The Early Modern Debate on the Problem of Matter's Divisibility: a Neo- Aristotelian Solution
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Achievements and Fallacies in Hume's Account of Infinite
-1- ACHIEVEMENTS AND FALLACIES IN HUME’S ACCOUNT OF INFINITE DIVISIBILITY James Franklin Hume Studies 20 (1994): 85-101 Throughout history,almost all mathematicians, physicists and philosophers have been of the opinion that space and time are infinitely divisible. That is, it is usually believedthat space and time do not consist of atoms, but that anypiece of space and time of non-zero size, howeversmall, can itself be divided into still smaller parts. This assumption is included in geometry,asinEuclid, and also in the Euclidean and non- Euclidean geometries used in modern physics. Of the fewwho have denied that space and time are infinitely divisible, the most notable are the ancient atomists, and Berkeleyand Hume. All of these assert not only that space and time might be atomic, but that theymust be. Infinite divisibility is, theysay, impossible on purely conceptual grounds. In the hundred years or so before Hume’s Tr eatise, there were occasional treatments of the matter,in places such as the Port Royal Logic, and Isaac Barrow’smathematical lectures of the 1660’s, 1 Theydonot add anything substantial to medievaltreatments of the same topic. 2 Mathematicians certainly did not take seriously the possibility that space and time might be atomic; Pascal, for example, instances the Chevalier de Me´re´’s belief in atomic space as proof of his total incompetence in mathematics. 3 The problem acquired amore philosophical cast when Bayle, in his Dictionary, tried to showthat both the assertion and the denial of the infinite divisibility of space led to contradictions; the problem thus appears as a general challenge to "Reason". -
Continuity Properties and Infinite Divisibility of Stationary Distributions
The Annals of Probability 2009, Vol. 37, No. 1, 250–274 DOI: 10.1214/08-AOP402 c Institute of Mathematical Statistics, 2009 CONTINUITY PROPERTIES AND INFINITE DIVISIBILITY OF STATIONARY DISTRIBUTIONS OF SOME GENERALIZED ORNSTEIN–UHLENBECK PROCESSES By Alexander Lindner and Ken-iti Sato Technische Universit¨at of Braunschweig and Hachiman-yama, Nagoya ∞ −Nt− Properties of the law µ of the integral R0 c dYt are studied, where c> 1 and {(Nt,Yt),t ≥ 0} is a bivariate L´evy process such that {Nt} and {Yt} are Poisson processes with parameters a and b, respectively. This is the stationary distribution of some generalized Ornstein–Uhlenbeck process. The law µ is parametrized by c, q and r, where p = 1 − q − r, q, and r are the normalized L´evy measure of {(Nt,Yt)} at the points (1, 0), (0, 1) and (1, 1), respectively. It is shown that, under the condition that p> 0 and q > 0, µc,q,r is infinitely divisible if and only if r ≤ pq. The infinite divisibility of the symmetrization of µ is also characterized. The law µ is either continuous-singular or absolutely continuous, unless r = 1. It is shown that if c is in the set of Pisot–Vijayaraghavan numbers, which includes all integers bigger than 1, then µ is continuous-singular under the condition q> 0. On the other hand, for Lebesgue almost every c> 1, there are positive constants C1 and C2 such that µ is absolutely continuous whenever q ≥ C1p ≥ C2r. For any c> 1 there is a positive constant C3 such that µ is continuous-singular whenever q> 0 and max{q,r}≤ C3p. -
Re-Construction and Definition of New Branches & Hierarchy of Sciences
Philosophy Study, July 2016, Vol. 6, No. 7, 377-416 doi: 10.17265/2159-5313/2016.07.001 D DAVID PUBLISHING New Perspective for the Philosophy of Science: Re-Construction and Definition of New Branches & Hierarchy of Sciences Refet Ramiz Near East University In this work, author evaluated past theories and perspectives behind the definitions of science and/or branches of science. Also some of the philosophers of science and their specific philosophical interests were expressed. Author considered some type of interactions between some disciplines to determine, to solve the philosophical/scientific problems and to define the possible solutions. The purposes of this article are: (i) to define new synthesis