The Young Carnaps Unknown Master

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THE YOUNG CARNAP’S UNKNOWN MASTER

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The Young Carnap’s Unknown Master Husserl’s Inﬂuence on Der Raum and Der logische Aufbau der Welt

GUILLERMO E. ROSADO HADDOCK University of Puerto Rico at Río Piedras, Puerto Rico

© Guillermo E. Rosado Haddock 2008 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., 1945– The young Carnap’s unknown master : Husserl’s inﬂuence on Der Raum and Der logische Aufbau der Welt 1. Carnap, Rudolf, 1891–1970 2. Carnap, Rudolf, 1891–1970. Raum 3. Carnap, Rudolf, 1891–1970. Logische Aufbau der Welt 4. Husserl, Edmund, 1859–1938 – Inﬂuence 5. Analysis (Philosophy) I. Title 193 Library of Congress Cataloging-in-Publication Data Rosado Haddock, Guillermo E., 1945– The young Carnap’s unknown master : Husserl’s inﬂuence on Der Raum and Der logische Aufbau der Welt / Guillermo E. Rosado Haddock. p. cm. Includes bibliographical references (p. ) and indexes. ISBN 978-0-7546-6158-0 (hardcover : alk. paper) 1. Carnap, Rudolf, 1891–1970. Logische Aufbau der Welt. 2. Carnap, Rudolf, 1891–1970. Raum. 3. Husserl, Edmund, 1859–1938– Inﬂuence. 4. Knowledge, Theory of. 5. Logical positivism. 6. Analysis (Philosophy) 7. Space and time. 8. Intersubjectivity 9. Quine, W. V. (Willard Van Orman) I. Title. B945.C164R67 2007 193–dc22 2007033294 ISBN: 978-0-7546-6158-0

Printed and bound in Great Britain by MPG Books Ltd, Bodmin, Cornwall.

Contents Preface

vii

Chapter 1: Carnap’s First Husserlian Book: Der Raum § 1 Introduction § 2 Introduction to the Study of Der Raum § 3 Formal Space: Topological, Projective and Metric § 4 Intuitive Space and its Sorts § 5 Physical Space and its Sorts § 6 Comparison of the Three Levels of Space § 7 Epistemological Assessment § 8 Carnap’s Conclusion § 9 Husserl and Carnap: Relation and Tensions

1 4 6 7 15 23 24 30 32

Chapter 2: On Der logische Aufbau der Welt § 1 Introduction § 2 Preliminaries: Methodology and Purpose of Aufbau § 3 Husserl’s Notion of Constitution and Carnap § 4 On the Autopsychological Basis § 5 A Permutation of Terminology § 6 An Unsuspected Ambivalence § 7 On the Constitutional System and Phenomenology § 8 On Carnapian Scholarship

35 37 42 48 59 63 66 71

Chapter 3: Carnap and Husserl on Intersubjectivity § 1 The Problem of Intersubjectivity § 2 Carnap’s Solution to the Problem of Intersubjectivity § 3 Husserl’s Solution to the Problem of Intersubjectivity § 4 A Critical Assessment of the Husserl-Carnap Solution

75 79 87 96

Chapter 4: Carnap, Husserl and Analytic Philosophy § 1 Trails of Husserl’s Inﬂuence in Carnap’s Middle Period § 2 Carnap’s Later Views and Analytic Philosophy § 3 On Quine, Against Quine and Beyond § 4 Against Quine’s Inscrutability of Meaning § 5 On Quine’s Holism § 6 Wither Analytic Philosophy

99 105 107 115 117 122

Bibliography Name Index Subject Index

125 133 137

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Preface The present work offers a more or less complete view of a forbidden chapter in the history of analytic philosophy, namely, the much more than casual inﬂuence exerted by Edmund Husserl on the young Rudolf Carnap’s writings. It is a forbidden chapter, since Carnap never acknowledged such an inﬂuence, though that inﬂuence was overwhelming and decisive, especially in Carnap’s Der Raum and Der logische Aufbau der Welt. In Carnap’s ‘Autobiography’ in the Schilpp volume Husserl is barely mentioned, and certainly not as a decisive force. More precisely, there are two irrelevant references on pp. 20 and 40, while there is a more important remark on p. 957 in his ‘Reply to Adolf Grünbaum’, though masked by a reference ﬁrst to Kant. It is not even acknowledged by Carnap that he was Husserl’s student, at least during three semesters in the years 1924–25, as attested in Karl Schuhmann’s Husserl-Chronik and in a letter of Ludwig Landgrebe to Husserl. Moreover, there is also the very plausible suspicion that while writing his dissertation, Der Raum, between 1919 and 1921 in Buchenbach, a small town on the outskirts of Freiburg, Carnap visited Husserl’s courses or had at least some contact with him. Although there is not any documentary evidence on this point, due to the fact of Husserl’s strong inﬂuence on Carnap’s dissertation, it would be extremely strange to believe that during those three years Carnap was never tempted to meet the master. That would be as improbable as a philosophy student writing a dissertation inspired on Quine’s views on the outskirts of Boston in the 1960s, but never succombing to the temptation of meeting Quine or visiting his courses. Nonetheless, in order to avoid some psychological stress, most Carnapian scholars surely prefer to believe that Carnap was never tempted to visit Husserl’s courses in those days – and some may never even accept, against all evidence, that he later did visit Husserl’s seminars. Incidentally, due to the structure of the German university system and its academic hierarchy, it is immensely more decisive in terms of intellectual and personal contact to take part in seminars – even more so if you are already a doctor or are writing your dissertation – than to visit lectures of some professor, especially, if you are nothing more than a usual student hearing the lectures and merely taking notes. Thus, if Carnap and Carnapian scholars are so eager to baptize Carnap as Frege’s student for visiting three of Frege’s lecture courses, it is by far more justiﬁed to call Carnap Husserl’s student. The fact that Carnap never acknowledged it does not detract from his being Husserl’s student. In any case, it could point to some obscure aspects of Carnap’s character, and I am perfectly conscious that the present work will shed some shadows on Carnap’s moral character. Nonetheless, that has never been a motivation for writing this book, but simply to bring light to an unknown and forbidden chapter of the history of analytic philosophy. Together with Husserl and Tarski, Frege and Kant, Carnap has been one of the thinkers who have had the greatest inﬂuence on my intellectual development. As in the case of Frege, whose political views were an

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aberration, one should clearly distinguish between the theoretical work in science or hard philosophy of a thinker, and the weaknesses or defects of his moral character. This small book has an extremely long history of maturation. My ﬁrst contact with some of the themes of this book occurred forty years ago. I was writing my MA thesis on Husserl’s theory of logical grammar, and after reading a paper by Yehoshua Bar-Hillel on the same theme, I read – probably during the summer or early autumn of 1967 – the English expanded version of Carnap’s Logische Syntax der Sprache. I immediately noticed the similarity between Husserl’s distinction between the laws that protect against nonsense and those that protect against countersense and govern over derivations, and Carnap’s distinction between formation rules and transformation rules. I was also surprised that there was no mention of Husserl in Carnap’s book on this issue. In the summer of 1967 I also read the English translation of Husserl’s Cartesianische Meditationen – though I had already studied German, I still could not read it with proﬁciency. I became very interested in the problem of intersubjectivity, that is, what Carnap called the problem of the other psyche. My treatment of the problem at the end of Chapter Three dates from 1967, though I have never dared until now to write about it. When I went to Germany in 1968 for my doctoral studies, I had two possible themes for my dissertation, namely, the problem of intersubjectivity in Husserl and Husserl’s philosophy of mathematics. I chose the second one because it would force me to seriously study contemporary logic and some mathematics – and it was the right choice. Around 1970 I read Carnap’s Der logische Aufbau der Welt in its German original, and I was impressed by the similarities between his and Husserl’s treatments of the problem of intersubjectivity. Since Carnap’s book was published a year before Husserl’s Cartesianische Meditationen, the similarity seemed at ﬁrst sight to be a pure coincidence. Moreover, my interest in logic and the philosophy of mathematics made me put aside, not only during my ﬁve years of studies in Germany (Göttingen and Bonn), but also for some three decades in my native country, Puerto Rico, any consideration of the problem of Carnap’s relationship to Husserl. The publication during the early 1990s of two important papers by Verena Mayer on Husserl’s inﬂuence on Der logische Aufbau der Welt reawakened my interest in the issue. I completely agree with her analyses and contentions on the Husserl-Carnap relation, though my treatment of that relation is not only more detailed but also more daring. Mayer did not seem to know about Carnap’s philosophical discussions with the young Ludwig Landgrebe in 1924–25, when the latter was Husserl’s assistant. At the end of the 1990s, I decided that I should begin reading Der Raum, a work not easy to ﬁnd. I asked my friend Werner Diederich, then professor at the University of Hamburg, to see if he could ﬁnd a copy of Der Raum somewhere in Germany. Some months later, he found out that Carnap’s dissertation had been reprinted in Liechtenstein by a relatively unknown publisher named ‘Topos Verlag’. He ordered the copy and sent it to me as a gift. The study of Der Raum was the clue to the mystery of the similarities. In that small and very interesting book the inﬂuence of Husserl is very prominent and undisguised. I then remembered that when I read Karl Schuhmann’s Husserl-Chronik some twenty-ﬁve years ago, I had read that Carnap had visited Husserl’s courses. I re-read the passage, wrote to Schuhmann, who answered me that he obtained the information from Ludwig Landgrebe. I also wrote to Hans-Rainer Sepp and to the Husserl Archives in Leuwen, and both Sepp and

Preface

ix

Sebastian Luft, who was then an assistant at the archives, answered immediately. Prof. Sepp and Dr Luft, as well as Prof. Schuhmann, did their best to help me, though not all my questions could be answered. At the suggestion of Prof. Sepp, I inquired elsewhere, but the main question remains to this day unanswered, namely: had Carnap already met Husserl during the years of 1919–21, while he was writing his dissertation less than a half hour by train from Freiburg? The ﬁrst two fruits of my systematic study of the young Carnap’s relation to Husserl are two critical studies in Spanish, different versions of which I have circulated among some scholars. One of the critical studies appeared recently in Manuscrito, namely, that of Carnap’s dissertation, while the other, more ambitious one is of a collection of papers edited by Ramón Cirera, Andoni Ibarra and Thomas Mormann under the title El Programa de Carnap, just appeared in Principia. My critique of Moulines’ interpretation of Der logische Aufbau der Welt, as well as some of my criticism of Quine had their origin in that critical study. Already in the new century some scholars have begun to relate some of Carnap’s views to Husserl’s. The most important of these efforts has been a paper by Sahotra Sarkar on Husserl’s inﬂuence on Carnap’s dissertation. Sarkar’s paper is very similar in analyses and conclusion to my recently published critical study of Der Raum, though the latter is more thorough and less compromising with Kantianizers of Carnap’s views. In his book Rudolf Carnap Thomas Mormann has also related Carnap’s views to Husserl’s, though he is even much more inclined than Sarkar to make concessions to the Kantian interpretation of Carnap’s views. A very recent book by Thomas Ryckman, namely, The Reign of Relativity, also mentions brieﬂy the similarities between Carnap’s Der logische Aufbau der Welt and Husserl’s writings. Finally, in the also very recent collection of papers Carnap Brought Home, edited by Steve Awodey and Carsten Klein, two of the contributors, namely, Jean-Michel Roy and Michael Beaney discuss some aspects of Carnap’s relation to Husserl. Roy’s paper tries to show that the speciﬁc relation of Carnap with Husserl under discussion is in the best of cases a superﬁcial one. On the other hand, Beaney points to a speciﬁc relation between Carnap’s late use of the word ‘explication’ and Husserl’s notion of explication. However, Beaney is ignorant of the fact that Carnap was Husserl’s student and, moreover, shows his lack of familiarity with Husserl’s two fundamental books, namely, Logische Untersuchungen and Ideen zu einer reinen Phänomenologie und einer phänomenologischen Philosophie I – which were included in the references both of Der Raum and of Der logische Aufbau der Welt – and with the fact that Carnap certainly studied those writings in his younger years. Thus, with the exception of Mayer’s two valuable papers and Sarkar’s also important one, there have been only partial and no in depth analyses of Carnap’s relation to Husserl. I hope that the present book will offer a deﬁnitive overview of the extraordinary inﬂuence of Husserl on the young Carnap’s views. It is clearly shown in Chapter 1 – which is essentially based on my critical study of Der Raum – that Husserl’s inﬂuence was by far the most decisive philosophical inﬂuence in Der Raum. Moreover, and contrary to Sarkar’s and Mormann’s renderings, it is argued that Carnap’s references to Kant, sometimes after referring to Husserl, are mostly cosmetic and seem to have had the purpose of appeasing his neo-Kantian Doktorvater, Bruno Bauch, and, in general, the academic powerful neo-Kantian milieu prevailing in many German

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The Young Carnap’s Unknown Master

universities at the time. On this point, one should not forget that Bruno Bauch obtained his position as full professor [Ordinarius] at the University of Jena, after the authorities decided, for still unclear reasons, not to hire Husserl, who was by far the ﬁrst choice of the faculty. Moreover, though Husserl’s views after the transcendental turn were not necessarily in direct conﬂict with those of neo-Kantians, being also in very friendly terms with Paul Natorp, Husserl dissented from Kant and the neoKantians in very important issues, particularly with respect to Kant’s views on the a priori character of Euclidean geometry, a view that Husserl already rejected more than a decade before the advent of Einstein’s theory of special relativity and communicated to Brentano in 1892. Furthermore, at the time in which Carnap wrote his dissertation, Husserl was clearly considered the most important living German philosopher. Thus, Carnap referred freely to Husserl in Der Raum, and an attentive reader can easily see, as Sarkar and Mormann have seen, the decisive inﬂuence of Husserl on that book. A very different issue is that of Carnap’s Der logische Aufbau der Welt. In that book, Carnap refers to Husserl a few times, usually masked among a long list of authors, whose inﬂuence on Carnap was much smaller. However, the inﬂuence of Husserl in Carnap’s Der logische Aufbau der Welt is immensely greater than Carnap has ever acknowledged. In Chapter 2 of this book I display most of that inﬂuence with extensive quotations both from Carnap and Husserl. I complete my discussion of Husserl’s inﬂuence on the young Carnap’s extremely ambitious book in Chapter 3, in which I discuss only one issue, namely, the problem of our knowledge of the other psyche, brieﬂy, the problem of intersubjectivity. Once more I show with the help of extensive quotations the overwhelming similarities between Carnap’s and Husserl’s views, and point out that in the years 1924–25, while Carnap was visiting Husserl’s seminars, as attested by Ludwig Landgrebe, Husserl’s assistant during that period – who was then working on the second volume of Ideen zu einer reinen Phänomenologie und einer phänomenologischen Philosophie, subtitled: Phänomenologische Untersuchungen zur Konstitution – Carnap and Landgrebe had extensive philosophical discussions. From Husserl’s two fundamental books, but especially from Husserl’s seminars and from his discussions with Landgrebe, Carnap learned a lot about Husserl’s views, but was particularly reluctant to acknowledge it. Some of the momentary reasons for such a silence could have been the attitudes of his new partners in Vienna, especially Schlick and Neurath. But that does not explain much, since the ﬁrst died in 1936, and then Carnap moved to the United States, whereas Neurath remained in Europe and died in 1945. In particular, that explanation is totally inadequate to explain Carnap’s silence in his Autobiography. Hence, the reasons for Carnap’s silence are not completely clear. Chapter 4 is somewhat different from the ﬁrst three. At the beginning of the chapter, I mention some other issues discussed in Carnap’s later works, in which some possible inﬂuence of Husserl is present. The most sure and most outstanding inﬂuence is the one I already mentioned above, namely, the distinction between formation rules and transformation rules. Husserl had already made that distinction, using a different terminology, in Logische Untersuchungen – a book included in the bibliography both of Der Raum and Der logische Aufbau der Welt, though, interestingly enough, not in the bibliography of Logische Syntax der Sprache – and

Preface

xi

had also discussed the distinction in his 1929 Formale und transzendentale Logik, a book that should have at least aroused Carnap’s curiosity. Indeed, in Logische Syntax der Sprache there is only one reference to Husserl, on p. 44 of the German 1934 edition, on p. 49 of the English 1937 revised edition, and it is a very marginal one, namely, that Felix Kaufmann distinguished, following Husserl, two sorts of generality. The fact of the matter, however, is that Carnap was acquainted with Husserl’s Logische Untersuchungen at least since the time in which he was writing his dissertation, and Husserl’s distinction appears in Chapter XI of the ﬁrst volume, that is, at the end of the ‘Prolegomena’. There are no excuses for such an omission, nor are there excuses for omitting to mention that the distinction between two sorts of nonsense in ‘Überwindung der Metaphysik durch logische Analyse der Sprache’ was already present in the Fourth Logical Investigation. But Chapter 4 is not primarily concerned with Husserl’s inﬂuence on Carnap. Most of that chapter discusses other issues, especially, the later development of analytic philosophy in the hands of Quine and his followers. It is emphasized that the very important use of logical and mathematical tools in rigorous philosophy is completely independent of its usage as servants of an empiricist philosophy, which in its most radical recent expression, that of Quine, has produced so many questionable theses, and has paved the way for scepticism and post-modernist nonsense. Some of Quine’s fundamental theses and assumptions are submitted to severe criticism, and that is done not as an attack on analytic philosophy but, quite on the contrary, as an attempt to rescue it from the route of self-destruction that Quine and his followers are steering it to. The last chapter, however, is not merely a critique of post-Carnapian analytic philosophy. On the other hand, some new approaches to philosophical problems are interspersed and argued for throughout most of the chapter. The ﬁrst draft of this book was written during the academic year of 2004–2005, in which I had a sabbatical from the University of Puerto Rico at Río Piedras, speciﬁcally, from November 2004 onwards, since until the beginning of that month I was working on my recently published A Critical Introduction to the Philosophy of Gottlob Frege. I returned sporadically to the Frege book until the beginning of 2006 and, thus, in some sense was working on the two books at the same time, even after my sabbatical. In fact, in my ﬁrst semester after the sabbatical I taught a graduate course on logical empiricism, which helped me to sharpen my ideas and to have an excuse to re-read the ﬁrst draft of the book. This time I did not ask anyone to revise my English, and can only hope that it is intelligible enough. As in the case of the book on Frege, though my native tongue is neither German nor English, all translations from German into English are my own. The present book was written in almost complete isolation from other philosophers. As I already pointed out in the Preface to my book on Frege, that is almost inevitable for a professor at the University of Puerto Rico working on such sophisticated philosophical issues. Nonetheless, I have discussed some of the issues of the book with my former students Pedro Manuel Rosario Barbosa and, especially, Carlos Rubén Tirado Negrón. I thank both of them for their patience and friendship. I also thank very especially my friend Werner Diederich for his valuable help of providing me with a copy of Der Raum, as well as Thomas Mormann for sending me a pair of interesting unpublished papers and for some technical observations. I

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also thank the late Prof. Karl Schuhmann and Profs Sepp and Luft for the valuable information they provided me. Of course, none of them has any responsibility for the daring theses offered in this book. I hereby thank Open Court for the permission to quote extensively from Rudolf Carnap’s Der Raum, and Felix Meiner Verlag for the permission to quote even more extensively from Carnap’s Der logische Aufbau der Welt. My thanks also go to Paul Coulan, formerly of Ashgate Publishing Ltd, who was instrumental for having this and my former book on Frege published by Ashgate, and once more to my friend Jan Srzednicki for putting me in touch with Paul Coulan and Ashgate a few years ago. I want also to thank the whole staff of Ashgate Publishing Ltd, who have been so diligent in the different stages of the production of the book. As in my former A Critical Introduction to the Philosophy of Gottlob Frege (Ashgate 2006), I have had the pleasure to work with Mrs Anthea Lockley in the correction of my English. Her thorough and careful reading of the book as well as her patience have been of extraordinary help in the ﬁnal steps of preparation of the deﬁnitive manuscript. I most sincerely thank her, as well as Ashgate for having chosen her once more as reader. I should also especially acknowledge my gratitude to Mrs Rachel Lynch, Managing Director of Ashgate, for her continuous support of my project, which included the not easy task of obtaining the permissions for extensively quoting from Carnap’s books. As in my joint book with Claire O. Hill, Husserl or Frege?: Meaning, Objectivity and Mathematics (Open Court 2000, 2003) and my recent A Critical Introduction to the Philosophy of Gottlob Frege (Ashgate 2006), I have received technical help from my wife, Dr Tinna Stoyanova, and from our friend and Director of the LABCAD of the University of Puerto Rico at Río Piedras, Dr Joel Donato. Once more, it is a pleasure to publicly acknowledge my debt to them and to thank them for their technical assistance. My part of my joint book with my friend Claire O. Hill was dedicated to my mother Asia and to the memory of her older sister América, who was for me like a second mother. My more recent book was partially dedicated to my mother on her 100th birthday. I once more partially dedicate this book to her, this time to her memory, since she passed away in July 2007 at the tender age of 102 years. I also dedicate it to the memory of América and of her husband, Rafael, who not only was like a second father to me – I lost my father when I was three years old – but, more importantly, exerted the most decisive inﬂuence on me, since I moulded my moral character after him. Guillermo E. Rosado Haddock 27 October 2007

Chapter 1

Carnap’s First Husserlian Book: Der Raum A few decades after the demise of most of the ofﬁcial theses of logical empiricism an interest in the origins of that important philosophical school has arisen among analytic philosophers. Special attention has been given to the writings of the young Moritz Schlick, and even more to those of the young Hans Reichenbach and the young Rudolf Carnap. Particularly, Carnap’s especially important book, Der logische Aufbau der Welt,1 published in 1928, has been the object of intensive discussion and a variety of interpretations among Carnapian scholars. However, very few of those scholars have seen the necessity of examining Carnap’s dissertation, Der Raum,2 in order to better understand the young Carnap’s views and the evolution of his thought. The present author belongs to that small group of scholars who believe that to better understand Carnap’s views in Der logische Aufbau der Welt, one has to begin with an assessment of Der Raum, a work published in 1922, that is, three years before the completion of the ﬁrst version of his 1928 book. Thus, this chapter is concerned with Carnap’s dissertation. We will see in an unadulterated state the great inﬂuence that Edmund Husserl exerted on the young Carnap. 1 Introduction According to Carnap’s Intellectual Autobiography in the Schilpp volume,3 Carnap – who was born in Northern Germany in 1891 – moved with his family to Jena in 1909. From 1910 to 1914 he studied physics, mathematics and philosophy mostly in Jena, though it seems that he did spend – as is very common in Germany – some semesters in another university, in this case in Freiburg in Brisgau. Carnap does not specify when he was a student in the latter university, though Gottfried Gabriel in his introductory paper to Carnap Brought Home4 asserts that it was from 1911 to 1912 and that he attended, among others, courses of the neo-Kantian Heinrich Rickert. In Jena, Carnap’s best-known professors were Bruno Bauch, the neo-Kantian, who was professor of philosophy at that university since 1911, and Gottlob Frege. Carnap attended three of Frege’s lecture courses. He did not take part, however, in any seminar given by Frege. This is very important, and has not been sufﬁciently stressed by 1 Der Logische Aufbau der Welt (1928, fourth edition, Hamburg, 1967). 2 Der Raum 1922 (reprint, Vaduz, Liechtenstein, 1991). 3 Paul A. Schilpp (ed.), The Philosophy of Rudolf Carnap (La Salle, 1963), p. 3. 4 ‘Introduction: Carnap Brought Home’, in Steve Awodey and Carsten Klein (eds), Carnap Brought Home (Chicago and La Salle: Open Court, 2004), pp. 3–23. See p. 6.

