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Promoting a New Synthesis of Fa Ith and Reason
March • April 2008 • Volume 40 • Number 2 Body and Soul – Rediscovering Catholic Orthodoxy AND SYNTHESIS NEW PROMOTING A Editorial Aquinas on the Subsistent Soul Kevin Flannery The Soul: Aquinas contra some Thomists et al REASON Francis Selman The Goodness of the Human Body Jeffrey Kirby OF Our regular features Diagnosis The soul and Pullman’s influence: The Truth Will Set You Free FAITH FAITH Shared shock at episcopal teaching: Comment on the Comments Prospects for heterodoxy: Notes from across the Atlantic Debate The value of discussing God and the soul: Road from Regensburg The nature of science: Cutting Edge Letting go of catholicity at a Catholic hospital: Other Angles Also Price: £4 Reviewing Newman: Bishop Philip Boyce Post-modernism: Margeurite Peeters and Letters Fit for Mission? What next?: William Oddie, James Arthur and the Editor www.faith.org.uk MAY PRICE INCREASE Due to further increases in costs regrettably annual faith we will be increasing the basic subscription rate to £25 and the cover price to £4.50 for the May summer session issue. Other rates will increase accordingly. We hope you will still find our full, frank and quality content very good value for money. Thank you for your continued support of our apostolate. Catholicism a new synthesis by Edward Holloway Monday 4th to Friday 8th August 2008 Pope John Paul II gave the blueprint for at Woldingham School catechetical renewal with the Catechism of the Catholic Church. Catholicism: A New Synthesis Four days of lectures, discussion seeks to show why such teaching makes perfect and seminars around a particular theme, sense in a world which has come of age in in a relaxed holiday environment, scientific understanding. -
ÉCLAT MATHEMATICS JOURNAL Lady Shri Ram College for Women
ECLAT´ MATHEMATICS JOURNAL Lady Shri Ram College For Women Volume X 2018-2019 HYPATIA This journal is dedicated to Hypatia who was a Greek mathematician, astronomer, philosopher and the last great thinker of ancient Alexandria. The Alexandrian scholar authored numerous mathematical treatises, and has been credited with writing commentaries on Diophantuss Arithmetica, on Apolloniuss Conics and on Ptolemys astronomical work. Hypatia is an inspiration, not only as the first famous female mathematician but most importantly as a symbol of learning and science. PREFACE Derived from the French language, Eclat´ means brilliance. Since it’s inception, this journal has aimed at providing a platform for undergraduate students to showcase their understand- ing of diverse mathematical concepts that interest them. As the journal completes a decade this year, it continues to be instrumental in providing an opportunity for students to make valuable contributions to academic inquiry. The work contained in this journal is not original but contains the review research of students. Each of the nine papers included in this year’s edition have been carefully written and compiled to stimulate the thought process of its readers. The four categories discussed in the journal - History of Mathematics, Rigour in Mathematics, Interdisciplinary Aspects of Mathematics and Extension of Course Content - give a comprehensive idea about the evolution of the subject over the years. We would like to express our sincere thanks to the Faculty Advisors of the department, who have guided us at every step leading to the publication of this volume, and to all the authors who have contributed their articles for this volume. -
Leibniz and China: a Commerce of Light Franklin Perkins Frontmatter More Information
Cambridge University Press 978-0-521-83024-9 - Leibniz and China: A Commerce of Light Franklin Perkins Frontmatter More information LEIBNIZ AND CHINA Why was Leibniz so fascinated by Chinese philosophy and culture? What specific forms did his interest take? How did his interest com- pare with the relative indifference of his philosophical contemporaries and near-contemporaries such as Spinoza and Locke? In this highly original book, Franklin Perkins examines Leibniz’s voluminous writ- ings on the subject and suggests that his interest was founded in his own philosophy: the nature of his metaphysical and theological views required him to take Chinese thought seriously. Leibniz was unusual in holding enlightened views about the intellectual profitability of cultural exchange, and in a broad-ranging discussion Perkins charts these views, their historical context, and their social and philosophical ramifications. The result is an illuminating philosophical study which also raises wider questions about the perils and rewards of trying to understand and learn from a different culture. franklin perkins is Assistant Professor of Philosophy at DePaul University, Chicago. He has published in early modern European philosophy, early Chinese philosophy, and comparative philosophy, with articles appearing in the Journal of the History of Ideas, the Journal of Chinese Philosophy, and the Leibniz Review. © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83024-9 - Leibniz and China: A Commerce of Light -