method, (ii) to define new perspective for the philosophy of science, (iii) to define relation between new philosophy perspective and philosophy of science, (iv) to define and organize name, number, relations, and correct structure between special science branches and philosophy of science, (v) to define necessary and sufficient number of branches for philosophy of science, (vi) to define and express the importance and place of new philosophy of science perspective in the new system, (vii) to extend the definition/limits of philosophy of science, (viii) to re-define meanings of some philosophical/scientific theories, (ix) to define systematic solution for the conflicts, problems, confusions about philosophy of science, sciences and branches of science, (x) to define new branches of science, (xi) to re-construct branches and hierarchy of science, (xii) to define new theories about science and branches of science. Author considered R-Synthesis as a method for the evaluation of the philosophy, philosophy of science, sciences and branches of science. -
Richard Swinburne's Arguments for Substance Dualism
Richard Swinburne’s arguments for substance dualism. MA by Research in Theology and Religion David Horner September 2018 Richard Swinburne’s arguments for substance dualism. Submitted by David Horner to the University of Exeter as a dissertation for the degree of MA by Research in Theology and Religion in September 2018 This dissertation is available for Library use on the understanding that it is copyright material and that no quotation from the dissertation may be published without proper acknowledgement. I certify that all material in this dissertation which is not my own work has been identified and that no material has previously been submitted and approved for the award of a degree by this or any other University. 1 Acknowledgements. I would like to thank my supervisors, Dr Jonathan Hill and Dr Joel Krueger for their support and encouragement in the writing of this dissertation and for their patience in trying to keep me on the straight and narrow. I want to acknowledge the many conversations, on this and other topics, I have had with my friend and philosopher, Dr Chris Boyne, who sadly died in June of this year. I thank all my other chums at The Bull, Ditchling, for listening to my metaphysical ramblings. And finally, I thank my wife, Linda, for once more putting up with this kind of thing. 2 Abstract This dissertation is a contribution to debates in the philosophy of mind and of personal identity. It presents a critical account of arguments for substance dualism to be found in Richard Swinburne’s Mind, Brain, and Free Will (2013). -
A Historical Introduction to the Philosophy of Science, Fourth Edition
A Historical Introduction to the Philosophy of Science, Fourth edition John Losee OXFORD UNIVERSITY PRESS A Historical Introduction to the Philosophy of Science This page intentionally left blank A Historical Introduction to the Philosophy of Science Fourth edition John Losee 1 3 Great Clarendon Street, Oxford ox2 6dp Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Athens Auckland Bangkok Bogotá Buenos Aires Calcutta Cape Town Chennai Dar es Salaam Delhi Florence Hong Kong Istanbul Karachi Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi Paris São Paulo Shanghai Singapore Taipei Tokyo Toronto Warsaw with associated companies in Berlin Ibadan Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © John Losee , The moral rights of the author have been asserted Database right Oxford University Press (maker) First published All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organizations. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose this same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available ISBN ––– Typeset in Adobe Minion by RefineCatch Limited, Bungay, Suffolk Printed in Great Britain by Biddles Ltd., Guildford and King’s Lynn Preface This book is a historical sketch of the development of views about scientific method. -
On Theodorus' Lesson in the Theaetetus 147D-E by S