2

The Young Carnap’s Unknown Master

Carnapian scholars. In German universities, traditionally a student did not have any contact with a professor offering a usual lecture course. The role of the students was essentially passive, and almost no one dared to interrupt a professor to ask questions. It was only in the seminars where the students got somewhat more acquainted with the professor, and the professor took notice of the existence of the students usually only when the student played an active role in the seminar. Moreover, only students who took part in seminars of a professor were considered to be his students, not those who merely heard lecture courses, but did not have any contact with the professor. Hence, it is not completely correct to assert – as some Carnapian scholars have done – that Carnap was a student of Frege in a strict sense. The relation that intrigues the present author, however – and has intrigued him for four decades – is that of Carnap with Husserl. Ofﬁcially, there was no contact between Carnap and Husserl. At least, Carnap seems never to have acknowledged such a contact and, superﬁcially, it seems to be so. During the years 1910 to 1914, Husserl was professor in Göttingen. Although in 1911 the University of Jena had Husserl ﬁrst in the list of possible candidates to occupy a vacant full professorship at that university, for some still unknown reasons, he did not receive the appointment, and instead it was precisely Bruno Bauch – Carnap’s future ‘Doktorvater’ – who was appointed. Moreover, Husserl received an appointment – as successor of Rickert – at the University of Freiburg in 1916, that is, during wartime, when Carnap was in military service. After the war, however, Carnap lived from 1919 to 1926 – with a few interruptions – in a town named Buchenbach, almost on the outskirts of Freiburg.5 During those years Husserl was generally regarded as the most important living German philosopher, and, moreover, one with an intellectual background very similar to that of Carnap, having studied mathematics, physics, philosophy and some astronomy.6 Nonetheless, Carnap seems never to have acknowledged that he had not resisted the temptation of meeting Husserl and taking part in his seminars or hearing his lectures. This selective amnesia is itself a mystery. In fact, there is some evidence that Carnap visited Husserl’s seminars three semesters in a row during the years 1924 to 1925,7 that is, exactly at the time when the former was ﬁnishing the ﬁrst version of Der logische Aufbau der Welt. In a letter to Husserl, Ludwig Landgrebe – Husserl’s former student and assistant during those years – mentions the fact that he got acquainted with Carnap in one of Husserl’s seminars during those years.8 But, as we will see, it is in Der Raum, ﬁnished in 1921 and published in 1922, where Husserl’s presence seems most explicit or, to put it in 5 See his ‘Intellectual Autobiography’in Paul Schilpp (ed.), The Philosophy of Rudolf Carnap, (La Salle, 1963), p. 10. 6 Analytic philosophers tend to ignore the fact that Husserl – like Frege and Whitehead – was a mathematician turned philosopher, who had been a student and assistant of Weierstraß, as well as a student of Kronecker. Moreover, he was a friend of Georg Cantor, and later of Felix Klein and David Hilbert, whose doctoral students during Husserl’s years in Göttingen used to study philosophy with Husserl. 7 See Karl Schuhmann’s Husserl-Chronik (Den Haag, 1977), p. 281. 8 See Edmund Husserl, Briefwechsel IV (Dordrecht, 1994), p. 298. See also Karl Schuhmann, Husserl-Chronik, p. 281. On that page, Schuhmann refers to a letter sent to him by Ludwig Landgrebe on 6 August 1976, conﬁrming that Carnap was Husserl’s student during that period.

Carnap’s First Husserlian Book: Der Raum

3

more exact terms, less censored. It remains an open question for historians of logical empiricism either to establish or to refute the hypothesis that Carnap visited Husserl’s courses or met Husserl personally during the years 1919 to 1921.9 In any case, the probability of Carnap not visiting Husserl during that period would be similar to that of someone writing his dissertation in the outskirts of Boston in the 1960s, referring very often to Quine in that work, but never having visited Quine’s lectures or seminars, or having met him, during that period. I have had the suspicion of a very strong Husserlian inﬂuence on the young Carnap for some forty years. I read the English expanded version of Carnap’s Logische Syntax der Sprache10 in the second half of 1967, while I was working on my MA thesis on Husserl’s theory of a purely logical grammar, and was impressed by the similarity between Carnap’s distinction between formation rules and transformation rules and Husserl’s distinction in the ﬁrst volume of Logische Untersuchungen11 and in Formale und transzendentale Logik12 between laws that protect against nonsense – the logico-grammatical ﬁrst layer of logic – and laws that protect against countersense and examine the validity of arguments – that is, the logical or deductive layer. Moreover, I was disturbed by the fact that Carnap does not acknowledge that such a nowadays so familiar distinction is essentially Husserl’s – not Carnap’s, nor Frege’s, Russell’s nor Hilbert’s – and presented to the philosophical public thirtyfour years before Carnap’s book. When some three years later I read Der Logische Aufbau der Welt – this time in German – I became convinced that the relation of that book with Husserl’s writings was much greater than that of Logische Syntax der Sprache. A few years ago I read Der Raum, and found Husserl’s inﬂuence on Carnap even more evident than in the other two writings. The sufﬁciently detailed exposition in the present chapter of Carnap’s views in that early neglected work will convince the reader of Husserl’s signiﬁcant inﬂuence on the young Carnap and will make very plausible the suspicion that Carnap had already visited Husserl’s seminars or lectures before he completed his dissertation, that is, during the years 1919 to 1921, when Landgrebe (born in 1901) almost surely was still not a student in Husserl’s seminars and certainly was not Husserl’s assistant.

9 There is a photograph on p. 294 of Hans-Rainer Sepp’s book Edmund Husserl und die phänomenologische Bewegung (Freiburg, second edition, 1988), of the (unidentiﬁed) participants in a seminar of Husserl in 1920. Among roughly twenty participants some faces seem familiar, namely, Martin Heidegger and Oskar Becker, at the extreme right, Husserl in the middle, and three places to the left of Husserl a student who looks somewhat like the young Carnap. Indeed, on p. 290 of the same book, there is a photograph of Carnap in 1923. However, in the unclear photograph, taken on an irregular terrain in a mountain, the student who looks like Carnap seems much shorter than Carnap was, and, thus, I am inclined to think that it is not him. That, of course, in no way weakens the suspicion that Carnap already visited Husserl’s courses while writing his dissertation. 10 Logische Syntax der Sprache 1934 (English expanded version, London 1937, Chicago et al., 2002). 11 Logische Untersuchungen (1900–1901, Den Haag, 1975 and 1984). 12 Formale und transzendentale Logik 1929 (Den Haag, 1974).

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2 Introduction to the Study of Der Raum The nineteenth century, especially its second half, and the ﬁrst two decades of the twentieth century were years of profound revolutionary transformations in the three most fundamental sciences, namely, physics, mathematics and logic. In mathematics, the development of non-Euclidean geometries by Bolyai and Lobatschevsky – already anticipated by Gauß – in the ﬁrst half of the nineteenth century, and the generalization and transformation of geometrical studies in the second half of that century in the hands of Riemann, Lie and Klein, among others, the emergence of algebraic structures as objects of mathematical research, as well as the rigourization of analysis at the hands of Bolzano and Cauchy in the ﬁrst half of that century, and its arithmetization at the hands of Weierstraß, Dedekind and Cantor in its second half, transformed our conception of mathematics, a transformation that was consolidated by the emergence of more abstract structures during the twentieth century, including general topology in its ﬁrst two decades. In logic, the pioneer work of Boole, De Morgan and others in the ﬁrst half of the nineteenth century was followed by the important contributions of Charles S. Peirce, Ernst Schröder and others in the second half of that century, culminating in the revolutionary contributions to logic of Frege, Peano, Russell and Whitehead. In physics, the development of electromagnetism in the middle of the nineteenth century represented the ﬁrst great challenge to Newtonian mechanics, whereas the emergence of the special and general theories of relativity, and of quantum mechanics in the ﬁrst decades of the twentieth century replaced our old Newtonian world with totally new conceptions. In philosophy, the Kantian foundation of science, which seemed to play the role of a philosophical foundation of Newtonian mechanics and Euclidean geometry, suffered a consequent earthquake, and had either to be abandoned or to be radically repaired, as some neo-Kantians attempted to do. In the same vein as other important philosophers of the ﬁrst half of the twentieth century well schooled in mathematics and physics – like Bertrand Russell, Moritz Schlick and Hans Reichenbach – Carnap begins his philosophical endeavours with a study of philosophical problems linked to the revolutionary development in our conception of space that occurred in the nineteenth century. However, in contrast to Russell, whose An Essay on the Foundations of Geometry13 of 1897 precedes the revolution in physics, as well as the development of general topology as an important area of mathematical research, and even some of the new developments in logic to which he would so decisively contribute some years later, Carnap – as well as his friend Reichenbach – had assimilated the development in the three fundamental sciences and was especially prepared and eager to put them to work in philosophical research.14 Thus, while in his above-mentioned book Russell contrasts the metric properties of space with the more general projective ones, he almost completely ignores the greater generality of topological spaces, and is not able to adequately assess the epoch-making 13 An Essay on the Foundations of Geometry 1897 (reprint, New York, 1956). 14 As attested by numerous passages in his Allgemeine Erkenntnislehre, English translation, General Theory of Knowledge (La Salle, 1985), Schlick had not beneﬁted from the development of logic from Boole to Hilbert.

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contributions of Riemann to our understanding of spatial structures.15 Carnap was perfectly conscious of the relevance of the topological properties of space for its adequate understanding, and since he wrote a few years after the emergence of the general theory of relativity, he was in a better position than Russell to appreciate Riemann’s views on spatial structures and, in general, on manifolds. As Carnap points out already in the Introduction to his valuable dissertation,16 his purpose in that small book is to offer an overview of the different sorts of space corresponding to the different meanings of the word ‘space’ in the philosophical and scientiﬁc literature. More speciﬁcally, Carnap distinguishes three different meanings of the word ‘space’, namely: (i) formal space, (ii) intuitive space, and (iii) physical space. With regard to the ﬁrst meaning, Carnap tells us17 that formal space is simply a relational structure, whose members lack of any determination, and about which one only knows that from some connections of a determined kind one can obtain conclusions about connections of another determined kind in the same region. On the other hand, Carnap explains the nature of intuitive space – on pp. 5–6 – as follows:18 By intuitive space, on the other hand, is understood the structure of relations between “spatial” ﬁgures in the usual sense … whose determined particularity we apprehend by means of perception or mere representation. One is still not concerned there with spatial facts present in empirical reality, but only with the “essence” of those ﬁgures, which can be recognized in any representative of the species. [Der Raum, pp. 5–6]

Any Husserlian scholar would easily recognize in the two quoted sentences of the Introduction to Der Raum three footprints of Husserlian thought. Firstly, one should mention the equivalence for the phenomenological apprehension of essences between perception and mere imaginative representation. Secondly, one should mention the interest for the essences of spatial ﬁgures, not for empirical facts. Finally, it should be mentioned that such essences are recognized in any representative of the species. With regard to physical space Carnap observes19 that its constituents are empirical spatial facts and, moreover, that our knowledge of physical space presupposes that of intuitive space, which, on the other hand, presupposes that of formal space. This presupposition is clearly not a psychological or empirical one, but one of a logical-epistemological nature, a foundational presupposition. Hence, Carnap will correspondingly examine ﬁrst formal space, then intuitive space, which is founded

15 See his Über die Hypothesen, welche der Geometrie zu Grunde liegen (third edition, Berlin, 1923, reprint, New York, 1960). 16 Der Raum, p. 5. 17 Ibid., pp. 5–6. 18 ‘Unter Aschauungsraum dagegen wird das Gefüge der Beziehungen zwischen den im üblichen Sinne ‘‘räumlichen’’ Gebilden verstanden, also den Linien-, Flächen- und Raumstücken, deren bestimmte Eigenheit wir bei Gelegenheit sinnlicher Wahrnehmung oder auch bloßer Vorstellung erfassen. Dabei handelt es sich aber noch nicht um die der Erfahrungswirklichkeit vorliegenden räumlichen Tatsachen, sondern nur um das ‘‘Wesen’’ jener Gebilde selbst, das an irgendwelchen Artvertretern erkannt werden kann.’ 19 Ibid.

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on formal space, and, ﬁnally, physical space, which is founded on the other two kinds of space. With respect to each of the three kinds of space Carnap distinguishes two sorts of subdivision. The ﬁrst subdivision concerns the number of dimensions, and here Carnap will essentially distinguish two cases, namely, the special case in which the number of dimensions of space is 3, and the general case in which the number of dimensions of space is n, where n is any positive integer. On the other hand, Carnap also distinguishes, in descending order from the more abstract to the more speciﬁc, three sorts of levels of spatial abstraction, namely, topological space, projective space, and metric space. Thus, Carnap will consider in Der Raum eighteen different sorts of space, namely, six formal ones, namely, R3T, R3P, R3M, RnT, RnP and RnM, six intuitive ones, namely, R’3T, R’3P, R’3M, R’nT, R’nP, and R’nM, and six physical ones, namely, R’’3T, R’’3P, R’’3M, R’’nT, R’’nP and R’’nM. 3 Formal Space: Topological, Projective and Metric In Chapter 1, Carnap considers formal space. According to Carnap,20 formal space is obtained by means of the tools of the new logic, especially the theory of classes and the theory of relations. In such a fashion ordered series are obtained, and, in particular, continuous series. Formal topological spaces of two or more dimensions can be introduced as continuous series of continuous series – thus, formal topological spaces of three dimensions as continuous series of continuous series of continuous series, that is, as continuous series of third level.21 The corresponding formal projective spaces are obtained from the formal topological ones by means of particularization. Finally, the corresponding formal metric spaces are obtained from the formal projective ones by further particularizations.22 Carnap stresses23 that only in this fashion can one obtain the complete generality required of formal space in order to include all possible subspecies. Thus, a continuous series of the third level – that is, a continuous series of a continuous series of a continuous series – is called by Carnap24 a formal topological space of three dimensions, in symbols: R3T. More generally, a formal topological space of n dimensions is a continuous series of nth level, in symbols: RnT. In this sort of abstract space, be it of 3 or of n dimensions, it does 20 Ibid., p. 7. 21 On this point, Carnap seems to have been inﬂuenced by Russell’s Principles of Mathematics of 1903. This would falsify Roberto Torretti’s assertion in his Philosophy of Geometry from Riemann to Poincaré (Reidel, 1977), p. 319, that Russell’s treatment of geometry in that work as the study of series of two or more dimensions had been completely ignored by philosophers and mathematicians. Indeed, in Der logische Aufbau der Welt (from now on, brieﬂy: Aufbau), p. 149, Carnap once more adheres to this Russellian procedure. Torretti does not mention either Der Raum or Aufbau in his otherwise valuable and encyclopedic book, probably since Carnap’s writings belong to a later period than the one considered by Torretti. 22 As Thomas Mormann stressed in an electronic communication, Carnap confused projective with afﬁne geometry and, thus, when he speaks about projective geometry the referent is usually afﬁne geometry. 23 Der Raum, p. 9. 24 Ibid., pp. 13–14.

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not make sense to speak of spatial ﬁgures. On the other hand, the particularizations that can be obtained from the formal topological spaces, thus, the formal projective spaces of 3 and n dimensions, and their further particularizations, the formal metric spaces of 3 and n dimensions, can only be justiﬁed, stresses Carnap,25 if one takes into consideration spatial ﬁgures properly. At this level, however, as Carnap puts it on p. 14:26 ‘Since here we are still concerned with mere formal relations, without presupposing the sort of objects that are in those relations with each other’. Carnap emphasizes27 that the relation between the formal topological space of three and, in general, of n dimensions, and the corresponding formal projective space of three – in symbols: R3P – respectively, of n dimensions – in symbols: RnP – is not the one existing between a species and an individual object belonging to the species, but that between a genus and a species, whereas the formal metric space of three dimensions – in symbols: R3M – respectively of n dimensions – in symbols: RnM – is a subspecies of R3P, respectively of RnP. Once more, both the terminology and the distinctions made by Carnap remind us, in the philosophical context in which Der Raum was written, of Husserl, who very frequently uses this Aristotelian terminology.28 4 Intuitive Space and its Sorts In Chapter 2 Carnap examines intuitive space, which is concerned not with purely formal relations, but with intuitive spatial ﬁgures and relations, thus, as Carnap clearly indicates,29 with points, lines, surfaces and spaces, as well as with relations like those of a point being on a line or the intersection of two lines. It should be stressed here that Carnap is not interested in the psychological origin of our representation of intuitive space, but only in the logical foundation of our knowledge of intuitive space, and, especially, in the axioms that serve as logical-formal basis of the remaining statements building up this knowledge. On this point, Carnap refers the reader to Hans Driesch, who had underscored the independence from experience of the axioms of intuitive space by saying that ‘… their knowledge does not become more secure, as is the case of empirical statements, by means of repeating the experience more and more’.30 Interestingly, when Carnap tries to explain why the repeated experience does not make such knowledge more secure – in other words, why repeated experience of

25 The German text reads: ‘Denn hier haben wir es ja immer noch mit bloß formalen Beziehungen zu tun, ohne daß vorausgesetzt wird, was für Gegenstände in diesen Beziehungen zu einander stehen.’ 26 Ibid. 27 Ibid. 28 See, for example, Ideen zu einer reinen Phänomenologie und einer phänomenologischen Philosophie I (from now on, brieﬂy Ideen I or II) (Den Haag, 1950), § 12, pp. 31–3, as well as Logische Untersuchungen I, § 63. 29 Ibid., p. 22. 30 Ibid. The German text reads: ‘… ihre Erkenntnis wird nicht, wie bei Erfahrungssätzen, durch die mehrfach wiederholte Erfahrung immer gesicherter.’

