approche spéculative lorsqu’il discute avec ses correspondants surla réforme musicale proposée à l’imitation des anciens et ne cesse de rappeler laperfection des rapports numériques des consonances lorsqu’il est prêt à les mettre enquestion en acceptant et en cherchant les fondements de la pratique de l’accordage desinstruments. Or, malgré cette complexité (voire ces contradictions) nous jugeons et nousprétendons montrer que cette transformation est indéniable et que l’épistémologie duMinime doit être analysée à la lumière des problématiques et de nouvelles expériencesscientifiques auxquelles il est confronté et non comme une manière de donner réponseaux arguments du scepticisme. / This PhD dissertation provides a critical perspective of the dominantinterpretation of the scientific and philosophical works of Father Marin Mersenne(1588-1648) entirely structured by the sceptical question. The development of his ideasabout music embodies the spirit of the scientific revolution which emerges in theseventeenth-century. His investigation has the capacity to put his methods into questionwith an insatiable quest for the truth; a quest that involves political and religiousconcerns. The aim of this study is to show a profound transformation in the conceptionof music. This transformation that leads from a science of the quadrivium (subordinateto mathematics and claiming superiority of the judgement of reason) to a physical andmathematical science grounded on experience that recognizes the individuality of theesthetic experience, the liberty of the imagination of the composers and the ineffabilityof the sublime. It is quite difficult however to identify the existence of two differentstages in Mersenne’s thought. It is surprising how he expresses doubts about therelevance of the speculative approach to music whereas a musical reform is proposed inhis apologetic writings, having as a model the perfection of proportions of consonancesand rhythmic combinations well known by the ancients. And also, when he accepts thepractice of musical temperament, challenging the observation of the mathematicalperfection, he will continue to remind the proportions underlying the consonances.Despite this complexity (even these contradictions) we consider and pretend to showthat this transformation is undeniable and that the Mersenne epistemology must beanalysed according to the scientific questions and experiences which he faces in hisinvestigations and not as a response to a sceptical crisis.

Thesis (Ph. D.)--Indiana University, 2005. / Computer printout. Source: Dissertation Abstracts International, Volume: 66-02, Section: A, page: 0404. Chair: Frank Samarotto. Includes bibliographical references (leaves 407-419), abstract, and vita.

Submitted by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-10-15T14:32:35Z No. of bitstreams: 1 arquivototal.pdf: 916082 bytes, checksum: 03e747a0ecd5819058ba4e050a1383b8 (MD5) / Approved for entry into archive by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-10-15T15:01:57Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 916082 bytes, checksum: 03e747a0ecd5819058ba4e050a1383b8 (MD5) / Made available in DSpace on 2015-10-15T15:01:57Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 916082 bytes, checksum: 03e747a0ecd5819058ba4e050a1383b8 (MD5) Previous issue date: 2013-08-15 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis we study some topics of the Theory of Numbers as an inspiration for future studies of Perfect Numbers and Mersenne Primes. We present some important results for our study and analyze some statements of Fermat's Little Theorem, showing the various mathematical demonstrations that proved under various logical aspects. We have clari ed some historical aspects and conjectures for perfect numbers, through a simple narrative of facts and this will certainly give us the emphasis that have motivated and still motivates many mathematicians for the study of Perfect Numbers. / Nesta dissertação fazemos um estudo de alguns tópicos da Teoria dos Números como motivação para o estudo dos Números Perfeitos e Primos de Mersenne. Apresentamos alguns resultados importantes para o nosso estudo e analisamos algumas demonstrações do Pequeno Teorema de Fermat, evidenciando a demonstração de vários matemáticos que os provaram sob vários aspectos lógicos. Evidenciamos alguns aspectos históricos e conjecturas para os números perfeitos, através de uma narrativa simples dos fatos e que certamente nos dão a ênfase que motivou e motiva vários matemáticos para o estudo dos números perfeitos.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-29T15:44:42Z No. of bitstreams: 1 arquivototal.pdf: 691607 bytes, checksum: 68ddd45857d5c0c6e60229a957089adf (MD5) / Approved for entry into archive by Fernando Souza (fernandoafsou@gmail.com) on 2017-08-29T15:47:36Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 691607 bytes, checksum: 68ddd45857d5c0c6e60229a957089adf (MD5) / Made available in DSpace on 2017-08-29T15:47:36Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 691607 bytes, checksum: 68ddd45857d5c0c6e60229a957089adf (MD5) Previous issue date: 2014-08-01 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work presents a study of prime numbers, how they are distributed, how many prime numbers are there between 1 and a real number x, formulas that generate primes, and a generalization to Bertrand's Postulate. Six proofs that there are in nitely many primes using reductio ad absurdum, Fermat numbers, Mersenne numbers, Elementary Calculus and Topology are discussed. / Este trabalho apresenta um estudo sobre os números primos, como estão distribu ídos, quantos números primos existem entre 1 e um número real x qualquer, fórmulas que geram primos, além de uma generalização para o Postulado de Bertrand. São abordadas seis demonstrações que mostram que existem in nitos números primos usando redução ao absurdo, Números de Fermat, Números de Mersenne, Cálculo Elementar e Topologia.