On Theodorus’ lesson in the Theaetetus 147d-e by S. Negrepontis and G. Tassopoulos In the celebrated Theaetetus 147d3-e1 passage Theodorus is giving a lesson to Theaetetus and his companion, proving certain quadratic incommensurabilities. The dominant view on this passage, expressed independently by H. Cherniss and M. Burnyeat, is that Plato has no interest to, and does not, inform the reader about Theodorus’ method of incommensurability proofs employed in his lesson, and that, therefore, there is no way to decide from the Platonic text, our sole information on the lesson, whether the method is anthyphairetic as Zeuthen, Becker, van der Waerden suggest, or not anthyphairetic as Hardy-Wright, Knorr maintain. Knorr even claims that it would be impossible for Theodorus to possess a rigorous proof of Proposition X.2 of the Elements, necessary for an anthyphairetic method, because of the reliance of the proof of this Proposition, in the Elements, on Eudoxus principle. But it is not difficult to see that Knorr’s claim is undermined by the fact that an elementary proof of Proposition X.2, in no way involving Eudoxus principle, is readily obtained either from the proof of Proposition X.3 of the Elements itself (which is contrapositive and thus logically equivalent to X.2), or from an ancient argument going back to the originator of the theory of proportion reported by Aristotle in the Topics 158a-159b passage. The main part of the paper is devoted to a discussion of the evidence for a distributive rendering of the plural ‘hai dunameis’ in the crucial statement, ’because the powers (‘hai dunameis’) were shown to be infinite in multitude’ in 147d7-8 (contrary to the Burnyeat collective, set-theoretic rendering), necessarily resulting in an anthyphairetic method for Theodorus’ proofs of incommensurability (contrary to the Cherniss-Burnyeat neutrality thesis). -
Early Greeks and Aristotle
Topics Moore Chaps 1 & 2: Early Greeks & Aristotle I. Early Greeks II. The Method of Exhaustion I. Early Greeks III.Aristotle 1. Anaximander (b. 610 B.C.) “to apeiron” - “the unlimited”, “unbounded” Solution to the Problem of the One and the Many: Observable objects = composites of the four elements: - fundamental substance of reality earth, air, fire, water. - underlying substratum for change Question: How do such opposing elements combine to form objects? - neutral substratum in which Answer: Through the mediation of to apeiron opposites/strife are reconciled 2. The Pythagoreans (Pythagoras b. 570 B.C.) the physical world = product of the imposition of “peras” (limits) on “a peiron” result = order/harmony basis for this order = natural numbers 3. The Eleatics Parmenides of Elea (515 B.C.) Claim: It is meaningless to speak of what is not. Everything is. “The One” - the metaphysically infinite - indivisible, homogeneous, eternal Further claim: Change is an illusion. (Change is a transition from what is, to what is not. This is impossible, since talk of what is not is incoherent.) Zeno (490 B.C.) Paradoxes of motion: intended to demonstrate that motion is not real - Achilles and the Tortoise - Paradox of the runner: ABE D C Claim: Achilles will never reach the finish-line at B. Proof: (1) To reach B, must reach C = AB/2. (2) To reach C, must reach D = AC/2, etc... (3) Thus there are an infinite number of finite line segments between A and B. (4) So Achilles would need an infinite amount of time to traverse them all! Assumptions: (a) AB is infinitely divisible. -
Lost in the Labyrinth: Spinoza, Leibniz and the Continuum Lost in the Labyrinth: Spinoza, Leibniz and the Continuum
LOST IN THE LABYRINTH: SPINOZA, LEIBNIZ AND THE CONTINUUM LOST IN THE LABYRINTH: SPINOZA, LEIBNIZ AND THE CONTINUUM By PATRICK RIESTERER, B.A. A Thesis Submitted to the School of Graduate Studies In Partial Fulfillment ofthe Requirements For the Degree Master ofArts McMaster University © Copyright by Patrick Riesterer, August 2006 MASTER OF ARTS (2006) McMaster University (Philosophy) Hamilton, Ontario TITLE: Lost in the Labyrinth: Spinoza, Leibniz and the Continuum AUTHOR: Patrick Riesterer, B.A. (Trinity Western University) SUPERVISOR: Professor Richard Arthur NUMBER OF PAGES: vi, 110 ii Abstract In this thesis, I address the extent ofSpinoza's influence on the development of Leibniz's response to the continuum problem, with particular emphasis on his relational philosophy