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relevant cases does not make them more probable – Carnap seeks explicit support in Husserl’s views. Thus, Carnap asserts:31 Since here one is not concerned, as Husserl has shown, with facts in the sense of empirical reality, but with the essence (“Eidos”) of certain given objectualities [Gegebenheiten], which being as they are, can be apprehended by means of [their] being given [Gegebensein] only once. [Der Raum, p. 22]

Moreover, adds Carnap:32 Since we refer here not to the isolated fact …, but to the non-temporal species, its “essence”, it can be important to distinguish this mode of experience from intuition in the strict sense, which refers to the fact itself, by means of the designation “contemplation of essences [Wesenserschauung]” (Husserl), where there could seem to be [some] confusion. But, in general, it can be the case that the expression intuition also includes the contemplation of essences, since in this wide sense is also used by Kant. [Der Raum, pp. 22–3]

The reference to Kant in this context seems to have been inserted by Carnap to appease his thesis director Bruno Bauch, who was not only a neo-Kantian, but also had been named professor of philosophy at Jena in 1911, after the university authorities opted at the last moment not to follow the recommendation of the faculty of naming Husserl to that position.33 The importance of that passage lies, however, in Carnap’s explicit acceptance of one of the cornerstones of Husserl’s philosophy, namely, the contemplation of essences, that seemed to separate orthodox Husserlians from non-Husserlians. Incidentally, he also uses expressions like ‘Gegebenheit’34 and ‘Gegebensein’, used very frequently in the same sense by Husserl. Thus, with

31 ‘Denn es handelt sich hier, wie Husserl gezeigt hat, gar nicht um Tatsachen im Sinne der Erfahrungswirklichkeit, sondern um das Wesen (“Eidos”) gewisser Gegebenheiten, das in seinem besonderen Sosein schon durch einmaliges Gegebensein erfaßt werden kann.’ 32 ‘Weil wir hierbei nicht auf die einzelhafte Tatsache eingestellt sind … sondern nur um seine zeitlose Art, sein “Wesen”, kann es von Wichtigkeit sein, diese Erfahrungsweise von der Anschauung im engeren Sinne, die auf die Tatsache selbst geht, durch die Benennung “Wesenserschauung” (Husserl) zu unterscheiden, wo Verwechslung möglich erscheint. Im Allgemeinen mag aber der Ausdruck Anschauung auch die Wesenserschauung mit umfassen, da er in diesem weiteren Sinne auch schon von Kant her gebräulich ist.’ 33 The reason for the change of mind of the university authorities is still unclear. It seems that someone intervened, but it is not clear who he was and why did he do it. A plausible hypothesis is that it was Rudolf Eucken, the other philosophy full professor, but even then it is not clear whether Frege or someone else urged him to intervene. A very questionable answer has been given by Uwe Dathe in his paper ‘Eine Ergänzung zur Biographie Edmund Husserls’, in Werner Stelzner (ed.), Philosophie und Logik (Berlin, 1993), pp. 160–66. According to Dathe, it was a letter by a former student of Husserl to Rudolf Eucken – reproduced on pp. 164–5 of the paper – that convinced the faculty of not opting for Husserl. It is, however, very doubtful that a full professor in nineteenth-century Germany would give so much credit to an undistinguished mere doctor. 34 For the extensive use of the technical word ‘Gegebenheit’in Husserl’s Ideen I, see the content index, p. 431, of the Husserliana edition.

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respect both to terminology and to a very distinctive issue of Husserlianism, the young Carnap of Der Raum sides with the Husserlians. As Carnap emphasizes,35 only the axioms of intuitive space need to be obtained from intuition, understood as intuition of essences, not as empirical perception. However, as Carnap also stresses,36 our intuition is limited to a determinate region of space, and, thus, from our intuition ‘… one can also only obtain knowledge about spatial ﬁgures of limited size. On the contrary, we are free with respect to the complete structure, which we build from the basic ﬁgures.’ Thus, for example, we obtain the notion of an unlimited straight line from a straight line in our limited intuitable region, by means of an iterated addition of similar straight lines. However, as Carnap correctly indicates,37 ‘… to the concept so obtained [of an unlimited straight line] there corresponds not only the inﬁnite straight line, but also the ﬁnite, though unlimited, closed straight line of elliptic [Riemannian] space’. Hence, Carnap adds38 that neither intuition properly nor the requirement of iteration of the intuitively given allows us to decide between the two possible unlimited extensions of a ﬁnite straight line. In the case of intuitive space, Carnap opts to proceed in the direction opposite to that followed in the case of formal space. Thus, he ﬁrst examines the more determined metric space, then the projective (or afﬁne) space and, ﬁnally, the topological space. Moreover, following Hilbert39 – and breaking with traditional Euclidean axiomatization of geometry, defended by his former professor Frege – instead of ﬁxing the meaning of the fundamental concepts and relations of intuitive space by means of explicit deﬁnitions, Carnap offers (in pp. 24–6) a list of eighteen axioms, which will play the role of implicit deﬁnitions of the concepts they contain. Axioms 1–12 are connection axioms, whereas the remaining axioms, with the exception of the last two, are axioms of congruence. The axioms are going to be valid in the limited region of intuitive metric space of three dimensions. In fact, axioms 17 and 18 differ from the corresponding axioms of Hilbert by limiting the congruence between triangles and the parallelism between straight lines to the immediately intuitable region. The next step will clearly consist of the extension of the validity of the axioms to the whole intuitive metric space of three dimensions R’3M. Carnap introduces40 six requirements for the extension of the validity of the axioms to the whole intuitive metric space of three dimensions. The ﬁrst requirement states that the axioms are going to be valid in any limited region of three-dimensional intuitive metric space, whereas the remaining requirements allow Carnap to extend the validity in limited regions to the whole space under consideration. Thus, axioms 35 Der Raum, p. 23. 36 Ibid. The German text reads: ‘… lassen sich ihr auch nur Erkenntnisse über räumliche Gebilde von beschränkter Größe entnehmen. Dagegen haben wir inbezug auf das Gesamtgefüge, das wir aus diesen Grundgebilden aufbauen, freie Hand.’ 37 Ibid. The German text reads: ‘… dem so gewonnenen Begriff entspricht dann nicht nur die unendliche Gerade, sondern auch die endliche, aber endlose, geschlossene Gerade des elliptischen Raumes.’ 38 Ibid. 39 David Hilbert, Die Grundlagen der Geometrie (1899, tenth edition, Stuttgart, 1968). 40 Der Raum, p. 26.

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1–4 and 13–16 will be valid for the whole three dimensional intuitive metric space, whereas in the case of axioms 17 and 18 to the sort of equality valid in the limited region – that is, to the congruence of triangles and the parallelism of lines – in the whole space under consideration there corresponds a relation that approximates to the corresponding sort of equality. In this way, as Carnap stresses,41 the whole space will have the property, whose importance was recognized for the ﬁrst time by Riemann,42 of Euclidicity in its smallest parts or, better, local Euclidicity. In other words, space will be a manifold, that is, it is required of space that it be locally homeomorphic to Euclidean space of n dimensions, where in the case under discussion n=3.43 Carnap reminds us44 that Riemann already exhibited the different possible structures of three-dimensional intuitive space compatible with the local Euclidicity, where what is decisive for each of these different sorts of intuitive metric spaces is the assignment of an ordered triple to each point in the space, the measure of curvature, in which each number corresponds to one of the three dimensions of space. As already mentioned and reiterated by Carnap,45 the purpose of the introduction of the six requirements is to allow the extension of intuitive properties and relations in the limited region to which we have intuitive access – and expressed in the eighteen axioms – to the whole three-dimensional intuitive metric space.46 Now, in order to obtain the properties and relations valid in that space, Carnap does not proceed by examining the different curved surfaces and ﬁxing for each point in that curved surface what is usually called the Gaussian curvature – applied by Gauß only to twodimensional spaces – but instead proceeds to examine the different planes in such a space, since neither the diversity of planes in that space is smaller than that of curved surfaces nor the diversity of relations in the planes is smaller than the diversity of relations in the curved surfaces. The study of the spatial relations in such planes is obtained by means of the assignment of an ordered triple to each point in the plane, and allows us to obtain the Riemannian curvature of each point in the plane.47 Of course, as Carnap emphasizes,48 when he talks about planes he does not have in mind the usual Euclidean notion of plane, but only that of a surface such that no matter which two points on the surface can be connected by a straight line lying completely on the surface. On the other hand, by ‘straight line’ is to be understood a line any 41 Ibid., p. 27. 42 See Riemann’s revolutionary monograph Über die Hypothesen, welche der Geometrie zu Grunde liegen referred to above. 43 See on this point, for example, Morris W. Hirsch, Differential Topology (New York et al., 1976), p. 1. 44 Der Raum, p. 27. 45 Ibid. 46 It should be emphasized here that Carnap did not state that we only have intuitive access to an inﬁnitesimal region of space or that his requirement of local Euclidicity concerns inﬁnitesimal regions of space. Our intuitive region of space is an extremely small but ﬁnite part of the space of the whole universe. 47 For a detailed discussion of Gaussian curvature of surfaces, Riemannian curvature of spaces, and their relation, see the excellent book by Lawrence Sklar, Space, Time and Spacetime (Berkeley et al., 1974), pp. 27ss. and pp. 42ss. 48 Der Raum, p. 28.

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segment of which, connecting no matter which two points P1 and P2, is the shortest line between such points. Now, if the ordered triples of numbers assigned to a region of the plane coincides with the ordered triples of numbers assigned to the points of a determined curved surface, then the same spatial relations are present in the plane and in the curved surface. In this way, the seemingly more complicated direct study of the structure of the diverse curved surfaces in the three-dimensional intuitive metric space is replaced by the study of the structure of the diverse planes. These speciﬁcations are perfectly compatible not only with the assignment of a measure of curvature to any point – thus, the corresponding ordered triple – but also with the possibility that the ordered triples assigned to the different points of a straight line do not coincide with <0,0,0>, that is, with the possibility of non-Euclidean geometries. In order to avoid possible misunderstandings, it should be emphasized here that Carnap in no way attempts to determine the structure of the whole intuitive metric space as a sort of extrapolation of the structure of intuitive metric space in the directly intuitable limited region. He only requires that the structure of intuitive metric space, be it parabolic, hyperbolic, elliptic or whatever, and be it of constant or of variable curvature, should be locally homeomorphic to Euclidean space. Before continuing the presentation of the fundamental issues treated in Carnap’s neglected dissertation, it is important to highlight the contrast between Carnap’s Der Raum and Russell’s dissertation An Essay on the Foundations of Geometry. Whereas Russell denies any consideration to spaces of variable curvature, thus, to spaces such that to different points in the space different measures of curvature are assigned, a possibility already stressed by Riemann, for Carnap such spaces are perfectly legitimate. Of course, one could argue that, contrary to Russell, Carnap’s dissertation was written after the emergence of general relativity, according to which the structure of our physical spacetime is that of a four-dimensional continuous manifold with variable curvature. Thus, Riemann’s views on space had been already vindicated by Einstein’s 1915 theory. However, in view of the high level of abstraction of Carnap’s dissertation, Carnap’s treatment of space could very well have been conceived, even if the theory of general relativity had not been already known. In fact, with respect to the level of abstraction, there is also an important difference between Carnap’s and Russell’s dissertations. Russell’s dissertation dates from 1897, thus, more or less a decade before general topology emerged as an autonomous abstract mathematical discipline. Hence, in Russell’s book topological considerations are by far less fundamental than in Carnap’s book. It is projective space, which offers the most fundamental framework. On the contrary, in Carnap’s dissertation general topological spaces not only offer the abstract framework, but also the role of what Carnap calls projective space is much more diminished. General topological spaces give the mathematical framework for Der Raum, whereas projective (or better: afﬁne) spaces, though considered as an intermediate stage of abstraction between topological and metric spaces, receive less and less attention as Carnap goes deeper in his analyses, especially when considering physical space. Continuing with the exposition of the fundamental aspects of Carnap’s dissertation, after stressing that three-dimensional intuitive metric space is completely determined once an ordered triple of numbers corresponding to the three different spatial directions is assigned to each point, Carnap examines spaces of constant curvature.

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Thus, he introduces the well-known deﬁnitions of homogeneity and isotropy,49 as well as their relation. We prefer to quote Carnap here ﬁrst: Now, if for each point in space the same three numbers are valid, then the same metrical relations are valid in each part of space as in any other. Every plane in this space has then in all its points the same measure of curvature, (“planes of constant curvature”), but it does not have to be the same for all planes. [Der Raum, p. 28]50

Moreover, though parallel planes of constant curvature would also need to have the same curvature, perpendicular planes of constant curvature do not need to have the same curvature. This is so because in homogeneous space the numbers assigned as coordinates to any given point do not have to coincide or, in other words, an interchange of coordinates – as happens when the direction of a plane is rotated – could change the curvature of the plane. Continuing with the other deﬁnition, Carnap says: If, on the other hand, in each point of space the three valid numbers are equal to each other, then there all directions of space are equivalent [gleichartig]. Space is called in such a case isotropic. If both conditions are met, then all points and all directions are equivalent [gleichartig]; all the distinctive numbers of this homogeneous and isotropic space are equal between them: the measure of curvature of “space of constant curvature”. In this case, all planes in space are not only planes of constant curvature, but all equivalent [gleichartig] with one another; the curvature is for all the same, and, incidentally, the same as that of space. [Der Raum, pp. 28–9]51

Clearly, if a space is isotropic but not homogeneous, its curvature could be arbitrarily variable from point to point, though in each point the three coordinates need to coincide. Thus, in an isotropic but not homogeneous plane, there can very well exist a point P with curvature <0,0,0> and another point P* with curvature <-1,-1,-1>, but no point with curvature <-1,0,0>. On the contrary, in a homogeneous but not isotropic plane a point can very well have curvature <-1,0,0>, though then all points in the plane must have the same curvature, since it is not possible that in such a plane two points have different curvature. Carnap goes on to consider the different sorts of planes determined by their curvature. Thus, if the curvature is negative, we have a hyperbolic plane; if it equals

49 See Der Raum, p. 28. 50 ‘Gelten nun für jeden Punkt des Raumes dieselben drei Zahlen, so herrschen auch an jeder Stelle des Raumes dieselben Maßverhältnisse wie an jeder andern. Eine jede Ebene dieses Raumes hat dann in allen ihren Punkten gleiches Krümmungsmaß (“Ebene konstanter Krümmung”), das aber nicht für alle Ebenen dasselbe zu sein braucht.’ 51 ‘Sind andrerseits in jedem Punkte des Raumes die drei dort geltenden Zahlen einander gleich, so sind dort alle Richtungen des Raumes gleichartig. Der Raum heißt in diesem Falle isotrop. Sind beide Bedingungen erfüllt, so sind alle Punkte und alle Richtungen gleichartig; alle Kennzahlen dieses homogenen und isotropen Raumes sind einander gleich: das Krümmungsmaß des “Raumes konstanter Krümmung”. In diesem Falle sind alle Ebenen des Raumes nicht nur Ebenen konstanter Krümmung, sondern alle untereinander gleichartig; die Krümmung ist für alle gleich, und zwar gleich der des Raumes.’

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zero, we have a parabolic (or Euclidean) plane; and if it is positive, we have an elliptic plane. Carnap examines some very well known properties of those three sorts of planes and, in general, of the corresponding three sorts of geometry. Consequently, for example, in the case of a plane with negative curvature the sum of the angles of a triangle is less than 180°, and through a point not on a given straight line passes more than one – more precisely: inﬁnitely many – straight lines parallel to the ﬁrst straight line; in the case of our familiar parabolic (or Euclidean) plane the sum of the angles of a triangle equals 180°, and through a point not on a given straight line passes exactly one straight line parallel to the ﬁrst straight line; whereas in the case of elliptic space the sum of the angles of a triangle is greater than 180°, and through a point not on a given straight line does not pass any straight line parallel to the ﬁrst straight line. Finally, Carnap stresses52 that whereas in the ﬁrst two cases the planes – and thus, the whole spaces – are inﬁnite, in the third case the plane – and also the whole space – is ﬁnite but unbounded. Carnap concludes his treatment of three-dimensional intuitive metric space as follows: ‘Beginning with facts, which intuition offers us for a limited spatial region, we have found, with the aid of some requirements, the diverse sorts of complete spatial structures, in all of whose limited regions those intuitive facts are valid’.53 Carnap’s next step consists in the consideration of more general intuitive spaces. Two different sorts of generalization are possible. The ﬁrst one is the obvious one of generalizing the dimensions of space by considering spatial structures of four or more dimensions. Thus, Carnap considers intuitive metric spaces of four – R’4M – and, in general, n dimensions – R’nM – for any natural number n. Clearly, the subdivision in hyperbolic, parabolic and elliptic subspecies obtained in the case of threedimensional intuitive metric space can be obtained in the case of any of its dimensional generalizations, and, moreover, the subspecies of three dimensional intuitive metric space will be parts of the corresponding subspecies of all the n-dimensional intuitive metric spaces R’nM, for all n>3. Carnap makes it clear,54 however, that already in the case of four-dimensional intuitive metric space our intuition requires some conceptual aid. Nonetheless, Carnap reminds us,55 that even in the case of three-dimensional space, we can only intuit limited regions of space, not the space as a whole, but such a limitation has not prevented us from considering the whole R’3M. Carnap points out56 that we can base our considerations on intuitive ﬁgures of three dimensions and, with the aid of some conceptual relations, in some sense represent four-dimensional ﬁgures, though such a possibility is not purely intuitive, but intuitive-conceptual.57 52 Ibid., p. 29. The German text reads: ‘Wir haben aus den Tatsachen, die uns die Anschauung für ein beschränktes Raumgebiet liefert, mit Hilfe der Aufstellung gewisser Forderungen die verschiedenen Arten vollständiger Raumgefüge gefunden, in deren beschränkten Gebieten überall jene Anschauungstatsachen zutreffen.’ 53 Ibid. 54 Ibid., p. 30. 55 Ibid. 56 Ibid. 57 On the issue of the presumed non-intuitivity of geometries different from our familiar three-dimensional Euclidean geometry see Henri Poincaré’s Chapter III, pp. 63–76 of his La Science et l’Hypothèse (1902, reprint, Paris, 1968), as well as Albert Einstein’s ‘Geometrie

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The other sort of generalization consists in abstracting from all properties of space dependent on its metrical relations, thus, in raising our considerations to the superordinate genera. On this point, Carnap introduces projective spaces as follows:58 A spatial structure built on the basis of the fundamental concepts of point, line and plane, together with the relation of lying on, without making use of segments or angles, can be formed [gestalten] in such a way that all those differences [between the three subspecies of R’3M – GERH] disappear. Such a structure is called projective [intuitive – GERH] space R’3P.59 [Der Raum, pp. 30–31]

Carnap adds60 that if we also ignore the concepts of straight line and plane, limiting ourselves to the consideration of points, lines and surfaces, then we obtain threedimensional intuitive topological space R’3T. Moreover, it should be clear that one can obtain the more general n-dimensional intuitive projective space R’nP and the still more general n-dimensional intuitive topological space R’nT in two different ways. Thus, one can combine the two sorts of generalization, applying to the spaces R’nM, for any natural number n, the same procedure used to obtain three-dimensional intuitive projective space and three-dimensional intuitive topological space from R’3M, or one can obtain R’nP and R’nT from n-dimensional formal projective space RnP, respectively, from n-dimensional formal topological space RnT, by introducing in them the corresponding intuitive spatial ﬁgures, thus, intuitive points, straight lines and planes in the case of projective (better: afﬁne) space, intuitive points, lines and surfaces in the topological case. Clearly, as Carnap stresses,61 n-dimensional intuitive topological space is the most general of all intuitive spaces, and contains all other intuitive spaces either as parts – for example, R’3T – as particularizations or specializations – for example, R’nP and R’nM – or as a combination of both – for

und Erfahrung’ (1918), translated and reprinted in his Sidelights of Relativity ( New York, 1921) pp. 27–56. 58 ‘Ein räumliches Gefüge, das auf den Grundbegriffen Punkt, Gerade und Ebene ihre Beziehungen des Aufeinenderliegens aufgebaut ist, ohne der Strecken- und Winkelgleichheit zu verwenden, läßt sich daher so gestalten, daß jene Unterschiede hier wegfallen. Ein solches Gefüge heißt projektiver Raum R’3P.’ 59 As mentioned in footnote 22, Mormann has pointed out that Carnap confounds projective with afﬁne space. For the distinction between both spaces, see Robert Coleman and Herbert Korté’s long survey of Hermann Weyl’s views ‘Hermann Weyl: Mathematician, Physicist, Philosopher’, in Erhard Scholz (ed.), Hermann Weyl’s Raum-Zeit-Materie and a General Introduction to His Scientiﬁc Work (Basel et al., 2001), pp. 161–386. See pp. 203–8. See also Lawrence Sklar’s particularly clear discussion of afﬁne geometry and afﬁne transformations in his already mentioned book Space, Time and Spacetime, pp. 50–51, Thomas Mormann’s unpublished papers Geometrical Leitmotifs in Carnap’s Early Philosophy’and ‘Carnap’s Metrical Conventionalism versus Differential Topology’, and, of course, Hermann Weyl’s classic and also especially clear Raum-Zeit-Materie , English translation, Space-TimeMatter (New York, 1952) pp. 17–26. 60 Der Raum, p. 31. 61 Ibid.

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example, R’3M, which can be conceived either as a specialization of R’3T, or as a part of R’nM. Before continuing with the exposition of the fundamental issues of Carnap’s Der Raum, it is convenient again to remind the reader that Carnap’s constant use of the terminology of genera, species and subspecies, as well as the distinction between specialization (or particularization) and singularization is very frequent in Husserl’s most important writings published before 1922, namely, Logische Untersuchungen62 and Ideen I.63 Such a similarity is, of course, no coincidence, especially after Carnap’s commitment to the contemplation of essences. 5 Physical Space and its Sorts In Chapter 3 Carnap considers the sorts of physical space. Thus, he is interested in examining spatial relations present in nature, that is, physical-spatial relations. As Carnap puts it:64 ‘The doctrine of physical space has, thus, the task of checking which of these [spatial] relations are valid for the determinate things present in experience.’ Before entering properly in the discussion of physical space, Carnap draws attention65 to a possible misunderstanding, especially since he is going to argue that there is very little to say about physical-spatial relations on the mere basis of observation. Thus, Carnap makes it clear that he is not interested in the popular opinion that physical-spatial ﬁgures cannot be determined with complete exactness. Such an opinion, probably based, adds Carnap,66 on the irregular form of bodies in nature, as well as in the physical limitations of the precision attainable by our measurement instruments, is irrelevant to his discussion of physical space. Carnap examines ﬁrst what is to be understood by a straight line in physical space, and observes67 that one has to presuppose something being straight, for example, light rays. Nonetheless, he immediately adds the following important remark:68 ‘It is impossible in principle to establish that [for example, that light rays are straight – GERH], if one considers only what proceeds exclusively from experience, without making some freely chosen stipulations about objects of experience. Such stipulations, which are presented as requirements, without they being capable of ever being conﬁrmed or refuted by experience…’. 62 See Logische Untersuchungen I, § 63. 63 See Ideen I, §§ 9–10. 64 Der Raum, p. 32. The German text reads: ‘Die Lehre vom physischen Raum hat also die Aufgabe, festzustellen, welche dieser Beziehungen für die bestimmten, in der Erfahrung vorliegenden Dinge gelten.’ 65 Ibid. 66 Ibid. 67 Ibid., p. 33. 68 The German text reads: ‘Es ist grundsätzlich unmöglich, dies festzustellen, wenn man sich nur an das hält, was eindeutig aus der Erfahrung hervorgeht, ohne freigewählte Festsetzungen über Erfahrungsgegenständen zu treffen. Solche Festsetzungen, die forderungsmäßig aufgestellt werden, ohne daß sie jemals durch Erfahrung bestätigt oder widerlegt werden könnten….’

