A Critical Introduction To The Philosophy Of Gottlob Frege

A CRITICAL INTRODUCTION TO THE PHILOSOPHY OF GOTTLOB FREGE This page intentionally left blank A Critical Introduction to the Philosophy of Gottlob Frege GUILLERMO E. ROSADO HADDOCK University of Puerto Rico at Rio Piedras, Puerto Rico © Guillermo E. Rosado Haddock 2006 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, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the publisher. Guillermo E. Rosado Haddock has asserted his moral right under the Copyright, Designs and Patents Act, 1988, to be identified as the author of this work. Published by Ashgate Publishing Limited Gower House Croft Road Aldershot Hampshire GU11 3HR England Ashgate Publishing Company Suite 420 101 Cherry Street Burlington, VT 05401-4405 USA Ashgate website: http://www.ashgate.com British Library Cataloguing in Publication Data Rosado Haddock, Guillermo E., 1945A critical introduction to the philosophy of Gottlob Frege 1.Frege, Gottlob, 1848-1925 2.Frege, Gottlob, 1848-1925. Begriffsschrift I.Title 193 Library of Congress Cataloging-in-Publication Data Rosado Haddock, Guillermo E., 1945A critical introduction to the philosophy of Gottlob Frege / Guillermo E. Rosado Haddock. p. cm. Includes bibliographical references and index. ISBN 0-7546-5471-0 (hardback : alk. paper) 1. Frege, Gottlob, 1848-1925. I. Title. B3245.F24R67 2006 193—dc22 2005031884 ISBN-13: 978-0-7546-5471-1 ISBN-10: 0-7546-5471-0 Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire. Contents Preface vii Chapter 1 Philosophy in Begriffsschrift § 1 An Epistemological Distinction § 2 On the Nature of Arithmetical Statements § 3 Concept-Script versus Natural Language § 4 Judgeable Content § 5 Conceptual Content § 6 The Universal Predicate of all Statements § 7 Abandonment of some Traditional Distinctions § 8 Identity Statements in Begriffsschrift § 9 Functions in Begriffsschrift § 10 Axiom Systems 1 2 3 4 5 6 7 9 11 15 Chapter 2 Die Grundlagen der Arithmetik: First Part (§§1-45) § 1 The Need for a Clarification of the Nature of Mathematics § 2 The Methodological Principles § 3 The Classification of Statements § 4 The Naturalist Conception of Mathematics § 5 The Nature of Geometry § 6 Numbers and Properties of Objects § 7 Psychologism in Mathematics § 8 Numbers and the Process of Abstraction 17 19 22 23 25 28 30 33 Chapter 3 Die Grundlagen der Arithmetik: Second Part (§§46-109) § 1 Predications about Concepts § 2 Concept and Object in Die Grundlagen der Arithmetik § 3 First Attempt at a Definition of Number § 4 Second Attempt at a Definition of Number § 5 Third Attempt at a Definition of Number § 6 A Brief Sketch of the System § 7 Frege’s Summary and his Assessment of Kant’s Views 35 37 39 42 49 57 62 Chapter 4 The Basic Distinctions I: Sense and Referent § 1 Sense and Referent § 2 The Context Principle and Frege’s Semantics of Sense and Referent 67 72 A Critical Introduction to the Philosophy of Gottlob Frege vi § 3 Critical Remarks I § 4 Critical Remarks II § 5 Critical Remarks III § 6 Critical Remarks IV § 7 Identity Statements 75 76 81 83 86 Chapter 5 The Basic Distinctions II: Function and Object § 1 The Nature of Functions § 2 The Predicative Nature of Concepts § 3 Value Ranges § 4 Some Difficulties § 5 Value Ranges and Extensions 91 94 99 102 105 Chapter 6 Fundamental Philosophical Issues in Grundgesetze § 1 Introduction § 2 Frege’s Criticism of Psychologism in Logic § 3 Logicism in Grundgesetze der Arithmetik § 4 Frege’s Platonism § 5 Frege’s Criticism of Formalism in Mathematics § 6 On the Nature of Definitions § 7 Some Critical Remarks 109 110 11