Logic in Reality
Logic in Reality argues that the fundamental physical structure of the world is logical as well as mathematical. The applicable formal logic of and in reality proposed (LIR) represents a radical departure from the standard notion of logic and its function
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Joseph E. Brenner
Logic in Reality
Joseph E. Brenner International Center for Transdisciplinary Research, Paris, France Postal address: P.O. Box 235 CH-1865 Les Diablerets Switzerland
ISBN 978-1-4020-8374-7
e-ISBN 978-1-4020-0000-0
Library of Congress Control Number: 2008926590 © 2008 Springer Science + Business Media B.V. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com
CONTENTS Foreword……...............………………………………………………………….. xi Acknowledgments……………………………………………………………….. xv INTRODUCTION ...............................................................................................xvii 1. REALITY AND LOGIC .............................................................................xvii 2. THE OBJECTIVE AND PLAN OF “LOGIC IN REALITY”..................... xix 1 LOGIC IN REALITY (LIR) AS A FORMAL LOGIC.................................. 1 1.1 INITIAL AXIOMATIZATION: THE FUNDAMENTAL POSTULATE .. 1 1.2 THE REAL AND REALITY ....................................................................... 6 1.2.1 Levels of Reality ................................................................................... 7 1.2.1.1 The Ontological Approach ............................................................ 8 1.2.1.2 The Physical Science Approach .................................................... 8 1.2.2 Contradiction, Counteraction or “Countervalence”.............................. 9 1.2.3 The Senses of Reduction..................................................................... 10 1.3 LIR VERSUS STANDARD LOGICS: DEDUCTION.............................. 11 1.3.1 Bivalence: Logical Truth, Logical Constants and Logical Consequence ................................................................................................ 12 1.3.2 Semantics ............................................................................................ 16 1.3.3 First-Order Predicate Logic (FOL) ..................................................... 19 1.4 NON-CLASSICAL LOGICS ..................................................................... 20 1.4.1 Intuitionist, Paraconsistent and Paracomplete Logics ........................ 20 1.4.1.1 Intuitionist Logic and Paracompleteness..................................... 20 1.4.1.2 Paraconsistent Logic.................................................................... 21 1.4.2 Many-Valued and Fuzzy Logics ......................................................... 22 1.4.3 Modal Logic ........................................................................................ 24 1.4.4 Relevance and Natural Logics ............................................................ 26 1.4.4.1 Rel
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