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Thus, experience alone cannot uniquely determine what is a straight line in physical space, and we need stipulations, that is conventions to ﬁx what is going to be understood by a straight line. On pp. 34–5, Carnap considers another approach to the ﬁxing of a straight line in physical space, albeit an indirect one. This well-known procedure consists in selecting a rigid body, usually a rigid rod, and selecting two points on the rod. Then one assigns a numerical measure, for example, unity to the distance between the two points on the rod, in determined physical circumstances, like those of temperature, direction and location in physical space. Then there are various ways of examining the presumed straightness of a line on the basis of the notion of rigid rod. Carnap examines two of them, but I consider it unnecessary to present them here. It is, however, important to have in mind that, at ﬁrst sight, the objective is to obtain the most simple stipulation of measurement, though the solution is not as straightforward as one might think. Carnap points out69 that, even in the case that the stipulation of measurement were completely conscious, one usually proceeds from some tacitly presupposed principles of scientiﬁc procedure. Those principles are in no way determined by empirical facts, whereas, on the other hand, the selection of a given stipulation of measurement is, as Carnap stresses70 not independent of such principles of scientiﬁc procedure, which, for example, require that the stipulations be consistent with empirical facts. Thus, the principles, among other things set limits to the arbitrariness of stipulations. Now, as Carnap emphasizes,71 the most decisive point in this whole discussion on the determination of a straight line in physical space is that such a determination cannot be obtained exclusively from empirical facts, but requires also a stipulation, be it direct, by means of ﬁxing what is going to be understood by a straight line – for example, a light ray – or be it indirect, by means of ﬁrst stipulating a unity of measurement and a rudimentary system of measurement, and on its basis ﬁxing what a straight line is. Carnap observes72 that this last procedure has a clear advantage over the ﬁrst one, namely, that one not only determines whether a given line segment is a straight line or not, but also establishes its quantitative relations. Carnap goes on to examine the different sorts of physical space. Thus, on pp. 37–8, Carnap points out that, as in the case of three-dimensional intuitive topological space, three-dimensional physical topological space R’’3T is not concerned with straight lines or with magnitude relations and thus, for it, neither stipulations about the nature of straight lines nor measurement stipulations are relevant. On the contrary, three-dimensional physical topological space is concerned with incidence relations of points, lines, surfaces and parts of physical space in the whole physical space, since they are the only relations required for the ordering of empirically given ﬁgures in that space. Hence, as Carnap stresses,73 for R’’3T only those relations between physicalspatial ﬁgures are relevant, which are independent of any sort of convention or stipulation. Since up to now our experience has not required physical spaces of more 69 70 71 72 73

Ibid., p. 35. Ibid., p. 36. Ibid. Ibid., p. 37. Ibid., p. 38.

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than three dimensions, Carnap will not examine the possible generalization of R’’3T to R’’nT, that is, to n-dimensional physical topological space, for any positive integer n. Nonetheless, R’’nT remains always as a possibility, and Carnap clearly stresses74 that three-dimensionality can in no way be seen as a condition of possibility of an object of experience in general, since it could very well be indicated what sort of empirical facts would have to be present in order that we could conceive them as fourdimensional ﬁgures. Although I prefer not to interrupt the exposition at this point, it should be emphasised that Carnap’s assertion already distances him from Kant, who viewed three-dimensional Euclidean space as a condition of possibility of objects of experience in general. We will later see that Carnap’s remark was in no way an isolated one. Continuing with the exposition, Carnap asserts,75 on the other hand, that, though three-dimensional physical topological space reproduces everything that is given in space without the aid of stipulations or conventions, both three-dimensional physical projective (better: afﬁne) space R’’3P, which requires the stipulation of what is a straight line, as well as three-dimensional physical metric space R’’3M, which requires a stipulation of measurement, are not uniquely determined by empirical facts. In either case, a selection is required among the various possibilities determined by the different stipulations of straight line, respectively, of measurement. On pp. 38–40, Carnap tries to make more precise the preceding important distinction. Thus, he ﬁrst deﬁnes as factual content [in German: Tatbestand] the experiential matter as it is present without having suffered any transformation. To determine whether an empirical statement is a statement solely about the factual content and, in general, to be able to differentiate between what in the statement concerns the factual content and what concerns the special form selected, one would have to examine whether the statement is valid for each and every spatial structure. This can be made precise by means of the mathematical notion of invariance under bijective continuous transformations, frequently called ‘homeomorphisms’ by mathematicians. Now, exactly the topological properties of a space are those that remain invariant under homeomorphisms. On the contrary, neither projective (or afﬁne) nor metric properties of a space are invariant under bijective continuous transformations. Thus, statements about the projective (or afﬁne) or metric properties of space are not statements solely about the factual content of experience, but also contain stipulations. More accurately, statements about straight lines and planes are – according to Carnap76 – statements about three-dimensional physical projective (really: afﬁne) space, whereas those concerned with equality (or congruence) of segments or angles are statements about three-dimensional physical metric space. In this especially elegant fashion, Carnap contends to have isolated what in physical space belongs to the factual content given in experience without adulteration of its form by means of some sort of stipulation.77 74 Ibid. 75 Ibid. 76 As mentioned in footnotes 22 and 59, Carnap seemed not to distinguish between projective space and afﬁne space. 77 Such a contention has been attacked from different angles. The most important critique questions, on the basis of results in differential topology, the presumed independence

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As Carnap puts it,78 the notion of factual content, which embraces the totality of the empirical content of statements, comprises exactly what is empirically given in physical space. Precisely that content is what is present in three-dimensional physical topological space, R’’3T. Nonetheless, from the point of view of our knowledge of physical nature, what is by far more important is not three-dimensional physical topological space – nor its projective specialization – but three-dimensional physical metric space, R’’3M, which is speciﬁcally concerned with measurement. To obtain it from three-dimensional physical topological space, as Carnap observes79 – it is convenient to have in mind that from now on, Carnap almost completely ignores projective space – one can, for example, ﬁx two different points on an iron bar and stipulate that the distance between those two points will play the role of unit of measurement. Of course, as Carnap stresses,80 in order to function as unit of measurement – or measurement scale [Maßstab] – the distance between the two given points is supposed to be rigid, that is, not changing or invariant through time and under spatial displacements. On the basis of the factual content and of the stipulation of the unit of measurement, and, as Carnap emphasizes,81 only on such a basis, is the nature of three-dimensional physical metric space, R’’3M, to be determined. Before continuing his discussion, Carnap makes it clear82 that in the whole discussion of physical space, be it topological, projective (or afﬁne) or metric, one is considering only a three-dimensional projection of the four-dimensional spatialtemporal multiplicity that constitutes, according to both the special and general theories of relativity, the structure of the physical world in which we live. As Carnap observes,83 we can obtain such a projection by selecting three coordinates from Minkowski’s four-dimensional spacetime for special relativity, with the condition that none of the three coordinates lies in the double temporal cone representing the past and future. Of course, there is plenty of liberty for a possible choice of such a three-dimensional projection. Carnap partially reduces such excessive liberty by restricting his consideration to those spatial relations independent of the determination of simultaneity, a restriction that can be obtained by limiting measurement to ﬁgures not in motion. After such explanations, Carnap goes on to deﬁne in the usual manner the notion of rigidity: ‘We want to call “rigid” a set of points, a line, a piece of surface or body with respect to a determined measurement stipulation, in case with respect to it the distance between no matter which points remains indeﬁnitely the same.’84 Of course, of the topology from the metric of space. See on this issue p. 54 of Sklar’s already mentioned book, and the more detailed discussion in Thomas Mormann’s unpublished paper ‘Carnap’s Metrical Conventionalism versus Differential Topology’. 78 Ibid., p. 40. 79 Ibid. 80 Ibid. 81 Ibid. 82 Ibid., pp. 40–41. 83 Ibid., p. 41. 84 Ibid., p. 42. The German text reads: ‘Wir wollen eine Punktmenge, ein Linien-, ein Flächenstück oder einen Körper “starr” inbezug auf eine Maßsetzung nennen, wenn inbezug auf sie der Abstand je zweier Punkte der Menge dauernd gleich bleibt.’

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the deﬁnition of rigidity given by Carnap presupposes the rigidity of the iron bar in which the scale is speciﬁed. The curvature of a plane in physical space can be established by examining the usual properties of geometrical ﬁgures in the plane, for example, the sum of the angles of a triangle. Carnap opts,85 however, for a less popular way of establishing such a curvature, namely, by ﬁxing a point in a plane and building six equilateral triangles around it. Thus, if the six equilateral triangles cover the whole region around the point without leaving any gaps and without any intersection between them, the plane is parabolic (or Euclidean); if there are no gaps left, but some of the triangles have a non-empty intersection, the plane is elliptic; ﬁnally, if the triangles do not intersect, but also fail to cover the whole region around the point, leaving, thus, gaps, the plane is hyperbolic. Carnap emphasizes86 that if one wishes to determine the curvature, one needs a procedure for measuring segments, a procedure obtained from the stipulation of measurement, with the aid of the scale. However, Carnap stresses87 that only the topological properties of the plane, thus, those that constitute the factual content – for example, the relation of a point lying on a line or segment of the plane – can be established by means of such a procedure. Once the curvature is ﬁxed in a part of the plane, one can do the same thing in other parts of the plane in order to determine the metrical relations in the whole plane. According to Carnap88 the number of points to be considered will depend on the greater or lesser divergences obtained in the different parts of the plane. Clearly, greater divergences would require the consideration of more points, whereas greater uniformity would make it unnecessary to consider as many points. What is important, however, is that Carnap believed that by means of such a procedure one can ﬁx the curvature of the whole region and, with its help, in principle, that of the whole physical space.89 Still more important is for Carnap ‘… ﬁrstly, that the determination of the metrical relations of physical space makes sense only if a freely selected measurement stipulation is exhibited [in German: ausgestellt], and, secondly, that such determination takes from experience only the factual content, that is, only considers and evaluates topological properties of physical spatial ﬁgures, without presupposing the straightness of any physical line…’.90 Up to now, Carnap has proceeded in such a way that the nature of physical space is a mathematical function of an empirical component, given by the factual content, and a conventional component, given by the stipulation of measurement. Carnap goes on to show that one could very well begin with the factual content and the metrical relations of space, and obtain the stipulation of measurement as a function of the other two. It is unnecessary to enter into the details of Carnap’s discussion of 85 Ibid., p. 43. 86 Ibid. 87 Ibid., p. 44. 88 Ibid., p. 45. 89 This is possible only if spaces of variable curvature are not considered. 90 Ibid. The German text reads: ‘… erstens die Feststellung der Maßverhältnisse des physischen Raumes nur einen Sinn hat, wenn eine frei wählbare Maßsetzung aufgestellt worden ist, und daß zweitens diese Feststellung dann aus der Erfahrung nur den Tatbestand benutzt, d. h. nur topologische Eigenschaften der physischen Raumgebilde beobachtet und verwertet, ohne Voraussetzungen über Geradheit irgend welcher physischer Linien …’.

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this issue. Nonetheless, it should be pointed out that Carnap rejects a superﬁcially very simple stipulation of measurement in order to avoid ulterior complications. That is the case of a stipulation of measurement such that on its basis the earth would not only be plane, but would have curvature 0 in all its points. Among the ulterior complications of such a simple stipulation, Carnap mentions,91 ﬁrstly, that the surface of the earth would have to be inﬁnite, and, secondly, that such a stipulation of measurement would require the existence of a privileged place in the plane. Such consequences of the said stipulation are, however, difﬁcult to reconcile with some extremely desirable properties of physical space, for example, homogeneity. Hence, Carnap asserts92 that one should select the simplest spatial structure compatible with the homogeneity and isotropy of space. Thus, physical space should have in all its points and in all directions of its surface the same curvature. Once the spatial structure is ﬁxed, one has to try to obtain the stipulation of measurement corresponding to that spatial structure and compatible with the factual content of physical experience.93 Carnap goes on to compare two stipulations of measurement, M1 and M0, applied to the earth, which Carnap designates with the letter ‘E’. The ﬁrst stipulation of measurement is the usual one, which takes the earth as approximately spherical, whereas the second takes the earth to be a plane, though one with positive curvature in all its points.94 M0 and M1 will coincide with respect to the metrical relations on earth. As Carnap points out,95 this means, among other things, that the equality between lines established in usual physics on the basis of M1 remains unaltered when one uses M0. Similarly, since on the basis of M1 the great circles of the spherical earth are the shortest lines between two points, on the basis of M0, the lines corresponding to the great circles are straight lines, and, thus, the property of being the shortest line between two points remains unaltered. Moreover, in both cases, any two points of E determine a unique straight line, with the exception of the poles, through which pass an inﬁnite number of straight lines. Hence, in this sort of ‘spherical plane’, which is our earth on the basis of M0, and which under the presupposition of homogeneity, Carnap calls ‘spherical space’,96 the same physical measurement scales are valid as in the usual terrestrial physics based on the usual stipulation of measurement M1. Nonetheless, there is a particularly important difference stressed by Carnap97 between the pair (E, M1) and the pair (E, M0). If one could connect two points on E by means of a tunnel, on the basis of M1 the distance between those two points thus connected would be shorter than the distance between those two points as connected by a straight line on the surface of E. On the other hand, in the case of M0 the result is the opposite, namely, the distance between any two points connected by a tunnel 91 Ibid., p. 47. 92 Ibid., p. 48. 93 It should be pointed out that in the light of general relativity, in which gravitational ﬁelds affect the curvature of the surrounding space, the requirements of both homogeneity and isotropy have to be abandoned. Since Carnap had already considered the possibility of spaces of variable curvature, it does not seem clear why he reverts to such requirements. 94 For Carnap’s understanding of plane, see p. 13 above and Der Raum, p. 28. 95 Ibid. 96 Ibid., p. 49. 97 Ibid., pp. 50–51.

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in E is longer than the straight line connecting the same two points on the surface of E. From the standpoint of M0, the difference between the measurements on the basis of the two stipulations M0 and M1 has its roots in the fact that on the basis of the usual M1, bodies expand under the inﬂuence of heat. The ‘rigid’ bar used for the measurement would expand in the interior of the earth and, thus, as Carnap points out,98 the tunnel connecting any two points is only seemingly shorter, measured by M1, because the measurement scales of M1 have expanded in the interior of the earth. That is not the case of (E, M0), for which any non-straight line between two points, be it external or internal, that is, through a tunnel, is longer than the straight line determined in E by those points. As Carnap puts it,99 in this sense E, on the basis of M0, is clearly a plane. Carnap ends his comparison of (E, M1) and (E, M0) concluding100 that, the mentioned coincidences between M1 and M0 with respect to E aside, the adoption of M0 would require changes in the interpretation of some physical facts and, thus, in the physical laws. Thus, for example, light rays would have to be viewed as (intrinsically) curved on the basis of M0. The comparison between (E, M1) and (E, M0) leads Carnap to the bold assertion that the factual content (T), the structure of space (R), and the stipulation of measurement (M) are so related that any of the three can be conceived as a function of the remaining two, that is, that given any two of them the third is uniquely determined. We have, thus, the following three functions of two arguments: R=f1(M,T), M=f2(R,T) and T=f3(M,R). With respect to the function f3, Carnap stresses101 that though given M and R, T is uniquely determined, one should not forget that, contrary to M and R, which can be freely ﬁxed, T is uniquely given. Hence, though T can theoretically be seen as a function of M and R, T is no matter of convention, and it would be extremely strange if someone would try to obtain T on the basis of the free selection of R and M, without any empirical observations. Carnap goes on to discuss an important related issue, namely, the issue of simplicity. Thus, he asserts102 that though one could obtain a simplest spatial structure – Euclidean spatial structure – without taking into account the remaining two components, and one could also select the most simple metrical stipulation – for example, M0 – the requirement of simplicity concerns neither M nor R independently of T, but the triple (T,M,R). In fact, as Carnap correctly asserts,103 theoretical possibility aside, neither R nor M ought to be chosen with independence of T. Therefore, the aim should be to obtain, given T, the simplest pair (M,R), which in no way implies either that R or that M be the simplest possible. Nonetheless, Carnap observes104 that T, together with the methodological requirement of simplicity, determine the most simple R. Hence, although R is independent of T and, thus, can be freely chosen, the requirement of

98 Ibid., p. 51. 99 Ibid. 100 Ibid., pp. 51–2. 101 Ibid., p. 54. 102 Ibid., p. 55. 103 Ibid., pp. 55–6. 104 Ibid., p. 56.

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simplicity added to T allows for the unique determination of R. Of course, since M is a function of T and R, M would also be uniquely determined. On the basis of the above discussion, Carnap concludes105 that it is now perfectly clear why physics – he, of course, means ‘general relativity’ – rejects the simplest isolated R – that is, Euclidean space – and why it has never adopted M0. In other words, for the young Carnap of Der Raum it is clear why physics opted to follow Einstein and rejected the conventionalist attempt of Poincaré to save Euclidean physical geometry. Physics maintains stipulation M1, which, as Carnap stresses,106 is such that the length of any bar is independent from place and direction in a gravitational ﬁeld, but is not independent from temperature, magnetism or elasticity. Carnap sums up succinctly the results of his discussion of physical space as follows: In the factual content of experience is given to us three-dimensional topological space R’’3T, but not a metric space. Such [a space] is obtained only on the basis of a stipulation of measurement, by means of which we can freely choose either this same [stipulation] or the metrical structure of space, but we better proceed in such a way that we do neither of the two, and determine the stipulation of measurement and its corresponding spatial structure in such a way that on their basis the factual content can be exhibited in the simplest way possible. [Der Raum, p. 59]107

The preceding quotation succinctly expresses the nucleus of the discussion of physical space in Der Raum. Firstly, it should be clear that in the case of physical space Carnap propounds a sort of conventionalism with respect to the metric. Neither the metric nor the projective (or afﬁne) structure of physical space are empirically determined, though the latter is not given any special consideration in Chapter 3 of Der Raum. Only the topological structure of physical space is empirically determined. Now, since what is of interest for physics is the metric structure of physical space, such metric structure has to be freely chosen. In fact, there are two components of physical space that are to be freely chosen, namely, the spatial structure R and the stipulation of measurement M. Once one of the two is freely chosen, it, together with the factual content T given in experience, determines the remaining component of the structure of physical space. However, if one takes into account not only the factual content T given in experience, but also the methodological requirement of simplicity, the arbitrary selection of R or M disappears, since on the basis of T and of the simplicity requirement, there is only one simplest R and one simplest M. Hence, in this early work of Carnap we have a defence of a moderate sort of conventionalism with respect to the non-topological features of physical space, made even milder – if not non-existent – by the methodological requirement of simplicity. It should 105 Ibid. 106 Ibid., p. 57. 107 ‘Im Tatbestand der Erfahrung ist uns der dreistuﬁge, topologische Raum R’’3T gegeben, dagegen nicht ein metrischer Raum. Ein solcher ergibt sich erst auf Grund einer Maßsetzung, wobei wir entweder diese selbst oder das metrische Raumgefüge frei wählen können, am besten aber so vorgehen, daß wir weder das eine noch das andere tun, sondern die Maßsetzung und das zu ihr gehörige Raumgefüge so bestimmen, daß auf Grund davon der Tatbestand möglichst einfach dargestellt werden kann.’