Le manuscrit 2884 est un autographe du père Mersenne, unique exemplaire conservé à la bibliothèque de l’Arsenal. Cet écrit constitué en livre et chapitres est une théorie spéculative du son et des consonances inachevée. Comme le manuscrit n’a jamais été édité nous en proposons la transcription selon deux pratiques différentes, une selon le modèle de l’École nationale des Chartes et l’autre diplomatique selon le laboratoire de l’ITEM spécialisé dans les brouillons d’écriture. La transcription est complétée par des notes critiques et historiques, une table des théorèmes reconstituée, d’un index des noms propres. Le fac-simile du manuscrit est proposé dans un volume à part. Dans la première partie une étude codicologique permet de situer le manuscrit dans son aspect matériel. Une étude génétique détermine ses liens avec les imprimés du père Mersenne et retrace son parcours général de rédaction. La dernière partie de la thèse tente de cerner les motifs de son abandon par une analyse comparative avec quelques livres de l’Harmonie Universelle. Notre hypothèse de départ repose sur un changement de philosophie naturelle, passage de la philosophie aristotélicienne à la philosophie d’inspiration galiléenne. En effet nous montrons que tout le discours tenu dans le manuscrit 2884 est ontologiquement fondé dans la conception aristotélicienne alors que les mêmes sujets abordés dans l’Harmonie Universelle manifestent une rupture avec ce fondement ontologique ainsi qu’une profonde évolution de ses idées. / Manuscript 2884 is an autograph by Marin Mersenne, a unique document preserved in the Arsenal Library. This writing formed of books and chapters is an unfinished speculative theory of sound and consonance. As the manuscript has never been edited we propose a transcription following two different usages, the first according to the model of the École nationale des Chartes and the second a diplomatic transcription according to the laboratory of the ITEM (Institut des Textes et Manuscrits modernes) specializing in drafts of texts. The transcriptions are supplemented by critical and historical notes, a reconstructed table of theorems and an index of proper names. The facsimile of the manuscript is proposed in a separate volume. In the first part, a codicological study makes it possible to describe the manuscript in its material aspect. A genetic study determines its links with the printed works of Marin Mersenne and traces its general course of writing. The last part of the thesis attempts to define the reasons for its abandonment by a comparative analysis with some books of Harmonie Universelle. Our initial hypothesis supposes a change in natural philosophy, a change from Aristotelian philosophy to a philosophy of Galilean inspiration. We show that the discourse held in manuscript 2884 as a whole is ontologically based in the Aristotelian conception whereas the same subjects approached in Harmonie Universelle show a break with this ontological foundation as well as a profound evolution of Mersenne’s ideas.

We investigate the origins of mathematical societies and journals. We argue that the origins of today’s professional societies and journals have their roots in the informal gatherings of mathematicians in 17th century Italy, France, and England. The small gatherings in these nations began as academies and after gaining government recognition and support, they became the ancestors of the professional societies that exist today. We provide a brief background on the influences of the Renaissance and Reformation before discussing the formation of mathematical academies in each country.