A New History of Western Philosophy Ebook Free Download
A NEW HISTORY OF WESTERN PHILOSOPHY PDF, EPUB, EBOOK Anthony Kenny | 1088 pages | 15 Oct 2012 | Oxford University Press | 9780199656493 | English | Oxford, United Kingdom A New History of Western Philosophy PDF Book Namespaces Article Talk. Politics Learn how to enable JavaScript on your browser. It is obvious that they This approach leads to a thoroughly engaging overview for anyone interested in Western philosophy. Choose your country or region Close. Many more analytically-minded philosophers are unlikely to be very familiar with the views of Schopenhauer, and many of any stripe tend not to be up on the sometimes very odd details of Peirce's views. Schools of Thought: From Aristotle to Augustine 3. Sign in to Purchase Instantly. Philosophy Break is a social enterprise dedicated to getting more people engaged with philosophy. Politics Though critics claim Kenny's account of philosophy, while generally good, is quite limited in the Islamic world, focusing only on those works that became important in the Latin tradition. The title of the first chapter -- "Bentham to Nietzsche" -- is indicative of this cosmopolitan approach, as is the inclusion of thinkers as diverse as Schopenhauer and Mill in one chapter. Follow Philosophy Break. God Chronology. He has published more than forty books on philosophy and history. A New History of Western Philosophy is a stimulating chronicle of the intellectual development of Western civilization, allowing readers to trace the birth and growth of philosophy from antiquity to the present day. Knowledge and its Limits 5. Enabling JavaScript in your browser will allow you to experience all the features of our site. -
Stephen Cole Kleene
STEPHEN COLE KLEENE American mathematician and logician Stephen Cole Kleene (January 5, 1909 – January 25, 1994) helped lay the foundations for modern computer science. In the 1930s, he and Alonzo Church, developed the lambda calculus, considered to be the mathematical basis for programming language. It was an effort to express all computable functions in a language with a simple syntax and few grammatical restrictions. Kleene was born in Hartford, Connecticut, but his real home was at his paternal grandfather’s farm in Maine. After graduating summa cum laude from Amherst (1930), Kleene went to Princeton University where he received his PhD in 1934. His thesis, A Theory of Positive Integers in Formal Logic, was supervised by Church. Kleene joined the faculty of the University of Wisconsin in 1935. During the next several years he spent time at the Institute for Advanced Study, taught at Amherst College and served in the U.S. Navy, attaining the rank of Lieutenant Commander. In 1946, he returned to Wisconsin, where he stayed until his retirement in 1979. In 1964 he was named the Cyrus C. MacDuffee professor of mathematics. Kleene was one of the pioneers of 20th century mathematics. His research was devoted to the theory of algorithms and recursive functions (that is, functions defined in a finite sequence of combinatorial steps). Together with Church, Kurt Gödel, Alan Turing, and others, Kleene developed the branch of mathematical logic known as recursion theory, which helped provide the foundations of theoretical computer science. The Kleene Star, Kleene recursion theorem and the Ascending Kleene Chain are named for him. -
Russell's Paradox in Appendix B of the Principles of Mathematics
HISTORY AND PHILOSOPHY OF LOGIC, 22 (2001), 13± 28 Russell’s Paradox in Appendix B of the Principles of Mathematics: Was Frege’s response adequate? Ke v i n C. Kl e m e n t Department of Philosophy, University of Massachusetts, Amherst, MA 01003, USA Received March 2000 In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege’s extant logical system, if Frege’s system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege’s logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therein. 1. Introduction Russell’s letter to Frege from June of 1902 in which he related his discovery of the Russell paradox was a monumental event in the history of logic. However, in the ensuing correspondence between Russell and Frege, the Russell paradox was not the only antinomy discussed. -
Historical Essays in Philosophy by Anthony Kenny Owen Goldin Marquette University, [email protected]