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be pointed out that, though in the references of Carnap’s dissertation writings of conventionalists, like Dingler and Poincaré are included, the mild conventionalism of Der Raum should be clearly distinguished not only from Dingler’s radical conventionalism, but also from Poincaré’s less radical one, according to which it was possible to defend the presumed Euclidicity of physical space in the face of physical evidence to the contrary, without taking into account that such a reinterpretation of physical evidence to save Euclidicity would convey unnecessary complications in our physical theory. In fact, when Carnap rejects the simpler stipulations of measurement, like M0, that could save the Euclidicity of physical space, and favours M1, he is consciously siding with Einstein against Poincaré – as Reichenbach had already done two years earlier in his Relativitätstheorie und Erkenntnis a priori108 and would also do in his Philosophie der Raum-Zeit-Lehre.109 6 Comparison of the Three Levels of Space At the beginning of Chapter IV on the relation between the three views of space, namely, formal, intuitive and physical space, Carnap introduces by means of an example two notions that he wants to differentiate. The ﬁrst notion is that of substitution, which consists in the replacement in a general statement of indeterminates (or variables) by determinates (or constants) – for example, when one obtains from the equation scheme m+n=n+m the concrete equation 6+4=4+6. The second notion is that of subsumption, by means of which one orders an empirical case under a general rule – for example, when one obtains from the equation 6+4=4+6 the concrete case that six pineapples + four pineapples = four pineapples + six pineapples. Carnap points out110 that with the aid of such notions one can make precise the relation between the three basic conceptions of geometry: the formal, the intuitive and the physical. Intuitive geometry is obtained from formal geometry by the procedure of replacement, whereas physical geometry is obtained from intuitive geometry by the procedure of subsumption. In order to assess the distinction between the three conceptions of geometry in a more general fashion, Carnap refers the reader to an important distinction made by Husserl. Thus, Carnap says: ‘It [the relation] corresponds (in Husserl’s terminology) to the stepwise transit: formal ontology (Leibniz’s “mathesis universalis”), regional ontology, factual science; and in Ostwald’s doctrine of science to the ﬁrst three levels of science’s pyramide.’111 Carnap adds112 that the same relation present between the three conceptions of geometry is also present between 108 Relativitätstheorie und Erkenntnis a priori 1920, English translation Relativity Theory and Knowledge a priori (Berkeley et al., 1965). 109 Philosophie der Raum-Zeit-Lehre (1928, English translation, Philosophy of Space and Time, New York, 1958). 110 Der Raum, p. 60. 111 Ibid., p. 61. The German text reads: ‘Es entspricht (in Husserls Ausdrucksweise) dem stufenweisen Fortgange: formale Ontologie (Leibniz’ “mathesis universalis”), regionale Ontologie, Tatsachenwissenschaft; und in der Ostwaldschen Wissenschaftslehre den ersten drei Stufen der Wissenschaftspyramiden.’ 112 Ibid.

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its objects, namely, R, R’ and R’’. Furthermore he asserts,113 once more making use of a terminology frequently used by Husserl, that both the relation between R and R’, as well as that between R’ and R’’ are relations between a genus and a singular object, though in a different sense. More precisely, Carnap states: The relation of R to R’ is that of a genus of structures of determinate order relations but undetermined objects to a structure with the same properties but determinate objects, namely, spatial intuitive ﬁgures. The relation between R’ and R’’ is that of a form of intuition to a structure of that form of empirical-real objects. [Der Raum, p. 61]114

Carnap emphasizes115 that the main interest of Der Raum is R’’, that is, physical space, and, particularly, the consistent reunion in a determinate physical space of the spatial empirical relations. Nonetheless, he justiﬁes the examination of intuitive and formal spaces, in order to have a deeper understanding of physical space. Carnap expresses this point as follows: Now, since for R’’ different possible sorts of R’’3M are available, depending on the selection of the stipulation of measurement, then the different corresponding kinds of R’3M have to be formed, which then are [generalized] in the way previously elucidated to the structures R’nM or R’3T and, ﬁnally generalized and at the same time resumed in R‘nT. And for these structures are built the formal frameworks of the corresponding R up to the most general RnT. [Der Raum, p. 61]116

7 Epistemological Assessment The ﬁfth and last chapter – on our knowledge of space and the role of experience – is of special interest in order to understand the philosophical and scientiﬁc inﬂuences present in the book. The discussion of the different sorts of space occurred in the ﬁrst three chapters, whereas the fourth chapter was concerned with the relations between the three conceptions of space. In this last chapter, Carnap elucidates more the three conceptions of space. Thus, he begins the last part of his dissertation by observing117 that formal space is simply a particular development of a chapter of the logical theory

113 Ibid. 114 ‘Das Verhältnis von R zu R’ ist das der Gattung von Gefügen bestimmter Ordnungseigenschaften aber unbestimmter Gegenstände zu einem Gefüge dieser selben Eigenschaften, aber bestimmter Gegenstände, nämlich der anschaulich räumlichen Gebilde. Das Verhältnis von R’ zu R’’ ist das einer Anschauungsform zu einem Gefüge dieser Form von erfahrungswirklichen Gegenständen.’ 115 Ibid. 116 ‘Da nun für R’’ sich je nach der Wahl der Maßsetzung die verschiedenen Arten des R’’3M als möglich erweisen, so müssen die ihnen entsprechenden Arten des R’ aufgebaut werden, die dann in früher erläuterter Weise zu den umfassenden Gefügen R’nM oder R’3T und schließlich zum R’nT verallgemeinert und zugleich zusammengefaßt werden. Und für diese Gefüge werden die formalen Gerüste der entsprechenden R bis zum allgemeinsten, dem RnT, aufgebaut.’ 117 Ibid., p. 62.

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of relations. Furthermore, he asserts118 that, as occurs with the theory of numbers, the theory of relations and, particularly, the theory of formal space with which he is concerned, are not only independent of all experience, but also derivable from logic. It is perfectly clear here the presence of the inﬂuence of the brand of logicism of Russell and Whitehead, as expounded in Russell’s Principles of Mathematics119 and in Russell’s and Whitehead’s seminal and monumental Principia Mathematica.120 It should be mentioned here that Frege’s logicism does not extend to geometry, a discipline conceived by the father of contemporary logic in a similar fashion to that of Kant, though defended with different arguments. Of special importance for the assessment of Carnap’s views in Der Raum is what he says about intuitive space, and which has been either ignored or misinterpreted by Carnapian scholars. Contrary to what most scholars have sustained, on this point the most decisive inﬂuence seems to be that of Husserl.121 On this point, it is pertinent to quote a long passage from Der Raum: Here [in intuitive space] we have distinguished between the principles in the strict sense and the requirements. Those build the result of a determined sort of “contemplation of essences” [Wesenserschauung] (in Husserl’s sense) and as such, like all knowledge from this source, do not need of the accumulation of empirical facts, [and] as such are not to be referred to as empirical knowledge, but also are not independent of every experience, since they are obtained from any representative of the kind of objects concerned. Requirements, on the other hand, are not knowledge but stipulations that have to be made in order to obtain a total structure “space” from such knowledge, which in virtue of their own nature [ihrem Wesen nach] seem limited to an incomplete region. For these extensions to a complete structure different possibilities were indicated. Topological space presents [darstellt] what is common to all [of those possibilities] and on this ground ought to be seen as the form of the spatial apprehensible in the contemplation of essences. Intuitive metric spaces, on the contrary, also depend on the choice of the stipulations; and as such lack the property of the unlimited validity, which possess [both] intuitive topological space and all knowledge originating in this source. [Der Raum, pp. 62–3]122 118 Ibid. 119 Principles of Mathematics 1903 (second edition London, 1937). 120 Principia Mathematica 1910–1913 , revised edition, (Cambridge, 1925, 1927). 121 One of the few exceptions is Sahotra Sarkar, in a very recent paper, namely, ‘Husserl’s Role in Carnap’s Der Raum’, in Thomas Bonk (ed.), Language, Truth and Knowledge (Dordrecht, 2003, pp. 179–90). Sarkar’s interpretation is, notwithstanding some minor points, very similar to that of the present author. I had already presented my interpretation in two somewhat lengthy critical studies – one of the book El Programa de Carnap and the second of Der Raum – in Spanish, written between 2001 and 2002. The ﬁrst was published in Principia 10, n. 2, 2006, pp. 209–35, the second in Manuscrito 29, n. 1, 2006, pp. 259–96. 122 ‘Hier haben wir unterschieden zwischen den Grundsätzen im engeren Sinne und den Forderungen. Jene bilden den Befund einer bestimmten Art der “Wesenserschauung” (im Husserlschen Sinne) und sind daher wie alle Erkenntnisse dieser Quelle nicht auf Häufung von Erfahrungstatsachen angewiesen, daher nicht als Erfahrungserkenntnisse zu bezeichnen, aber auch nicht unabhängig von jeder Erfahrung, insofern als sie an irgendwelchen Vertretern der betrefﬂichen Art von Gegenständen gewonnen werden. Die Forderungen dagegen sind nicht Erkenntnisse, sondern Festsetzungen, die getroffen werden, um ein geschlossenes Gesamtgefüge “Raum” aus jenen Erkenntnissen zu gewinnen, die ihrem Wesen nach auf ein

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The preceding quotation makes it perfectly clear that Carnap considered that the principles of intuitive space were known by means of Husserlian intuition of essences, and that they completely determine intuitive topological space. In that important passage Carnap refers neither to Kant, nor to Helmholtz,123 nor to any other author besides Husserl. With respect to physical space, Carnap observes,124 without much need for any further grounding, that our knowledge of its properties is empirical, based on the factual content of experience, and inductive. Therefore, it can never possess the property of absolute certainty, though it could have it as an unreachable goal towards which it tries to approximate. Once more, Carnap stresses125 that only physical topological space is uniquely determined by the factual content of experience, whereas to determine physical metric space we need freely chosen measurement stipulations. On pp. 63–4, Carnap assesses our knowledge of the three levels of space on the basis of the traditional distinctions, namely the analytic-synthetic distinction and the a priori-a posteriori one. With respect to the principles and theorems of formal space, Carnap stresses126 that they are analytic and a priori, since they are derivable from the logical principles. On the other hand, the principles of intuitive space are a priori but not analytic; they are synthetic. It is pertinent here to insert a quotation of a long passage dealing with this issue. Thus, says Carnap: The principles of intuitive space are equally a priori. According to the well-known distinction of Kant between “originate [Entspringen] in experience” and “begin [Anheben] with experience”, this does not mean apprehensible without experience, but “independent of the quantity of experience” (Driesch) and on this ground does not contradict that for the contemplation of essences what is given in experience is required, be it immediately [given] in perception or mediately in intuition. In these principles of intuitive space we have before us the synthetic a priori propositions asserted by Kant. But the same is not valid of the theorems derived from them, except to the point in which they concern only topological space, since those [theorems] that refer us to metric spaces are dependent not only on the principles, but also on the requirements, on whose base the complete structure of intuitive space is obtained, thus, on determinations which are not a priori knowledge, since they are not knowledge, but stipulations. Kant’s assertion is, thus, indeed correct, nicht vollständiges Gebiet beschränkt erscheinen. Für diese Erweiterungen zum vollständigen Gefüge zeigten sich verschiedene Möglichkeiten. Der topologische Raum stellt das ihnen allen gemeinsame dar und ist deshalb als Form des in der Wesenserschauung des Räumlichen faßbar anzusehen. Die metrischen Anschauungsräumen dagegen sind auch noch von der Wahl jener Festsetzungen abhängig; daher fehlt ihnen die dem topologischen Anschauungsraum wie allen dieser Quelle entstammenden Erkenntnissen zukommende Eigenschaft der unbedingten Gültigkeit.’ 123 In his excellent dissertation, Konventionalität in der Physik (Berlin, 1974) p. 99, Werner Diederich links without much argumentation Carnap’s views on the synthetic a priori in geometry with Helmoltz’s views. However, there do not seem to be any grounds in Carnap’s Der Raum for this assertion of the distinguished scholar. 124 Der Raum, p. 63. 125 Ibid. 126 Ibid.

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but is not valid for the whole domain of those propositions to which he referred. [Der Raum, pp. 63–4]127

Although in the preceding quotation the name of Kant is repeatedly mentioned, a careful examination of the passage shows that those Carnapian scholars who try to approach the young Carnap to Kant and the neo-Kantians cannot ﬁnd much support in it. Of course, Carnap refers to Kant’s important distinction between having its grounding in experience and merely taking experience as starting point. He also mentions the well-known thesis of Kant concerning the presumed synthetic a priori nature of geometrical knowledge. But besides such references and the belief in the existence of synthetic a priori statements, thus, besides the general discussion framework, there are no other coincidences with Kant. In fact, Kant was the ﬁrst, but not the only philosopher who had propounded synthetic a priori knowledge: Carnap’s professors, Frege and Husserl, also did it. Now, what Carnap asserts in the quoted passage is that we obtain synthetic a priori propositions solely about the topological constituents of intuitive space – thus, neither about its metric nor its projective (or afﬁne) constituents – by means of Husserl’s method of the intuition of essences. Hence, the passage in no way tries to vindicate Kant but shows once more Carnap’s allegiance to Husserl. The other philosopher mentioned in that passage is the now almost forgotten Hans Driesch, who as Carlos Ulises Moulines has correctly asserted,128 seems to have had some inﬂuence on Carnap, or at least was much respected by the latter. Finally, with respect to propositions about physical space, it is perfectly clear that they are both synthetic and a posteriori. Carnap then goes on to offer – on pp. 64–5 – another classiﬁcation, indeed an especially interesting one, of our geometrical knowledge of the different sorts of spaces. Carnap uses the letters ‘W’, ‘S’ and ‘T’ as abbreviations of the following expressions for sources of knowledge: ‘contemplation of essences’, ‘freely chosen stipulation’, and ‘factual content’, respectively. Such letters will always occur accompanied by a subscript, namely, either ‘1’, which expresses the presence of that source of knowledge, or ‘0’, which expresses the absence of that source of 127 ‘Die Grundsätze des Anschauungsraumes sind gleichfalls a priori. Nach der bekannten Unterscheidung Kants zwischen dem “der Erfahrung Entspringen” und dem “Anheben mit der Erfahrung” bedeutet dies ja nicht: ohne Erfahrung erfaßbar, sondern “unabhängig von der Menge der Erfahrung” (Driesch) und steht deshalb nicht im Widerspruch dazu, daß zu der Wesenserschauung des Gegebenseins von Erfahrung, entweder unmittelbar in der Wahrnehmung oder mittelbar in der Vorstellung, erforderlich ist. In diesen Grundsätzen des Anschauungsraumes haben wir die von Kant behaupteten synthetischen Sätze a priori vor uns. Dasselbe gilt aber nicht allgemein für die aus ihnen abgeleiteten Lehrsätze, sondern nur, soweit sie den topologischen Raum betreffen; denn diejenigen, die sich auf einen der metrischen Räume beziehen, sind nicht nur von den Grundsätzen, sondern auch von den Forderungen abhängig, auf Grund deren das vollständige Gefüge des Anschauungsraumes sich ergibt, also von Bestimmungen, die nicht Erkenntnisse a priori sind, weil überhaupt nicht Erkenntnisse, sondern Festsetzungen. Kants Behauptung ist also zwar richtig, aber nicht für den ganzen Bereich derjenigen Sätze gültig, auf die er selbst sie bezog.’ 128 See his ‘Las Raíces Epistemológicas del Aufbau de Carnap’ 1982, reprinted in Ramón Cirera, Andoni Ibarra and Thomas Mormann (eds), El Programa de Carnap, pp. 45–74, especially pp. 56, 58–9 and 70.

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knowledge. Thus, we have the following classiﬁcation: W1 applies to all spaces R, and, hence, there is no space R such that W0(R); neither S nor T apply to R3T (and a fortiori not to RnT), and, hence, S0(R3T) and T0(R3T) are valid; T does not apply also to R3M, and, thus, we have T0(R3M), whereas S applies to R3M, and thus, we have S1(R3M), since the principles of such a space are the formal conditions – or formal skeleton – of a relational structure based on freely chosen stipulations. Obviously, T does not apply to any intuitive space, whereas S applies neither to R’nT nor to R’3T, but applies to R’3M. Finally, in the case of physical space we do not need to consider R’’nT, and S does not apply to three-dimensional physical topological space R’’3T, though it clearly applies to R’’3M. Carnap points out129 that though W applies in all cases, in the case of formal topological space, be it n-dimensional or three-dimensional, the application is of a formal nature. Here Carnap refers once more to Husserl, and it is appropriate to quote him again. Thus, Carnap says: ‘W is present in all cases, but only in the last cases is properly “spatial”, in the ﬁrst two in a formal way (Husserl: “formal ontology”).’130 Here Carnap seems to refer to Husserl’s distinction, already present in the Sixth Logical Investigation, but most clearly emphasized in Ideen I131 between material essences – the usual essences – and formal essences, referred to also in other writings as ‘objects of the understanding’132 or ‘categorial objects’.133 In the case of three-dimensional intuitive topological space, Carnap asserts134 that though it needs some freely chosen requirements to be completed, it does not depend on any particular chosen stipulation, since it contains only those spatial determinations common to all possible stipulations. Hence, the requirements for extending our consideration from the intuitively given region of intuitive topological space to the whole intuitive topological space should not be confused with (or assimilated to) the stipulations that ﬁx the metric of physical space. Carnap goes on to examine in detail the Kantian issue of the conditions of possibility of experience. He asserts135 that since in experience that which is uniquely given without any intervention of freely chosen stipulations is the factual content, only such spatial determinations present already in the factual content, hence, the topological conditions – thus, neither the projective (or afﬁne) nor the metric – are conditions of possibility of experience. As Carnap states it,136 only the mere topological form of space, which is invariant under homeomorphisms, constitutes conditions of possibility of experience. Now, as Carnap stresses,137 the topological spatial relations that are conditions of possibility of each and every object of experience are those of intuitive topological space and formal topological space, not those particular relations 129 Der Raum, p. 65. 130 Ibid. The German text reads: ‘W tritt überall auf, ist aber nur in den letzten Fällen eigentlich “räumlicher”, in den beiden ersten dagegen formaler Art (Husserl: “formale Ontologie”).’ 131 See Ideen I, § 10. 132 See Erfahrung und Urteil (1939, sixth edition, Hamburg, 1985). 133 See Logische Untersuchungen II, U. VI, Second Part, Chapters Six and Seven. 134 Der Raum, p. 65. 135 Ibid. 136 Ibid., pp. 65–6. 137 Ibid., p. 66.

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that are characteristic of physical topological space, since the latter is concerned with topological relations of empirically given objects, which are, thus, dependent on the factual content of experience. On this point, Carnap says: The determinations of intuitive topological space, in their independence from experience, and in the universal validity [Allgemeingültigkeit] assigned to them on the basis of its source of knowledge, and, hence, also those of formal topological space, that general structure of relations between undetermined objects, of which intuitive topological space forms a determined singular case, are the only that can have that grounding validity for experience. [Der Raum, p. 66]138

On the other hand, Carnap most emphatically rejects139 that any determined number of dimensions, and very especially three-dimensionality, could be considered a condition of possibility of experience. Although we, human beings, can intuit in the limited region of space to which we have access only spatial ﬁgures of up to three dimensions, such a peculiarity is seen correctly by Carnap as accidental and irrelevant for the conditions of possibility of experience. In fact, as Carnap already had pointed in Chapter 2, it is not excluded that when we extend our intuitive space beyond the region of space to which we have direct access new spatial dimensions would have to be admitted. Moreover, from the fact that we can have ﬁgures up to three dimensions – or, more generally, up to k dimensions – we cannot infer, stresses Carnap,140 any upper bound to the number of dimensions. On the contrary, we can infer a lower bound, namely, that space must have at least 3 dimensions – respectively, k dimensions. Carnap makes it clear141 that neither physical topological space, which is dependent on the factual content of experience, nor formal topological space, which considers all dimensions in similar fashion, could be of any help to a priori determine any upper bound to the number of dimensions. Furthermore, Carnap rejects the argument that only three-dimensionality can guarantee the uniqueness of empirical determination. On the contrary, Carnap considers that the attempt to ﬁx an upper bound could open the door to an ambiguity corresponding to the diversity of possibilities of such an upper bound.142 Hence, Carnap concludes143 that one has to admit an unlimited number of dimensions. Thus, it is intuitive topological space of n dimensions, for any positive integer n – which includes also the determinations 138 ‘Die Bestimmungen des topologischen Anschauungsraumes, in ihrer Erfahrungsunabhängigkeit und in der auf Grund ihrer Erkenntnisquelle ihnen zukommenden Allgemeingültigkeit, und infolgedessen auch die des formalen topologischen Raumes, jenes allgemeinen Beziehungsgefüges unbestimmter Dinge, von dem der topologische Anschauungsraum einen bestimmten Einzelfall bildet, können allein jene erfahrungstiftende Geltung haben.’ 139 Ibid., pp. 66–7. 140 Ibid. 141 Ibid., p. 67. 142 On the other hand, though 3 would be a lower bound to the dimensionality of intuitive topological space – since there are, of course, three-dimensional ﬁgures – it is not the only lower bound, since we have to admit the intuitability of two-dimensional and even onedimensional ﬁgures. 143 Der Raum, p. 67.