oftime and space. I expend the first chapter carefully reconstructing Spinoza's position on infinity and time. We see that Spinoza developed a threefold definition ofinfinity to explain the difference between active substance and its passive modes. Spinoza advances a syncategorematic interpretation ofinfinity, and founds a causal theory oftime directly on this conception ofinfinity. In the second chapter, I examine the changes Leibniz's understanding ofthe continuum problem underwent during 1676 and immediately thereafter. During this period, Leibniz's interacted extensively with Spinoza's ideas. We see that several fundamental features ofLeibniz's philosophy oftime take shape at this time. Leibniz adopts a Spinozistic definition ofdivine eternity and immensity, he reevaluates several analogies in an attempt to understand how the attributes ofa substance interrelate, and he develops the notion ofthe law of the series that will become an essential feature ofmonadic appetition. Leibniz synthesizes several ofthese discoveries into a first philosophy ofmotion. -
Copyright © 2008 by Lydia R
ABSTRACT Analogy, Causation, and Beauty in the Works of Lucy Hutchinson Evan Jay Getz, Ph.D. Dissertation Chairperson: Phillip J. Donnelly, Ph.D. Lucy Hutchinson's translation of the ancient epic De Rerum Natura is remarkable in light of her firm commitments to Calvinist theology and the doctrine of Providence. David Norbrook and Jonathan Goldberg offer strikingly different explanations for the translation exercise. For instance, Norbrook argues that Hutchinson translates Lucretius in order that she might learn from the false images in Lucretius and make better ones in such works as Order and Disorder (Norbrook, “Margaret” 191). In contrast, Goldberg argues for compatibility between Lucretian atomism and Hutchinson‟s Christianity, seeing no contradiction or tension (Goldberg 286). I argue that neither critic accounts for the aesthetics of beauty in Hutchinson's poetry; both critics instead attribute an aesthetics of the sublime to Hutchinson. In making this argument, I show that Hutchinson's theory of causation has much in common with Reformed Scholasticism, whereby she is able to restore a metaphysics of formal and final cause. Hutchinson also revives the doctrine of the analogy of being, or analogia entis, in order to show that the formal cause of creation is visible as God's glory. After a discussion of her metaphysics and ontology, I then show that Hutchinson's poetry reflects a theological aesthetics of beauty and not the aesthetics of the sublime. In the fourth chapter, I compare the typological accounts of Abraham found in Thomas Hobbes' Leviathan and Hutchinson's Order and Disorder with a view to virtue as the proper basis of authority. -
The Generative Dimension, in the Light of Aristotle's Substance
90 THE GENERATIVE DIMENSION, IN THE LIGHT OF ARISTOTLE’S SUBSTANCE (HYPOKEIMENON) THEORY Xiaoyu XU1 and Xinlei LIU1 ABSTRACT: The paper is dedicated to the analysis of Aristotle’s substance theory within the overall Organicist perception of the universe as a living organism. The suggested analytical pathway begins with the generative substance (in Stagirite’s original term – generative hypokeimenon) and leads to the primary causes, prompted by the constant movement of the “thing”. We argue that Aristotle’s analysis of “matter and form” (in his original texts: “ὕλη – hyle” and “μορφή – morphe”)2 leads to the generative function, reaffirming its dynamism and process expression. KEYWORDS: Aristotle, hypokeimenon, hyle, morphe, potential, reality, dynamism, universe, organism, process, generative function Contents Introduction 1. From the studying of Aristotle’s theory of substance (hypokeimenon) – to realizing the generative dimension 2. From Aristotle’s analysis of “hyle” and “morphe” – to examining the generative potentials that are their natural essences Conclusion 1 Northeast Petroleum University, Daqing, CHINA. 2 Following the approach of the BCnA-journal, we consider it essential to apply the genuine terms and notions, used by the Stagirite in his original works, in expressing the authentic (and our own – neo-Aristotelian) conceptual constructions. Thus, we use (adding Italics); hyle – instead of “matter”; morphe – instead of “form”; hypokeimenon – instead of “substance”, etc. Vol. 8, No. 1, BIOCOSMOLOGY – NEO-ARISTOTELISM Winter 2018 91 ГЕНЕРАТИВНОЕ ИЗМЕРЕНИЕ, В СВЕТЕ АРИСТОТЕЛЕВСКОЙ ТЕОРИИ СУБСТАНЦИИ (ГИПОКЕЙМЕНОНА) Чиаю ЗЮЕ и Шинлей ЛЬЮ АБСТРАКТ: Статья посвящена анализу теории субстанции (гипокейменона) Аристотеля в общем восприятии органической вселенной как живого организма. Предлагаемый аналитический путь начинается с порождающего вещества (в первоначальном выражении Стагирита – порождающего гипокейменона) и приводит к основным причинам, побуждающим постоянное движением «вещи». -