Marquette University e-Publications@Marquette Philosophy Faculty Research and Publications Philosophy, Department of 1-1-2009 Review of From Empedocles to Wittgenstein: Historical Essays in Philosophy by Anthony Kenny Owen Goldin Marquette University, [email protected] Published version. Notre Dame Philosophical Reviews, Vol. 3, No. 9 (2009). Permalink. © 2009 University of Notre Dame Philosophy Department. Used with permission. Anthony Kenny From Empedocles to Wittgenstein: Historical Essays in Philosophy Anthony Kenny, From Empedocles to Wittgenstein: Historical Essays in Philosophy, Oxford University Press, 2008, 218pp., $60.00 (hbk), ISBN 9780199550821. Reviewed by Owen Goldin, Marquette University From Empedocles to Wittgenstein is a collection of essays written by Kenny during the last few years. In his preface Kenny tells us that most are attempts to justify somewhat controversial positions taken in his introductory A New History of Western Philosophy.[1] Most, but not all, have been previously published; some have been revised for this collection. As the title declares, all have their source in issues in the history of philosophy. Together they document the most recent phase in the evolution of the thought of one of the most significant philosophers working today. "Seven Concepts in Creation" offers a synoptic view of the philosophic contours of what Kenny identifies as the seven major concepts of creation found in the Western tradition: "the Platonic concept, the Mosaic concept, the Augustinian concept, the Avicennan concept, the Thomist concept, the Scotist concept, and the Cartesian concept" (12). Kenny presents a taxonomy of these by way of seven aspects of those accounts: what they say of the nature of the creator, what existed prior to creation, whether there was a blueprint for creation (and if so, what it was), the reason for creation, the things created, and when creation took place. -
Computability Computability Computability Turing, Gödel, Church, and Beyond Turing, Gödel, Church, and Beyond Edited by B
computer science/philosophy Computability Computability Computability turing, Gödel, Church, and beyond turing, Gödel, Church, and beyond edited by b. Jack Copeland, Carl J. posy, and oron Shagrir edited by b. Jack Copeland, Carl J. posy, and oron Shagrir Copeland, b. Jack Copeland is professor of philosophy at the ContributorS in the 1930s a series of seminal works published by university of Canterbury, new Zealand, and Director Scott aaronson, Dorit aharonov, b. Jack Copeland, martin Davis, Solomon Feferman, Saul alan turing, Kurt Gödel, alonzo Church, and others of the turing archive for the History of Computing. Kripke, Carl J. posy, Hilary putnam, oron Shagrir, Stewart Shapiro, Wilfried Sieg, robert established the theoretical basis for computability. p Carl J. posy is professor of philosophy and member irving Soare, umesh V. Vazirani editors and Shagrir, osy, this work, advancing precise characterizations of ef- of the Centers for the Study of rationality and for lan- fective, algorithmic computability, was the culmina- guage, logic, and Cognition at the Hebrew university tion of intensive investigations into the foundations of Jerusalem. oron Shagrir is professor of philoso- of mathematics. in the decades since, the theory of phy and Former Chair of the Cognitive Science De- computability has moved to the center of discussions partment at the Hebrew university of Jerusalem. He in philosophy, computer science, and cognitive sci- is currently the vice rector of the Hebrew university. ence. in this volume, distinguished computer scien- tists, mathematicians, logicians, and philosophers consider the conceptual foundations of comput- ability in light of our modern understanding. Some chapters focus on the pioneering work by turing, Gödel, and Church, including the Church- turing thesis and Gödel’s response to Church’s and turing’s proposals. -
Fundamentalism Themenheft 8
Themenheft 8 Herbert Rainer Pelikan Fundamentalism Themenheft 8 Herbert Rainer Pelikan Fundamentalism Extreme Tendencies in modern Christianity, Islam and Judaism (= Evang. Rundbrief, SNr. 1/2003) Wien 2003 Vorwort Der Begriff Fundamentalismus ist ein Thema der aktuellen Diskussion; Grund genug, sich damit auch aus ethischer Sicht zu beschäftigen. Fundamentalismus, der sich nach der iranischen Ayatollah-Revolution (1979) verbreite- te, ist heute fast ein Schimpfwort geworden. Fundamentalismus ist keineswegs ein speziell christliches oder islamisches Phänomen, son- dern die Gefahr einer jeden - auch säkularen - Weltanschauung und Religion. Anstelle eines vertrauenden und Wachstumsfähigen Glaubens wird ein absoluter und endgültiger Wahrheits- standpunkt bezogen, der nicht in der Diskussion einsichtig gemacht, sondern nur mit Macht behauptet wird. Fundamentalismus ist ein sehr ambivalentes Thema. Denn grundsätzlich ist es ja zu begrüßen, wenn Menschen ihr Leben auf einem festen Funda- ment aufbauen. Das gilt ja auch für den Glauben, wie das Gleichnis Jesu Vom Hausbau (Mt. 7, 24-29) sehr deutlich zeigt: 24 Darum, wer diese meine Rede hört und tut sie, der gleicht einem klugen Mann, der sein Haus auf Fels baute. 25 Als nun ein Platzregen fiel und die Wasser kamen und die Winde wehten und stießen an das Haus, fiel es doch nicht ein; denn es war auf Fels gegrün- det. 26 Und wer diese meine Rede hört und tut sie nicht, der gleicht einem törichten Mann, der sein Haus auf Sand baute. 27 Als nun ein Platzregen fiel und die Wasser kamen und die Winde wehten und stießen an das Haus, da fiel es ein und sein Fall war groß. Ins Politische übertragen könnte man hier von einem Hochhalten einer Werteorientierung in positiver Abgrenzung gegenüber einem Opportunismus sprechen. -
Frege and the Logic of Sense and Reference