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of formal topological space of n dimensions – the space that contains precisely the totality of the spatial conditions of possibility of experience. In this way, Carnap concludes his excellent but neglected dissertation, stressing,144 on the one hand, the correction of Kant’s thesis, according to which space contains conditions of possibility of experience, but at the same time making it clear that the space that contains the conditions of possibility of experience, namely, n-dimensional intuitive topological space, is essentially different from that which Kant had in mind – in Carnap’s terminology, three-dimensional intuitive metric Euclidean space. 8 Carnap’s Conclusion Carnap’s conclusion deserves some commentaries. Carnap’s thesis director [Doktorvater] at the University of Jena was Bruno Bauch, a well-known neo-Kantian. After the surge of Einstein’s special theory of relativity, and, more urgently, after the surge of the general theory of relativity, neo-Kantians felt compelled to defend Kant’s doctrine of space against the new conception of physical space (better: space-time), and, if possible, to show its compatibility with the latter. Nonetheless, besides the general remarks at the end of Chapter 5, which essentially consist in acknowledging that Kant was right when he said that something in intuitive space was a priori and condition of possibility of experience, the whole discussion in that chapter, and its conclusion, precisely show that Kant’s speciﬁc theses about the aprioricity of space were mistaken. Furthermore, when Carnap examines the grounding for the aprioricity of intuitive topological space and its epistemological source it is not to Kant to whom he refers the reader, but to Husserl. Indeed, in Der Raum, besides the clear inﬂuence of those who contributed the most to our present conception of physical space, that is, Riemann and Einstein, the most important philosophical inﬂuence is without much doubt that of Husserl, especially with respect to intuitive space – in whose axiomatization there is, of course, the inﬂuence of Hilbert – but also with respect to formal space, though in the latter there are also clear inﬂuences of Russell, Whitehead and also Riemann. In particular, the rejection of the speciﬁc theses of Kant about intuitive space, namely, the Euclidicity and the three-dimensionality can also be linked to Husserl. In the ﬁrst volume of his Logische Untersuchungen,145 Husserl classiﬁed Kant’s views as a sort of speciﬁc relativism, that is, a relativism to the species, in this case, to the human species, and, thus, as an anthropologism. Indeed, Kant’s transcendental subject is a general human subject, something the transcendental subject of Husserl’s later transcendental phenomenology was not. Euclidicity and three-dimensionality could not be seen as essential properties of intuitive space, but in the best of cases a clear indication of our human limitations. Moreover, both Husserl and Carnap were well acquainted with the revolutionary development of geometry in the nineteenth century and, thus, would not favour Euclidicity or three-dimensionality even as presumed consequences of our human limitations.

144 Ibid. 145 Logische Untersuchungen I, Chapter Seven, § 38.

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On this point, I will digress a little to make two important points related to Husserl’s views. Husserl’s mature philosophy of mathematics – originating in the mid-1890s and essentially maintained during the rest of his life – was especially inﬂuenced by Riemann’s views, and the former’s theory of all theories and its ontological counterpart, his theory of manifolds, can be seen as a still more abstract generalization of Riemann’s theory of manifolds. On the other hand, in his correspondence with the neo-Kantian Paul Natorp, Husserl rejects Kant’s famous argument of incongruent counterparts, which pretended to establish the three-dimensionality of space. Husserl mentions that in a similar way in which a two-dimensional hand would require a third dimension in order to occupy the same region of space as the other perfectly similar hand, a right-handed screw would require a fourth dimension in order to occupy the same region of space occupied by a perfectly-similar left-handed screw. In this fashion, Husserl shows Kant’s conclusion to be a non sequitur.146 In fact, it should be pointed out that in that letter Husserl stresses both his serious doubts about Euclidean geometry as well as the difference between his views of what is a priori in space and those of Natorp or Kant. Another important earlier reference on this issue is Husserl’s letter of 29 December 1892 to Franz Brentano, in which Husserl communicates his old professor of his abandonment of any belief in Euclidean geometry as well as his favourable assessment of the works of Riemann and Helmholtz.147 Thus, more than a decade before Einstein’s epoch-making special theory of relativity and more than two decades before his not less revolutionary general one, Husserl had already abandoned the belief in Euclidicity as an a priori feature of space. Hence, though, of course, Carnap had no access to such correspondence, he correctly understood that it was to Husserl and not to Kant to whom he should turn in order to try to obtain any synthetic a priori features of space. However, there is an important difference between Husserl and Carnap, since though Husserl rejected the a priori nature of both Euclidicity and three-dimensionality, his geometric synthetic a priori was in no way limited to the topological properties of space. Thus, in his recently published Alte und Neue Logik: Vorlesungen 1908/09 Husserl stresses that the geometrical arguments based on geometrical congruence are synthetic a priori. However, since the notion of ‘congruence’ is deﬁned in terms of the notion of ‘isometry’, which is a special case of an afﬁne transformation, Husserl’s geometrical synthetic a priori must include both the afﬁne properties of space and even some of its metric properties.148 It should be mentioned here, however, that Husserl’s student and life-long friend, the great mathematician and physicist Hermann Weyl, propounded another sort of a priori component of space, which at ﬁrst sight seems nearer to Husserl’s views than Carnap’s. Thus, Weyl sustained that there was a sort of a priori metrical structure given by a source of geometrical ﬁeld present in space devoid of matter. Such a metrical 146 See Husserl’s letter to Natorp of 7 September 1901, in his Briefwechsel V, pp. 80–86, as well as the Appendix [Textkritischer Anhang], pp. 233–6. 147 See Briefwechsel I, pp. 10–11. 148 The notion of ‘congruence’ is deﬁned in terms of isometries, which are afﬁne transformations that preserve distances. For a clear recent treatment of those notions, see Judith N. Cederberg’s A Course in Modern Geometries (New York et al., 1989, second revised edition, 2001), pp. 136 and 138.

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structure would differ essentially from that of non-empty physical space in being of constant curvature, thus, homogeneous and isotropic, whereas physical – generalrelativistic – space (more exactly space-time), due to the presence of matter, would be neither homogeneous nor isotropic, but of variable curvature.149 Whether Husserl would have seen Weyl’s views as a mirror of his own views on space, though not completely clear, seems, however, very questionable. In any case, it could be argued against Weyl that even if he were right in considering that space devoid of matter has a metrical structure, such structure would not remain invariant under the presence of matter and, thus, should not be considered a priori in the sense of that word current both in Kant and in Husserl. Incidentally, Weyl’s views on the aprioricity of the metrical structure of space devoid of matter could be used as an argument against Carnap’s thesis that only the n-dimensional topological intuitive (and formal) structure of space is a priori, since we could not isolate the topological from the metrical component of space. It should be pointed out, however, that, at least analytically, topological structure is more fundamental than and independent from metrical structure. Other arguments, of a more mathematical character, have been recently raised against the feasibility of Carnap’s views on the aprioricity of the topological intuitive (and formal) components of space.150 Although I cannot dwell on this issue, it should ﬁrstly be clearly determined whether such mathematical results really apply to Carnap’s views or to what some authors believe that are Carnap’s views. I would like to ﬁnish the presentation of Carnap’s Der Raum mentioning that in Appendix II of that work, which contains the suggested readings, there are a substantial number of references to Husserl’s views, which is pertinent to enumerate. There are references to Husserl on p. 78 (two references to p. 7), on p. 79 (a reference to pp. 8–9 and a reference to p. 12), on p. 80 (a reference to p. 22 and a reference to p. 24), on p. 85 (two references to p. 60, in one of which one reads ‘The doctrine of R – of R’ – of R’’ as particular cases of the more general scientiﬁc relation: “formal ontology, regional ontology, factual science”, thus Husserl…’,151 and one reference to p. 62.), and on p. 86 (a reference to pp. 63ff.). 9 Husserl and Carnap: Relation and Tensions As expressed at the beginning of this chapter, the relation between Carnap and Husserl is one of the most intriguing, even enigmatic, in the history of recent philosophy. It is already known that Carnap attended Husserl’s seminars during three semesters between 1924 and 1925, when he was working on Der logische Aubau der Welt, a 149 See on this point the already mentioned monograph by Robert Coleman and Herbert Korté ‘Hermann Weyl: Mathematician, Physicist, Philosopher’, in Erhard Scholz (ed.), Hermann Weyl’s Raum-Zeit-Materie and a General Introduction to his Scientiﬁc Work, especially pp. 228–9. 150 See on this point, Thomas Mormann’s forthcoming paper ‘Geometrical Leitmotifs in Carnap’s Early Philosophy’. 151 The German text reads: ‘Die Lehre vom R – vom R’– vom R’’ als Fall des allgemeineren Wissenschaftsverhältnisses; “formale Ontologie – regionale Ontologie – Tatsachenwissenschaft”, so Husserl…’.

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book inﬂuenced by Husserl – as already pointed out in two valuable papers by Verena Mayer152 – but not as clearly and explicitly Husserlian as Der Raum. Although there is still no conﬁrmation of the suspicion that Carnap was Husserl’s student in the years 1919–1921, it seems very difﬁcult to believe that living so near to Freiburg for some three years and writing a dissertation so strongly inﬂuenced by Husserl that it can very well be labelled ‘Husserlian’ with the same right as the writings of other of the latter’s students, the young Carnap never succumbed to the temptation of visiting Husserl’s lectures or seminars during those years. I would like to conclude this chapter by observing that from the other side, that is, on Husserl’s side, there seems not to have existed, at least in later years, much sympathy for Carnap. Besides the letter of Ludwig Landgrebe to Husserl mentioned above, I have found only three other references to Carnap in Husserl’s correspondence. There is a reference to Carnap in a letter of Malvine Husserl to Roman Ingarden of 14 January 1936 in Volume III, in which she tells one of Husserl’s most beloved students that her husband’s planned lectures in Prague were organized by the Centre Philosophique de Prague, and, in view of the Centre’s anti-positivist philosophical views, Husserl could avoid having to meet Carnap.153 In the same volume there is an indirect reference to Carnap in a letter of Husserl to Ingarden, in which the former refers to a paper of the latter, ‘L’essai logistique d’une refonte de la philosophie’, directed mostly against Carnap.154 Probably the clearest reference to the old Husserl’s lack of sympathy for Carnap appears, however, in a letter of Husserl to Heidegger, dated 9 May 1928, in Volume IV of the correspondence.155 There was a vacancy at the University of Kiel after the departure of Heinrich Scholz. The three main candidates were three of Husserl’s earlier students, namely, Rudolf Carnap, Moritz Geiger and Oskar Becker. In a somewhat shocking assessment for the present day readers, Husserl recommends Oskar Becker over Moritz Geiger, and both of them by far over Carnap. The assessment is especially disturbing not only because of the relative evaluation of the three candidates, but also because Husserl used to be particularly sympathetic and generous to his former students, no matter whether they had followed him in his philosophical endeavours or not, or even continued their lives far away from philosophy. Indeed, Husserl’s correspondence with his former students is very extensive, and in it the great philosopher shows genuine enthusiasm in helping his former students attain their academic goals and even in dealing not only with their academic difﬁculties, but also, interestingly, with their personal problems, be they psychological – as was the case of Dietrich Mahnke, one of his nearest students – or economic – as was once Heidegger’s case. Of all Husserl’s correspondence with his extremely diverse students, only in the case of Hugo Dingler, who was Husserl’s student in the very ﬁrst years of the twentieth 152 See her ‘Die Konstruktion der Erfahrungswelt: Carnap und Husserl’, in Wolfgang Spohn (ed.), Erkenntnis Orientated: A Centennial Volume for Rudolf Carnap und Hans Reichenbach (Dordrecht, 1991), pp. 287–303; and ‘Carnap und Husserl’, in David Bell and Wilhelm Vossenkuhl (eds), Wissenschaft und Subjektivität ( Berlin, 1992), pp. 185–201. 153 See Briefwechsel III, pp. 304–6. The reference to Carnap is on p. 305. 154 Ibid., footnote p. 304. 155 Briefwechsel IV, pp. 157–8.

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century, and another now forgotten student from those years, did Husserl seem to have lacked any sympathy. Moreover, besides those two cases, and even if we add the case of other former students, with which no correspondence has been preserved, but about which Husserl just casually refers – for example, Max Born – Carnap’s is the only case for which there is not the slightest sign of sympathy. A very plausible explanation of this fact could be that, in view of Husserl’s open conﬂict with Moritz Schlick, Husserl could have interpreted Carnap’s allegiance to the Vienna Circle as a sort of philosophical treason. In any case, as we will see in the next two chapters, after the publication of Der logische Aufbau der Welt there could exist additional reasons for that lack of sympathy. Certainly, that book is not simply a Husserlian book like Der Raum, but it is still much more Husserlian than Kantian – contrary to what some recent scholars have said – and also more Husserlian than Fregean, Russellian or Machian – as some others have believed. Der logische Aufbau der Welt is in some sense an eclectic book, being the result of diverse inﬂuences, for example, that of Russell, Whitehead and Frege on the formal side. Nonetheless, as will be seen in the next two chapters, the by far most decisive philosophical inﬂuence is still that of Husserl, though this inﬂuence was, by whatever reasons, purposely masked by its author.

Chapter 2

On Der logische Aufbau der Welt 1 Introduction As shown in Chapter One, Der Raum was written from the standpoint of Husserl’s philosophy. Of course, it deals with a problem that obtained prominence with the discovery of general relativity, and in some sense tried to secure a place for the synthetic a priori between the formal space based on the theory of relations, and physical space, with its mixture of experience and stipulations. But philosophically it is a defence of a non-Kantian synthetic a priori, much nearer to Husserl’s views than to Kant’s. The interpretation of Der logische Aufbau der Welt is a much more difﬁcult task. In that work – as in other later works – Carnap refers to such a diversity of sources that it makes it very difﬁcult to determine which are the decisive inﬂuences and which the marginal ones, or even the authors with whom Carnap’s views are just very vaguely related, if at all. In some sense, it is not unfair to say that the diversity of sources referred to serves to mask the decisive inﬂuences. Thus, Carnap’s Aufbau – as I, following other authors, will frequently abbreviate the title – has been rendered in the most diverse ways and still remains a sort of riddle for Carnapian scholars. Following the empiricist tradition of Anglo-American twentieth-century philosophy, the book has been rendered as an empiricist attempt, in the tradition of Russell’s Our Knowledge of the External World,1 to construct our knowledge of the world from an empiricist basis. Thus, Carnap would in some sense be seen simply as a continuator of the empiricist English tradition from Locke to Hume, and to Russell. At ﬁrst sight, a somewhat more probable variant is the interpretation of Aufbau as a book in the Machian phenomenalist tradition. Indeed, the book was published in 1928, when Carnap was already a member of Schlick’s Vienna Circle, and the circle revered Ernst Mach as one of its predecessors. Incidentally, Schlick occupied the chair at the university of Vienna, which had been occupied before by Mach. But there are too many authors referred to in Aufbau, which did not belong either to the English empiricist tradition or to the tradition of Mach, Avenarius and Cornelius. For example, there were references to Frege, to Whitehead, to Kant and the neo-Kantians, to Husserl, to the conventionalists Poincaré and Dingler, to Hans Driesch and many others. Hence, in order to disentangle the important inﬂuences from the marginal ones, the distinguished scholar Carlos Ulises Moulines opted to apply a quantitative method in the analysis of Carnap’s Aufbau.2 Thus, authors referred to in Aufbau n times or more were presumably main inﬂuences, whereas 1 Our Knowledge of the External World (1914, London 1922, revised edition, 1926). 2 See Moulines’ paper ‘Las Raíces Epistemológicas del Aufbau’, referred to in footnote 128 of Chapter 1.

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authors only referred to n-1 times or less were marginal inﬂuences. As a result of such a quantitative examination, Moulines obtains a list of frequently cited authors that include, besides Frege, Russell and Whitehead, mostly – though not always – referred to because of their contributions to logic, among others, authors as diverse as Mach and Natorp, Dingler and Weyl, Jacoby, Schlick and Driesch. Hence, a potpourri of authors is obtained, which, according to Moulines, have a sort of family resemblance. Moulines’ contention is very questionable, to say the least, since the differences between those authors by far exceed any similarities. But Moulines’ quantitative method is in itself indefensible on other grounds. First of all, the choice of the number n is perfectly arbitrary. It is presumably ﬁve, since the least referred author of all mentioned by Moulines is Dingler, who was referred to ﬁve times in Aufbau. Nonetheless, Husserl was also referred to ﬁve times in Aufbau, but not included in Moulines’ list. Just this fact makes Moulines’ list sound very suspiciously biased. Moreover, one of the authors mentioned in the list, Hans Driesch, was referred to eleven times in Aufbau, that is, more than twice as many times as Dingler. Thus, if Moulines wanted to exclude Husserl, he could very well have put n=6, since in that way also none of the authors in which he is interested – that is, neither Frege nor Russell nor Whitehead – would have been referred to in Aufbau more than twice as many times as any other of the authors included in the list. Of course, in such a case Dingler would have been excluded from the list, but such exclusion clearly was contrary to what Moulines wanted to obtain. Another at least equally important reason to reject Moulines’ quantitative method to determine the main inﬂuences in Aufbau is that it does not take into account the qualitative importance of the references. An author can very well be more frequently referred to than a second author, but in a perfectly inconsequential manner, whereas the references to the second author are much more decisive. As we will see, precisely that occurs in Aufbau. Hence, Moulines’ quantitative method is completely inadequate. Still another rendering of Aufbau has ﬂourished recently, namely, its interpretation as a sort of Kantian or neo-Kantian work. This rendering, propounded among others by Werner Sauer, Michael Friedman and his former student Alan Richardson, is part of a more general reaction to Anglo-American empiricism and pragmatism of the Quinean sort. Thus, especially – but not only – in Anglo-American analytic philosophy there has been a recent trend to reinterpret some of the most important analytic philosophers as Kantians or neo-Kantians. The most prominent example of this trend is the Kantianization of Gottlob Frege’s views by Hans Sluga, Joan Weiner and many other Fregean scholars. A consequence of my analysis in this and the next chapter will be the completion of the refutation of the Kantian rendering of Carnap already begun in Chapter 1. Finally, as already mentioned in Chapter 1, some ﬁfteen years ago, Verena Mayer propounded in two important papers a Husserlian rendering of Carnap’s Aufbau. In this and the next chapter I will argue for such an interpretation, but will go much deeper than Mayer in the relation between Carnap’s Aufbau and Husserl. That is the main reason for writing two chapters on that issue. The present chapter will be concerned with Husserl’s whole inﬂuence on Aufbau, with the exception of the problem of our knowledge of what Carnap calls the ‘heteropsychological’, that is, the ‘foreign psyche’ and which I will call, following Husserl, the problem of

On Der logische Aufbau der Welt

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‘intersubjectivity’. The treatment of the problem of intersubjectivity both by Carnap and Husserl will be discussed in Chapter 3. To better assess the enormous inﬂuence of Husserl on various fundamental features of Aufbau, the present chapter will not follow the expository line of the ﬁrst one, but will concentrate on a discussion of those fundamental features of that work that are of Husserlian origin. Contrary to what happened in Der Raum, where Husserl is referred to very frequently and where Carnap openly accepts Husserl’s great inﬂuence, in Aufbau Husserl is referred to only ﬁve times, and sometimes merely as one in a list of many authors who have said something about the issue under discussion. However, as we will see in this and the next chapter, Husserl’s inﬂuence on Carnap’s Aufbau is not only a decisive one, but goes much further than Carnap acknowledges. To put it succinctly, Husserl’s inﬂuence on Aufbau was masked by Carnap, and not casually but intentionally masked. 2 Preliminaries: Methodology and Purpose of Aufbau As Carnap states on the very ﬁrst page of Aufbau, the purpose of his research is to exhibit an epistemological-logical system, which he called Konstitutionsystem – and which I will translate into English as ‘constitutional system’ rather than as ‘constitution system’ – of concepts or objects. Incidentally, Carnap immediately stresses3 that his use of the word ‘object’ is a very broad one, namely, as including ‘everything about which a statement can be made’, thus, ‘not only things, but also properties and relational properties [Beziehungen], classes and relations [Relationen], states and events, moreover actual [Wirkliches] and non-actual [Unwirkliches]’. Already this terminological ﬁxation of the word ‘object’ clearly separates Carnap from most empiricists, as well as from nominalism, physicalism and strict phenomenalism. Classes and relations are not mere ﬁctional constructions for the author of Aufbau, but legitimate entities in their own right, namely, objects of higher level. Carnap understands the word ‘object’ in Aufbau in a similar fashion as Husserl understood it and also the word ‘objectuality’ [Gegenständlichkeit] in his whole work.4 Presently, however, I want to examine the fundamental notion of a constitutional system. This notion is so important to understand Carnap’s views in Aufbau that he even considered to use the expression ‘constitutional system’ in the title of the book, which was already basically written when he arrived in Vienna in 1926 as a lecturer 3 Der logische Aufbau der Welt, p. 5. 4 Of course, in most of the book he seems to qualify this liberal use of the word ‘object’ by calling classes and relations ‘quasi-objects’. This, however, should not be understood – see on this issue p. 72 – as if he were to consider classes and relations as a sort of ﬁctions, and were propounding a sort of nominalism. The notion of quasi-object is simply a convenient device to establish a relative distinction between objects of any level and the classes or relations of which they are members. Thus, as Carnap stresses on p. 72, actual physical (concrete) objects are all quasi-objects relative to the elementary experiences of consciousness. Moreover, it should also be mentioned that in the constitutional system of Aufbau the most basic of all objects is not any elementary experience of consciousness, but – as stressed by Carnap on p. 83 – the basic relation of recollection of similarity, thus, a relation.