Leibniz's Ontology of Individual Substance
THE SCIENCE OF THE INDIVIDUAL: LEIBNIZ’S ONTOLOGY OF INDIVIDUAL SUBSTANCE TOPOI LIBRARY VOLUME 6 Managing Editor: Ermanno Bencivenga, University of California, Irvine, U.S.A. Editorial Board: Daniel Berthold-Bond, Bard College, Annandale-on-Hudson, U.S.A. William James Earle, Baruch College, City University of New York,NewYork, U.S.A. Ann Ferguson, University of Massachusetts, Amherst, U.S.A. David Lloyd, Scripps College, Claremont, U.S.A. Topoi Library is sponsoredbythe Department of Philosophy and theSchool of Humanities at the University of California, Irvine Scope: Likethe journal TOPOII, the TOPOI Library is based on the assumption that philosophy isa lively, provocative, delightful activity, which constantly challenges our inherited habits, painstakingly elaborates on how things could be different, in other stories, in counterfactual situations, inalternative possibleworlds. Whatever its ideology,whether with the intent of uncovering a truer structure of reality or of shooting our anxiety, of exposing myths or of following them through, the outcome of philosophical activity is always the destabilizing, unsettlinggeneration ofdoubts, of objections, of criticisms. It follows that this activity is intrinsically a dialogue, that philosophy is first andforemost philosophicaldiscussion, that it requires bringing out conflicting points of view, paying careful, sympathetic attention to their structure, and using this dialectic to articulate one’s approach,tomake itricher, more thoughtful, more open to variation and play.Andit follows that thespiritwhich one bringstothis activity must be one of tolerance, of always suspecting one’s own blindness and consequently looking with unbiased eye in every corner, without fearing to pass a (fallible)judgment on what isthere but also without failing to show interest and respect. -
Mind, Body, Motion, Matter Eighteenth-Century British and French Literary Perspectives Edited by Mary Helen Mcmurran and Alison Conway MIND, BODY, MOTION, MATTER
Mind, Body, Motion, Matter Eighteenth-Century British and French Literary Perspectives edited by Mary Helen McMurran and Alison Conway MIND, BODY, MOTION, MATTER Eighteenth-Century British and French Literary Perspectives Mind, Body, Motion, Matter Eighteenth-Century British and French Literary Perspectives EDITED BY MARY HELEN MCMURRAN AND ALISON CONWAY UNIVERSITY OF TORONTO PRESS Toronto Buffalo London © University of Toronto Press 2016 Toronto Buffalo London www.utppublishing.com Printed in the U.S.A. ISBN 978-1-4426-5011-4 (cloth) Printed on acid-free, 100% post-consumer recycled paper with vegetable-based inks. ___________________________________________________________________ Library and Archives Canada Cataloguing in Publication Mind, body, motion, matter : eighteenth-century British and French literary perspectives / edited by Mary Helen McMurran and Alison Conway. Includes bibliographical references and index. ISBN 978-1-4426-5011-4 (cloth) 1. English literature – 18th century – History and criticism. 2. French literature – 18th century – History and criticism. 3. Philosophy in literature. 4. Materialism in literature. 5. Vitalism in literature. 6. Aesthetics in literature. I. Conway, Alison Margaret, editor II. McMurran, Mary Helen, 1962–, author, editor PR448.P5M55 2016 820.9'384 C2015-908168-8 ___________________________________________________________________ CC-BY-NC-ND This work is published subject to a Creative Commons Attribution Non-commercial No Derivative License. For permission to publish commercial versions please