FREGE AND THE LOGIC OF SENSE AND REFERENCE Kevin C. Klement Routledge New York & London Published in 2002 by Routledge 29 West 35th Street New York, NY 10001 Published in Great Britain by Routledge 11 New Fetter Lane London EC4P 4EE Routledge is an imprint of the Taylor & Francis Group Printed in the United States of America on acid-free paper. Copyright © 2002 by Kevin C. Klement All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any infomration storage or retrieval system, without permission in writing from the publisher. 10 9 8 7 6 5 4 3 2 1 Library of Congress Cataloging-in-Publication Data Klement, Kevin C., 1974– Frege and the logic of sense and reference / by Kevin Klement. p. cm — (Studies in philosophy) Includes bibliographical references and index ISBN 0-415-93790-6 1. Frege, Gottlob, 1848–1925. 2. Sense (Philosophy) 3. Reference (Philosophy) I. Title II. Studies in philosophy (New York, N. Y.) B3245.F24 K54 2001 12'.68'092—dc21 2001048169 Contents Page Preface ix Abbreviations xiii 1. The Need for a Logical Calculus for the Theory of Sinn and Bedeutung 3 Introduction 3 Frege’s Project: Logicism and the Notion of Begriffsschrift 4 The Theory of Sinn and Bedeutung 8 The Limitations of the Begriffsschrift 14 Filling the Gap 21 2. The Logic of the Grundgesetze 25 Logical Language and the Content of Logic 25 Functionality and Predication 28 Quantifiers and Gothic Letters 32 Roman Letters: An Alternative Notation for Generality 38 Value-Ranges and Extensions of Concepts 42 The Syntactic Rules of the Begriffsschrift 44 The Axiomatization of Frege’s System 49 Responses to the Paradox 56 v vi Contents 3. -
9 Alfred Tarski (1901–1983), Alonzo Church (1903–1995), and Kurt Gödel (1906–1978)
9 Alfred Tarski (1901–1983), Alonzo Church (1903–1995), and Kurt Gödel (1906–1978) C. ANTHONY ANDERSON Alfred Tarski Tarski, born in Poland, received his doctorate at the University of Warsaw under Stanislaw Lesniewski. In 1942, he was given a position with the Department of Mathematics at the University of California at Berkeley, where he taught until 1968. Undoubtedly Tarski’s most important philosophical contribution is his famous “semantical” definition of truth. Traditional attempts to define truth did not use this terminology and it is not easy to give a precise characterization of the idea. The under- lying conception is that semantics concerns meaning as a relation between a linguistic expression and what it expresses, represents, or stands for. Thus “denotes,” “desig- nates,” “names,” and “refers to” are semantical terms, as is “expresses.” The term “sat- isfies” is less familiar but also plausibly belongs in this category. For example, the number 2 is said to satisfy the equation “x2 = 4,” and by analogy we might say that Aristotle satisfies (or satisfied) the formula “x is a student of Plato.” It is not quite obvious that there is a meaning of “true” which makes it a semanti- cal term. If we think of truth as a property of sentences, as distinguished from the more traditional conception of it as a property of beliefs or propositions, it turns out to be closely related to satisfaction. In fact, Tarski found that he could define truth in this sense in terms of satisfaction. The goal which Tarski set himself (Tarski 1944, Woodger 1956) was to find a “mate- rially adequate” and formally correct definition of the concept of truth as it applies to sentences. -
Lambda Calculus and the Decision Problem
Lambda Calculus and the Decision Problem William Gunther November 8, 2010 Abstract In 1928, Alonzo Church formalized the λ-calculus, which was an attempt at providing a foundation for mathematics. At the heart of this system was the idea of function abstraction and application. In this talk, I will outline the early history and motivation for λ-calculus, especially in recursion theory. I will discuss the basic syntax and the primary rule: β-reduction. Then I will discuss how one would represent certain structures (numbers, pairs, boolean values) in this system. This will lead into some theorems about fixed points which will allow us have some fun and (if there is time) to supply a negative answer to Hilbert's Entscheidungsproblem: is there an effective way to give a yes or no answer to any mathematical statement. 1 History In 1928 Alonzo Church began work on his system. There were two goals of this system: to investigate the notion of 'function' and to create a powerful logical system sufficient for the foundation of mathematics. His main logical system was later (1935) found to be inconsistent by his students Stephen Kleene and J.B.Rosser, but the 'pure' system was proven consistent in 1936 with the Church-Rosser Theorem (which more details about will be discussed later). An application of λ-calculus is in the area of computability theory. There are three main notions of com- putability: Hebrand-G¨odel-Kleenerecursive functions, Turing Machines, and λ-definable functions. Church's Thesis (1935) states that λ-definable functions are exactly the functions that can be “effectively computed," in an intuitive way.