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[Privatdozent], but was persuaded by Schlick and Neurath to change the title. The notion of a constitutional system is also important for the discussion between different interpretations of Aufbau, and has been emphasized by interpreters trying to see Carnap as especially inﬂuenced by Kant and neo-Kantianism. As is well known, Kant used the word konstitutiv, and if one were to superﬁcially and irresponsibly identify konstitutiv with konstruktiv and Konstitution with Konstruktion, then the bridge from Kant to Carnap’s Aufbau would have already been ‘constructed’. However, that interpretation is groundless.5 As happened with the expression ‘synthetic a priori’ in Der Raum, though Kant used the word konstitutiv, the meaning of that word in Kant is different from that given by Carnap to the same word. As stated in the subject index [Sachregister] of Kant’s Kritik der reinen Vernunft, konstitutiv is used by Kant as ‘determining objectively’ [objektiv bestimmend], ‘law-giving’ [gesetzgebend], and is related to the axioms and principles. Thus, as Herbert J. Paton puts it on p. 179 of the second volume of his Kant’s Metaphysics of Experience, for Kant the Mathematical Principles are constitutive, whereas the Analogies are merely regulative. Interestingly enough, the distinguished Kant specialist and prominent Kantianizer of the young Carnap, Michael Friedman, expressed similar views in his book Kant and the Exact Sciences. Indeed, on p. 51 of that book there is a passage that deserves to be quoted before discussing Carnap’s conception of a constitutional system. Thus, Friedman says:6 For, as we have seen, the regulative procedure of reﬂective judgement and the constitutive procedure of the understanding move, as it were, in two contrary directions. The latter proceeds from the top down, as it were, by schematizing the pure concepts of the understanding in terms of sensibility so as to provide for a mathematical science of nature, in particular, the Newtonian theory of gravitation. The former proceeds from the bottom up, by systematizing lower-level empirical concepts and laws so as to approximate thereby to an ideal complete science of nature. [Kant and the Exact Sciences, p. 51]

Thus, not only does Kant’s use of the word konstitutiv express ‘law-giving’ or ‘determining objectivity’,7 but, more importantly, as Friedman stressed in the above passage, the constitutive procedure goes from the top to the bottom, not the other way around, as occurs with the regulative procedure. It is time now to consider what Carnap understood by a constitutional system and how it proceeds. On p. 2 of Aufbau, Carnap makes it clear that the principal thesis of that work is that there exists a hierarchy of concepts such that all scientiﬁc concepts can be constituted on the basis of some fundamental ones. A constitutional system is essentially such a hierarchy of concepts (or objects) of different levels, in which the 5 See on this issue Carnap’s pledge for neutrality of the technical words ‘constitution’ and ‘to constitute’ in Aufbau, pp. 5–6. 6 I have expressly quoted Friedman in view of his Kantian interpretation of Carnap. 7 See also ibid., pp. 180 and 303 for Kant’s use of the word ‘constitutive’ as concerned with the principled conditions of possibility of experience, which, as we will see, is at best vaguely related to Carnap’s use of the word ‘constitution’. See also the ‘Sachregister’ to the Kritik der reinen Vernunft, where the word ‘constitutiv is not only rendered as determining objectivity and law-giving, but is also explicitly related to principles or axioms.

On Der logische Aufbau der Welt

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concepts (respectively, objects) of higher levels are constituted by – or founded, or grounded on – those of the lower levels and, since the relation of ‘being constituted’ is a transitive relation, all concepts are constituted on the basis of a few primitive concepts of the most basic level. On this extremely important point, it is convenient to quote Carnap: By a “constitutional system” we understand a hierarchical order of the objects such that the objects of each level are constituted from those of the lower levels. In view of the transitivity of the reducibility, all objects of the constitutional system will in this way be indirectly constituted from the objects of the ﬁrst level; these “basic objects” form the “basis” of the system. [Der logische Aufbau der Welt, p. 2]8

To avoid possible misunderstandings, it must be emphasized here that Carnap speaks indistinctly of a hierarchy of objects and a hierarchy of concepts. This should not necessarily be interpreted as a double hierarchy, one ontological and the other more conceptualist, but simply as an expression of the minimal importance that Carnap assigns to the distinction between concept and object. On this point, Carnap explicitly rejects – see p. 5 – Frege’s distinction between concept and object, and even goes so far as considering that Fregean distinction as psychologistic. It is worth quoting the passage: Whether a determined sign for an object refers [bedeutet] to a concept or to an object, whether a proposition is valid for concepts or for objects that does not signify [bedeutet] any logical difference, but at most a psychological [one], that is, a difference of the representing ideas. [Der logische Aufbau der Welt, p. 5]9

Continuing with Carnap’s notion of constitution, other pertinent passages are scattered along the whole book. It is convenient to refer to a few of them. Thus, for example, on p. 47, Carnap says: ‘To constitute a concept means: to offer a constitutional deﬁnition on the basis of other concepts’,10 where a constitutional deﬁnition of a concept is to be meant as expressing a reduction of this concept, in the form of a translation rule, to concepts of a lower level in the constitutional system, allowing for the replacement of the constituted concept by the constitutive concepts 8 ‘Unter einem ‘‘Konstitutionssystem’’ verstehen wir eine stufenweise Ordnung der Gegegenstände derart, daß die Gegenstände einer jeden Stufe aus denen der niederen Stufen konstituiert werden. Wegen der Transitivität der Zurückführbarkeit werden dadurch indirekt alle Gegenstände des Konstitutionssystems aus den Gegenständen der ersten Stufe konstituiert; diese ‘‘Grundgegenstände’’ bilden die ‘‘Basis’’ des Systems.’ 9 ‘Ob ein bestimmtes Gegenstandszeichen den Begriff oder den Gegenstand bedeutet, ob ein Satz für Begriffe oder für Gegenstände gilt, das bedeutet keinen logischen Unterschied, sondern höchstens einen psychologischen, nämlich einen Unterschied der representierenden Vorstellungen.’ In the above passage I have rendered the word ‘bedeutet’ in two different ways, the ﬁrst time in Frege’s unusual use, the second time as it is usually used in German, namely, to signify (or mean, or express). I have also rendered the word ‘Vorstellung’ as ‘idea’ instead of ‘representation’ to avoid the phrase ‘representative representation’. 10 The full German text reads: ‘Einen Begriff aus anderen Begriffen zu ‘‘konstituieren’’ soll bedeuten: seine ‘‘konstitutionale Deﬁnition’’ auf Grund der anderen Begriffe angeben.’

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in any propositional function in which the ﬁrst occurs. A similar passage, in which the notion of reduction is central, occurs on p. 65. Thus, Carnap says:11 We call an object a “reducible to objects b, c,…” when for the existence of each state of affairs concerning the objects a, b, c, … one can offer a necessary and sufﬁcient condition that depends only on the objects b, c, …. [Der Logische Aufbau der Welt, p. 65]

As Carnap points out,12 the familiar explicit deﬁnitions are the simplest examples of constitutional deﬁnitions. They are, however, not the only kind of deﬁnition. On this point, Carnap diverges once more from Frege, allowing, following Russell – see pp. 53–4 – for contextual deﬁnitions. On the other hand, in case an object is constituted on the basis of other more fundamental objects, Carnap calls it13 a ‘complex’. It follows immediately that all classes and relations – with the exception of the basic relation of “recollection of similarity” – being always objects of higher level, are complexes. Thus, since classes and relations are the only kinds of objects of higher level,14 as Carnap puts it,15 from the deﬁnitions of a constitutional system and of a complex it follows that all objects of the constitutional system that are not basic objects are complex objects. Incidentally, in order to avoid possible misunderstandings derived from Carnap’s later empiricist views, it should be emphasized that reduction is not to be understood in Aufbau as meaning that the entities of higher levels – relations and classes – are mere convenient ﬁctions that dissolve like castles of sand into the basic objects. On this issue, there is a relatively late passage from pp. 202–3 that does not leave much room for ambiguities. … the constitution of an object on the basis of other determined objects not only does not mean that the object is of a similar kind as the others, but, on the contrary, if the constitution (as it frequently happens with the spiritual objects, particularly those of the higher levels) leads to the formation of new logical levels, then the constituted objects belong to a different kind of being, more precisely: to a new sphere of objects. Thus, in our kind of constitution of the spiritual objects no psychologism is present. [Der logische Aufbau der Welt, pp. 202–3]16

11 ‘Wir nennen einen Gegenstand a ‘‘zurückführbar auf die Gegenstände b, c, …’’, wenn sich für das Bestehen jedes beliebigen Sachverhaltes in bezug auf die Gegenstände a, b, c, … eine notwendige und hinreichende Bedingung angeben läßt, die nur von den Gegenständen b, c, … abhängt.’ 12 See p. 47. 13 Ibid., p. 48. 14 See ibid., pp. 93–4. 15 Ibid., p. 49. 16 ‘… die Konstitution eines Gegenstandes auf Grund bestimmter anderen Gegenstände nicht nur nicht besagt, daß der Gegenstand mit den anderen gleichartig sei, sondern im Gegenteil wenn die Konstitution (wie es bei den geistigen Gegenständen besonders der höheren Stufen in hohem Grade der Fall ist) zur Bildung neuer logischen Stufen führt, so gehören die konstituierten Gegenstände einer anderen Seinsart, genauer: einer neuen Gegenstandssphaäre an. In unserer Art der Konstitution der geistigen Gegenstände liegt also kein Psychologismus.’

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Another related point that Carnap emphasizes in the ﬁrst pages of Aufbau is the neutrality of the terminology used in the constitutional system. On pp. 5–6, he distances himself from the discussion between realists and idealists. In particular, he stresses the neutrality of the language of the constitutional system, making it clear that the expression ‘to constitute’ and, of course, related expressions like ‘constitution’ are perfectly neutral, and should not be rendered either as ‘generated’ or ‘constructed’, or as ‘recognized’. Thus, the attempt to assimilate the word ‘constitution’ to the word ‘construction’ – as occurs in the English translation of Aufbau, but not only there – is unfortunate and misleading.17 It should by now be perfectly clear that Carnap’s notions of ‘constitution’, ‘constitutive’ and ‘to constitute’ have almost nothing in common with Kant’s similar terminology. In particular, constitution should not be rendered as construction, but is perfectly neutral between the acknowledgement of something already existing and the construction, or generation, of something non-existent before the construction or generation. More decisively, the constitution of objects (or concepts) is a procedure of grounding the higher level objects (or concepts) on the more basic ones and, in view of the clear transitivity of such a relation, the grounding of all higher level objects (or concepts) ultimately on the basic objects (or concepts). In fact, as we will later see, Carnap will base his constitutional system on only one kind of basic object and only one dyadic relation between such objects. In clear opposition to what Friedman stressed about the constitution procedure in Kant, in Carnap’s constitutional system the constitution is not from top down, not downwards, but upwards, from the basic object(s) and relation(s) to an unlimited hierarchy of ever more complex relations and classes of higher levels. Finally, I will say a few words about a related notion used by Carnap, namely that of ‘Fundierung’, which I will translate into English as ‘grounding’. The notion of grounding used by Carnap seems to have been obtained from Husserl’s Third Logical Investigation – as will become clear from the following section. In the context of Carnap’s constitutional system, the relation of grounding runs parallel to that of constitution, that is, upwards. However, grounding is a more general relation, applicable in other contexts, in which there is no such hierarchy of levels, for example, in a relation of logical implication, or in the relation of the parts to a whole. But no matter its greater generality, it has nothing to do with Kant’s notion of constitutive principles, and never runs from the top to the bottom.18 Carnap introduces the notions of ‘grounding’ and ‘grounded relation’ explicitly on pp. 206 and 207 of Aufbau, and stresses19 that grounding is the most basic notion of the constitutional system and as such undeﬁnable in the system. Moreover, he adds20 that the notion of grounding is

17 See footnote 4 above. The most glaring example of this unfortunate assimilation is the title of Alan Richardson’s book, namely: Carnap’s Construction of the World (Cambridge, Cambridge University Press, 1998). 18 Of course, in ordinary usage, one speaks often of something α being grounded on another thing β. Nonetheless, despite such frequent misleading usage, the relation of grounding in such a case is from β to α, that is from the bottom to the top, not from the top to the bottom. 19 Der logische Aufbau der Welt, p. 207. 20 Ibid.

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also undeﬁnable by means of logical notions. Hence, he concludes – see p. 207 – that such a notion, applicable to the most varied domains of objects, must be a primitive of logic, that is, a fundamental logical notion. 3 Husserl’s Notion of Constitution and Carnap Husserl’s use of the notions of ‘constitution’, ‘constitutive’ and ‘to constitute’ is by far more frequent and decisive than that of Kant’s, as can be clearly seen, for example, by comparing the subject index of Kant’s Kritik der reinen Vernunft with the subject index of Ideen I. The notion of constitution is at the very basis of Husserl’s phenomenology, and it is of such importance that the second volume of that book – published only posthumously – has the subtitle Phänomenologische Untersuchungen zur Konstitution, that is: Phenomenological Investigations on Constitution. Before getting into deep waters related to that book, I want ﬁrst to stress that Husserl understands by constitution something very different from Kant. Indeed, I will not attempt to tackle all aspects of Husserl’s notion of constitution, but only those that are especially relevant for our purpose. Constitution, as conceived by Husserl, is indissolubly linked to conscience and to the experiences of consciousness in the stream of consciousness of the I, that is, in that continuous medium intimately related to inner time. Thus, Husserl says:21 No matter how foreign to each other, even essentially, can experiences of consciousness be, they are in their totality constituted as a stream of time, as members in the one phenomenological time. [Ideen I, p. 292]

Although in some sense the experiences of consciousness are also constituted in the stream of consciousness, let us limit the discussion here to the constitution of objects. Precisely the diverse experiences of consciousness constitute the different sorts of objects. All intentional acts of conscience are, in a general sense, objectifying acts in a wide sense, that is, acts that constitute objects – where constitution shall be understood in a neutral sense, neither meaning that the objects are constructed or generated by the experiences of consciousness, nor that the objects pre-exist and are simply recognized. Indeed, it should be pointed out that phenomenology does not consider any existential theses, but is completely neutral on matters of existence.22 As Husserl puts it on p. 171, phenomenology is ‘a descriptive doctrine of essences of the transcendentally pure experiences of consciousness in the phenomenological attitude’.23 This phenomenological attitude precisely suspends any existential judgement about the intentional objects. With respect to the general nature of

21 ‘Wie fremd Erlebnisse einander im Wesen auch sein können, sie konstituiren sich insgesamt als ein Zeitstrom, als Glieder in der einen phänomenologischen Zeit.’ 22 Probably on this point also Husserl inﬂuenced Carnap and left an enduring mark on his whole philosophy. 23 The full (relevant) German text reads: ‘Was die Phänomenologie anbelangt, so will sie eine deskriptive Wesenslehre der transzendental reinen Erlebnisse in der phänomenologischen Einstellung sein….’

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constitution, it is pertinent here to quote a passage, in which Husserl stresses the objectifying, constituting nature of experiences of consciousness. After all of this results that all acts in general – even the acts of emotion or will – are “objectifying”, originally “constituting” objects, necessary sources of diverse regions of being and with it also of the corresponding ontologies. [Ideen I, p. 290]24

Another related passage, this time from the posthumously published second volume of that book – whose ﬁrst version was, however, written in 1914 – deserves being quoted. But then the concerned objectuality is already constituted before these theoretical acts by means of certain intentional experiences of consciousness and at the same time by no means by all, which in the pure subject are to be designated as related to this objectuality. [Ideen II, p. 4]25

Moreover, not only are all constituted objects constituted by means of intentional experiences of consciousness, but this constitution is a stratiﬁed one, going from the most basic objects to the more complex ones. The following passages make that point perfectly clear. Both passages also serve to establish that for Husserl, as for Carnap, the relation of grounding – the German word used by both Husserl and Carnap is Fundierung – is the more general notion of which the notion of constitution is a special case. Each synthetic-unitary conscience, no matter how many particular theses and syntheses were to be ordered [under] it, possesses the total object corresponding to it as syntheticunitary conscience. It is called total object in contrast to the objects that belong intentionally to the synthetic members of lower or higher level, since they all also contribute to it in the manner of grounding and are ordered [under] it. [Ideen I, pp. 293–4]26 Clearly, in the case of all these forms of constitution of objects we will be brought back to objects, which do not remit to already given objects of the sort that are originated by means of some theoretical, value-giving or practical spontaneity …, then we eventually arrive in a series of steps to grounding objectualities, respectively noemata, that do not contain any such reductions, that are originally apprehended or apprehensible in the simplest theses and do not remit to any theses already present and ﬁrst of all to be reactivated, [and] that contribute to the constitutive constituency of the object. The objects phenomenologically characterized in this peculiar fashion – at the same time the fundamental objects, to which

24 ‘Nach all dem ergibt es sich, daß alle Akte überhaupt – auch des Gemüts – und Willensakte – ‘‘objektivierend” sind, Gegenstände ursprünglich ‘‘konstiuierend’’, notwendige Quellen verschiedener Seinsregionen und damit auch zugehöriger Ontologien.’ 25 ‘Dann ist aber die betreffende Gegenständlichkeit schon vor diesen theoretischen Akten bewußt konstituiert durch gewisse intentionale Erlebnisse und dabei keineswegs durch alle, welche im reinen Subjekt als auf diese Gegenständlichkeit bezogene zu bezeichnen sind.’ 26 ‘Jedes synthetisch-einheitliche Bewußtsein, wie viele besondere Thesen und Synthesen ihm eingeordnet mögen, besitzt den ihm als synthetisch-einheitlicher Bewußtsein, zugehörigen Gesamtgegenstand. Gesamtgegenstand heißt er gegenüber den Gegenständen, die zu den synthetischen Gliedern niederer oder höherer Stufe intentional gehören, sofern sie alle auch in der Weise der Fundierung zu ihm beitragen und sich ihm einordnen.’

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The Young Carnap’s Unknown Master remit in virtue of their phenomenological constitution all possible objects – are the objects of the senses. [Ideen II, p. 17]27

An especially important point that should be emphasized here is that for Husserl, though the higher level objects in the hierarchy of constitution are grounded on the lower level ones – and ultimately on the objects of the senses – that does not mean that they are mere compounds or complexions of the latter. For Husserl, in each new level of constitution the objects are essentially different from the objects of lower levels. They have their respective irreducible objectualities. Moreover, this is true not only for the constitution of the objectualities of the different material regions of objects, but also for the categorial objects of the logical-mathematical sciences. Categorial objects are grounded on the objects of the senses but by no means reducible to them. But seen free of prejudices and phenomenologically brought back to its sources, the grounded unities are both grounded and novel, the new that can be constituted with them, as the intuition of essences shows, can never and nevermore be reduced to mere sums of other realities. [Ideen I, p. 375]28

In the above-quoted passage, as well as in that from pp. 293–4 of his Ideen I quoted before, Husserl uses the terms Fundierung and fundiert, which I have translated as ‘grounding’ and ‘grounded’, in the same sense as Carnap, namely, where grounding – as in Carnap’s usage – is the general relation, of which the relation of constitution is a special case. Moreover, Husserl had already introduced the very important notion of grounding in the Third Logical Investigation, having even offered a group of theorems characterizing that notion.29 A somewhat long passage on p. 377 of Ideen I sketches the way in which categorial entities – also called by Husserl ‘entities of the understanding’ – for example sets, sets of sets, and relations, are constituted. A much more detailed treatment of this extremely important issue was given by Husserl in the second part of the Sixth Logical

27 ‘Offenbar werden wir bei allen diesen Formen der Konstitution von Gegenständen zurückgeführt auf Gegenstände, welche nicht mehr auf vorgegebene Gegenstände der Art zurückweisen, die ursprünglich durch irgend welche theoretischen, wertenden oder praktischen Spontaneitäten entsprungen sind …, so kommen wir ev. in einer Reihe von Schritten, auf fundierende Gegenständlichkeiten bzw. Noemata zurück, die nichts mehr von solchen Rückdeutungen enthalten, die in schlichtesten Thesen ursprünglich erfaßt oder erfaßbar sind und auf keine voranliegenden und allererst zu reaktivierenden Thesen zurückweisen, die zum konstitutiven Bestand des Gegenstandes Beiträge liefern. Die phänomenologisch in dieser Eigentümlichkeit charakterisierten Gegenstände – gleichsam die Urgegenstände, auf welche alle möglichen Gegenstände ihrer phänomenologischen Konstitution nach zurückweisen – sind die Sinnengegenstände.’ 28 ‘Aber vorurteilsfrei angesehen und phänomenologisch auf seine Quellen zurückgeführt, sind die fundierten Einheiten eben fundierte und neuartige; das Neue, das sich mit ihnen konstituiert, kann, wie die Wesensintuition lehrt, nie und niemmer auf bloße Summen von anderen Realitäten reduziert werden.’ 29 See Logische Untersuchungen II, U. III, § 14.

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Investigation.30 A similar more succinct passage occurs on p. 18 of the posthumously published second volume of the former book. I will quote this one:31 We know that objects, no matter how constituted (objects of completely arbitrary region, completely arbitrary genus and species), can be substrata precisely for categorial syntheses, can enter as constitutive elements in “categorial” formations of objects of higher level. [Ideen II, p. 18]

It is unnecessary to quote further similar passages, especially since I am here only marginally concerned with logical-mathematical entities. A passage, however, that I will presently quote is one in which Husserl relates the sequence of ontological levels both of objects of the material and of the formal sciences with the sequence of levels of constitutive phenomenology. This adds to my contention of the central importance of constitution for Husserl’s phenomenology. Thus, on p. 379 of the ﬁrst volume, Husserl says: The sequence of levels of the formal and material doctrines of essences in some way depicts the sequence of levels of constitutive phenomenology, determines its level of generality and gives them the “guides” in the ontological and material eidetic fundamental concepts and principles. [Ideen I, p. 379]32

It is pertinent to ask now to what extent reach the similarities between Husserl’s views of constitution and those of Carnap’s in Aufbau. The most decisive and convincing point can be obtained from the structure of the second volume of Ideen II. Not only is the subtitle of that book – as already mentioned – Phänomenologische Untersuchungen zur Konstitution but it is divided in three parts that correspond exactly to those of Carnap’s constitutional system. Thus, the ﬁrst part is titled Die Konstitution der materiellen Welt, whereas the second part is titled Die Konstitution der animalischen Natur – and includes prominently a discussion of intersubjectivity – and the third part is titled Die Konstitution der geistigen Welt. Hence the structure of the constitutional steps of Carnap’s Aufbau and that of Husserl’s Ideen II is the same. We will see in the next section that the basis of the system is also the same, namely, the stream of consciousness of the I, in which the experiences of consciousness are given. I will now quote a few passages that can help us understand very deﬁnitely how Husserl proceeds.

30 Logische Untersuchungen II, U. VI. See also my paper ‘Husserl’s Epistemology of Mathematics and the Foundation of Platonism in Mathematics’, 1987, reprinted as Chapter 12 in Hill and Rosado Haddock, Husserl or Frege?: Meaning, Mathematics and Objectivity (Chicago et al., 2000, 2003), pp. 221–39. 31 ‘Wir wissen, daß wie immer konstituierte Gegenstände (Gegenstände ganz beliebiger Region, ganz beliebigen Gattungen und Arten) Substrate für gerade kategoriale Synthesen sein können, als konstitutive Elementen in ‘‘kategoriale’’ Bildungen von Gegenständen höherer Stufe eintreten können.’ 32 ‘Die Stufenfolge der formalen und materialen Wesenslehren zeichnet in gewisser Weise die Stufenfolge der konstitutiven Phänomenologie vor, bestimmt ihre Allgemeinheitsstufen und gibt ihnen in den ontologischen und eidetischen Grundbegriffe die ‘‘Leitfaden’’’.

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The Young Carnap’s Unknown Master Originally the real world is constituted by steps, in such a way that as basic layer is structured the manifold of objects of sense … in the unity of the spatial form. At the same time the objects of sense are constituted in the subjective manner of “orientation” and for us … in such a way that is given a distinguished object of sense “[the] body” as the permanent bearer of the orientation. [Ideen II, p. 65]33

On this peculiar material – but not merely material – object, which is the body, and which is the centre of orientation, the so-called zero of the ‘Cartesian coordinate system’ of the pure subject, Husserl had already expressed the following some pages before:34 And also the distinction is clearly connected with this, that the body becomes the bearer of the null point of orientation and of the here and now, from which the pure I intuits space and the whole world of sense. Thus, each object that appears has eo ipso a relation of orientation with the body, and not only the actually appearing, but each object that shall possibly appear. [Ideen II, p. 56]

With respect to the peculiar material thing ‘the body’ another passage stresses its peculiarity, and once more brings to the fore that grounding should by no means be understood as complete reduction, as if only the material world existed and everything else were in principle eliminable by means of complete reductions. Thus, Husserl says:35 The objects of nature in the second extended sense are in complete concretion: animal realities, characterized as animated bodies. They are grounded realities, which presuppose in them as basic level material realities, so called bodies. Now, they have, that is the novelty, together with the material determinations, also new systems of properties…. [Ideen II, pp. 32–3]

Finally, I would like to quote a passage concerned with the constitution of the objects of the spiritual world.

33 ‘Ursprünglich konstituiert sich die reale Welt stufenweise so, daß als Unterschicht sich die Mannigfaltigkeit der Sinnendinge … in der Einheit der Raumform aufbaut. Dabei konstituieren sich die Sinnendinge in der subjektiven Weise der ‘‘Orientierung” und für uns … derart, daß ein ausgezeichnetes Sinnending ‘‘Leib’’ als beständiger Träger des Zentrums der Orientierung gegeben ist.’ 34 ‘Und auch die Auszeichnung hängt offenbar hiermit zusammen, daß der Leib zum Träger der Orientierungspunkte Null wird, des Hier und Jetzt, von dem aus das reine Ich den Raum und die ganze Sinnenwelt anschaut. So hat also jedes Ding, eo ipso Orientierungsbeziehung zum Leib, und nicht nur die wirklich erscheinende, sondern jedes Ding, das soll erscheinen können.’ 35 ‘Die Gegenstände der Natur im zweiten erweiterten Sinne sind in voller Konkretion: animalische Realitäten, charakterisiert als beseelte Leiber. Es sind fundierte Realitäten, welche in sich als Unterstufe materielle Realitäten, sogenannte Leiber voraussetzen. Diese haben nun, das ist das Neue, neben den speziﬁschen materiellen Bestimmungen, noch neue Systeme von Eigenschaften….’

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These communities, though essentially grounded on psychic reality, that itself is grounded on physical [reality], turn out to be novel objectualities of higher level…. Thus, all sorts of objects of value and practical objects, all concrete cultural formations, that determine our actual life as hard realities, for example, state, law, custom, church and so forth. All these objectualities must, so as they are given, be described according to fundamental forms and in the orders of their levels and for them the problems of constitution shall be stated and solved. [Ideen I, pp. 374–5]36

The quotations offered in this section and the preceding one are more than enough to show without any doubt the similarities, even in details, of Carnap’s and Husserl’s views on constitution and of their respective constitutional projects in Aufbau and Ideen. Together with the results of the following section – which shows that also their basis was essentially the same – they establish a complete parallelism between the two projects. Although in philosophy – as in science – there are cases of simultaneous discovery or postulation of a theory, for example Husserl’s and Frege’s almost simultaneous discovery of the distinction between sense and reference,37 and Gupta’s and Herzberger’s almost simultaneous discovery of the revision theory of truth, you need an extreme dose of naiveté to sustain that the case under discussion in this book is also a case of simultaneous discovery. As already mentioned in the ﬁrst chapter, Carnap visited Husserl’s seminars – at least – from the summer semester of 1924 to the summer semester of 1925, that is, from April 1924 to July 1925, thus, precisely at the time he was working on Aufbau. As Ludwig Landgrebe, who was then Husserl’s assistant, wrote in a letter to Husserl much later, Carnap and Landgrebe were then on friendly terms and used to discuss philosophical issues. But

36 ‘Diese Gemeinschaften, obschon wesentlich fundiert in psychischen Realitäten, die ihrerseits in physischen fundiert sind, erweisen sich als neuartige Gegenständlichkeiten höherer Ordnung…. So alle Arten von Wertobjekten und praktischen Objekten, alle Kulturgebilde, die unser aktuelles Leben als harte Wirklichkeiten bestimmen, wie z. B. Stadt, Recht, Sitte, Kirche usw. Alle diese Objektitäten müssen so, wie sie zur Gegebenheit kommen, nach Grundarten und in ihren Stufenordnungen beschrieben und für sie die Probleme der Konstitution gestellt und gelöst werden.’ 37 This case is an interesting one, since it has occurred almost exactly the opposite as with the case under consideration. Husserl obtained the distinction already in 1890, as attested by some remarks in his posthumously published paper ‘Zur Logik der Zeichen’ see Appendix B I to the second edition of his Philosophie der Arithmetik (Den Haag, 1970), pp. 340–73, especially pp. 343–4. His ﬁrst published writing in which the distinction appears is his review of the ﬁrst volume of Ernst Schröder’s Vorlesungen über die Algebra der Logik I, which appeared at the beginning of 1891 and of which he immediately sent a copy to Frege, together with a copy of his Philosophie der Arithmetik. In a letter to Husserl dated 24 May 1891, Frege acknowledged that Husserl had made the distinction independently of him – whose ﬁrst published work in which the distinction appears is ‘Funktion und Begriff’, also published at the beginning of 1891 – and comments on some differences, for example that for Husserl the referent of a conceptual word was the extension of the concept, whereas for him it was the concept. Nonetheless, still many Fregean scholars – and even some Husserlian ones like Føllesdal – believe that Husserl obtained the sense-reference distinction from Frege, though in order for that to be the case, our universe should be so structured that backward causation would be possible, and the future could causally inﬂuence the past.

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The Young Carnap’s Unknown Master

Landgrebe was ten years younger than Carnap and was never to be an especially original thinker. Moreover, precisely in those years he was organizing and preparing for publication the material for the second volume of Ideen, that is, for the volume completely dedicated to the constitutional problems. Since Carnap had already read the ﬁrst volume and referred to it in Der Raum, and was then especially interested in those constitutional problems, it is very probable that Carnap simply obtained his views on such issues from Husserl via the indiscrete young Landgrebe. I am conscious that the above is a very bold contention – and one with ethical components – but what still follows will serve to establish that it is much nearer to the truth than all other interpretations of Aufbau ever made. 4 On the Autopsychological Basis Much has been written about Carnap’s choice of an autopsychological basis for the constitutional system of Aufbau. Clearly, under the later inﬂuence of Neurath’s physicalism, which Carnap partially adopted at the beginning of the 1930s, a physicalist basis would seem to have been more adequate. Indeed Carnap tried to minimize the importance of his choice and already toyed in Aufbau with the possibility of a physicalist basis for the constitutional system, which in some sense would at ﬁrst sight seem more adequate for the sciences.38 However, as Carnap stresses, on epistemological grounds – and Aufbau intends to be an epistemologicallogical reconstruction of our (non-logical-mathematical) knowledge – the autopsychological basis is more adequate than the physicalist (or materialist) one. Thus, Carnap states: From the standpoint of the theory of knowledge (in contradistinction to that of the real sciences) we are driven to another order of concepts: to the constitutional system with autopsychological basis. [Der logische Aufbau der Welt, p. 81]39

Similar justiﬁcations, on epistemological grounds, of his choice of an autopsychological basis are made on pp. 82 and 83, in which he also rejects the possibility of using the whole auto- and hetero-psychological region as basis, since, as he stresses,40 our knowledge of the heteropsychological is not possible without the mediation of the physical. Thus, as Carnap puts it,41 the epistemological grounding in the constitutional system of Aufbau of the most important regions of objects is the following: (i) autopsychological, (ii) physical, (iii) heteropsychological, (iv) spiritual (or cultural). Incidentally, it is of special importance for our discussion that in the Preface to the second edition Carnap also considered the possibility of using another kind of 38 See § 59, pp. 80–81 and § 62, pp. 83–4. 39 ‘Vom erkenntnistheoretischen Standpunkt aus (im Unterschied zum realwissenschaftlichen) werden wir zu einer anderen Ordnung geführt: zu dem Konstitutionssystem mit eigenpsychischen Basis.’ 40 Der Logische Aubau der Welt, p. 83. 41 Ibid., p.79.

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autopsychological basis, clearly different from the one adopted in Aufbau. Thus, on p. XII Carnap asserts that he in that moment – 1961 – would have chosen an autopsychological constitutional basis similar to Mach’s elements, namely, one of concrete sense data – thus, also nearer to Quine. Such an assertion is important for different reasons. First of all, it is an acknowledgement by Carnap that his constitutional system in Aufbau did not have a phenomenalist Machian basis, and was simply not a phenomenalist system or a version of empiricist system dear to the tradition usually traced from Russell to Quine. Moreover, such an assertion, combined with a passage from p. 4 of Aufbau, is an example of the present author’s contention that some references in Aufbau and in other writings of Carnap, instead of serving to identify the sources of major inﬂuences, serve to mask those sources. Thus, on p. 4 Carnap states: The most important motivations for the solution of the problem [of] how the scientiﬁc concepts are to be reduced to the “given” were given by Mach and Avenarius. Points of contact are also present with Husserl’s indicated objective of a “mathesis of experiences of consciousness”. [Der logische Aufbau der Welt, p. 4]42

However, as I will establish in this book, the fact of the matter is approximately the opposite of what Carnap states in the above passage. It is from Husserl that Carnap receives the by far most important inﬂuence in Aufbau, whereas Mach and Avenarius play a very marginal role. In fact, Carnap’s particular choice of an autopsychological basis does not consist of sense data, or sensations, or Machian elements, but of ‘Erlebnisse’ – see, for example p. 8 – which I have already translated in the above passage as ‘experiences of consciousness’. It is pertinent to offer here some quotations difﬁcult to reconcile with the above quotation from p. 4, namely, the following passages from pp. 82, 91–2, 93 and 130: Our use of such a form of a system [with a psychological basis] by no means signiﬁes that we are presupposing a sensualistic or positivistic conception. [Der logische Aufbau der Welt, p. 82]43 After the autopsychological was chosen as basic domain, thus, the processes of consciousness or experiences of consciousness of the I, it must still be determined which

42 The German original reads as follows: ‘Die wichtigsten Anregungen für die Lösung des Problems, wie die wissenschaftlichen Begriffe auf das ‘‘Gegebene’’ zurückzuführen sind, haben Mach und Avenarius gegeben. Berührungspunkte liegen ferner auch vor mit dem von Husserl als ‘‘mathesis der Erlebnisse’’ angedeuteten Ziel.’ It is extremely difﬁcult to translate the German word ‘Erlebnis’ into English. Richardson, for example, translates it simply as ‘experience’, though the usual German word for experience is ‘Erfahrung’, and ‘Erfahrung’ and ‘Erlebnis’ are by no means synonymous. Moreover, rendering the word in English as ‘experience’ could very easily lead to misunderstandings, due to the use of that word in the empirical tradition, and possible associations either with sensory outer experience or with the psychological inner experience of my emotions. But the word ‘Erlebnis’ refers to contents of consciousness, no matter whether they refer to external objects or to emotions or so-called states of mind. Hence, I will always translate ‘Erlebnis’ as ‘experience of consciousness’. 43 ‘Unsere Anwendung einer solchen Systemform [mit psychischer Basis] bedeutet aber keineswegs, daß wir eine sensualistische oder positivistische Anschaung zugrunde legen.’

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The Young Carnap’s Unknown Master formations of this region are going to serve as basic elements. One could, let us say, consider taking as basic elements the ultimate constituent parts obtained by means of psychological and phenomenological analysis of the experiences of consciousness, thus, let us say, the simplest sensory sensations (as Mach), or more generally: psychic elements of different sorts, from which the experiences of consciousness are formed. On a closer examination, however, we must acknowledge that in this case not the given itself, but abstractions from it, thus something epistemologically secondary, has been taken as basic elements…. Since we, however, wanted also to require from our constitutional system the consideration of the epistemological order of the objects, we shall, thus, start from what is epistemologically primary to everything else, from “[the] given”, and those are the experiences of consciousness themselves in their totality and closed unity…. To the chosen basic elements, those experiences of consciousness of the I as unities … we refer as “elementary experiences of consciousness”. [Der logische Aufbau der Welt, pp. 91–2]44 The elementary experiences of consciousness shall be the basic elements of our constitutional system. On this basis shall be constituted all other objects of our prescientiﬁc and scientiﬁc knowledge, including also the objects that one is accustomed to refer to as the constituent parts of the experiences of consciousness or as components of the psychic processes, and which are obtained as result of the psychological analysis. [Der logische Aufbau der Welt, p. 93]45 … in our constitutional system the qualities are not constituted from the sensations (let us say, as classes of those) (as it would correspond to a determinate positivistic conception), but, on the contrary, the sensations from the qualities; really, these qualities then [are constituted] (as it is in the general sense of positivism) from the elementary experiences of consciousness. That the sensations are constituted from the quality classes and not the other way around, is a consequence of our basic conception, namely, that the singular constituent parts of an experience of consciousness are not manifest in the singular experience of consciousness, but can be obtained only by abstraction, and certainly by

44 ‘Nachdem als Basigebiet das eigenpsychische gewählt ist, also die Bewußtseinsvorgänge oder Erlebnisse des Ich, muß noch festgelegt werden welche Gebilde dieses Gebietes als Grundelemente dienen sollen. Man könnte etwa daran denken die letzten Bestandteile, die sich bei psychologischer und phänomenologischer Analyse der Erlebnisse ergeben, als Grundelemente nehmen, also etwa einfachste Sinnesempﬁndungen (wie Mach), oder allgemeiner: psychische Elemente verschiedener Arten, aus denen die Erlebnisse aufgebaut werden könnten. Bei näherer Betrachtung müssen wir jedoch erkennen, daß in diesem Falle nicht das Gegebene selbst, sondern Abstraktionen daraus, also etwas erkenntnismäßig Sekundäres, als Grundelemente genommen werden…. Da wir jedoch von unserem Konstitutionssystem auch die Berücksichtigung der erkenntnismäßigen Ordnung der Gegenstände verlangen wollten, so müssen wir von dem ausgehen, was zu allem anderen erkenntnismäßig primär ist, vom ‘‘Gegebenem’’, und das sind die Erlebnisse selbst in ihrer Totalität und geschlossenen Einheit…. Die gewählten Grundelemente, jene Erlebnisse des Ich als Einheiten … bezeichnen wir als ‘‘Elementarerlebnisse’’.’ 45 ‘Die Elementarerlebnisse sollen die Grundelemente unseres Konstitutionssystems sein. Auf dieser Basis sollen alle anderen Gegenstände der vorwissenschaftlichen und wissenschaftlichen Erkenntnis konstituiert werden, somit auch die Gegenstände, die man als Bestandteile der Erlebnisse oder als Komponenten der psychischen Vorgänge zu bezeichnen pﬂegt, und die als Ergebnis der psychologischer Analyse gefunden werden.’

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means of the insertion of the experience of consciousness in orders that include the other experiences of consciousness. [Der logische Aufbau der Welt, p.130]46

I hope that the somewhat extensive quotations immediately above will serve to put the ﬁnal nail in the cofﬁn of all those renderings of Aufbau as a phenomenalist book in the tradition of Machian phenomenalism, as well as of those renderings that conceive it as a book inserted in the empiricist tradition originating with Locke and Hume, thus, following in the footsteps of Russell’s Our Knowledge of the External World, and culminating in Quine. Incidentally, in an extensive remark on pp. 163–5, Carnap rejects Russell’s choice of an epistemological basis on the same grounds as those on which he based his rejection of Mach’s phenomenalism.47 For Carnap in Aufbau, as for Husserl, sensations, sense data or whichever are never encountered in experience, being abstractions from what is really present in experience. Although some Carnapian scholars have tried to trace Carnap’s use of the word ‘Erlebnis’ and other related features to ‘Gestalt psychology’, the fact of the matter is that Carnap – and also the Gestalt psychologists – obtained the terminology and the related features from Husserl.48 In fact, Carnap’s autopsychological basis of the constitutional system is not any autopsychological basis, but a very particular one, a so-called solipsistic basis. This solipsistic basis should not be understood, as a metaphysical claim that there exists only one subject, and that the other presumed subjects are not real. Carnap’s solipsism is a methodological one, explicitly based on Husserl’s εποχη, or phenomenological reduction, for which there is no difference with respect to reality or non-reality between different sorts of experiences of consciousness [Erlebnisse]. It seems pertinent to quote one of the most decisive passages of Aufbau, ignored by almost all Carnapian scholars, but more important for an adequate understanding of Aufbau than the totality of references to Poincaré, Dingler and others referred to as often or more often than Husserl in that book. It should 46 ‘… in unserem Konstitutionssystem nicht die Qualitäten aus den Empﬁndungen (etwa als Klassen von solchen) konstituiert werden (wie es einer bestimmten positivistischen Auffassung entsprechen würde), sondern umgekehrt die Empﬁndungen aus den Qualitäten; freilich diese Qualitäten dann (wie es im allgemeinen Sinne des Positivismus liegt), aus den Elementarerlebnissen. Daß die Empﬁndungen aus den Qualitätsklassen konstituiert werden und nicht umgekehrt, ist eine Konsequenz unserer Grundauffassung, daß nämlich die Einzelbestandteile eines Erlebnisses nicht in dem Einzelerlebnis hervortreten, sondern erst durch Abstraktion gewonnen werden, und zwar durch Einfügung des Erlebnisses in Ordnungen, die die übrigen Erlebnissen mit umfassen.’ 47 Der logische Aufbau der Welt, pp. 163–5, especially p. 164. 48 For an attempt to relate the basis of the constitutional system to Gestalt psychology, see, for example, Alan Richardson’s Carnap’s Construction of the World, p. 9 – in which already the title is misleading – as well as Thomas Mormann’s Rudolf Carnap, Munich, C.H. Beck, 2000, p. 93, where Mormann refers to writings of Gestalt psychologists published in 1922 and 1925, that is, the period in which Carnap wrote and ﬁnished the ﬁrst version of Aufbau. It is incredible that Carnap began to write Aufbau without having a clear idea of the basic domain and basic relation on which he was going to ground his constitutional system, and in the meantime obtained it from those works. Moreover, the distinguished Carnapian scholar seems to have forgotten that Carnap refers to Husserl’s Ideen not only in Aufbau, but already in Der Raum, where, as shown in Chapter 1, is the most important philosophical inﬂuence.

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help to make clear both that Carnap’s Aufbau has a Husserlian phenomenological basis and, in particular, that Carnap’s use of the basic term ‘Erlebnis’ is clearly Husserlian. Thus, Carnap says on p. 86: The distinction between actually real and not actually real is not present at the beginning of the constitutional system. For the basis no differentiation will be made between the experiences of consciousness, which on the basis of later constitution will be differentiated as perceptions, hallucinations, dreams, and so forth. This distinction and with it that between actually real and not actually real objects appears for the ﬁrst time in a sufﬁciently high constitutional level. At the beginning of the system the experiences of consciousness are simply to be taken as they are given; the postulations (or determinations) of reality and postulations (determinations) of unreality present in them will not be included, but “put in parenthesis”; thus, the phenomenological suspension (“εποχη“) in Husserl’s sense [is] exercised. [Der logische Aufbau der Welt, p. 86]49

The above passage is of extreme importance, not only for the purpose of the present research, namely, to establish that Husserl was the main philosophical inﬂuence in Aufbau, but also as an interpretation of Husserl’s phenomenological reductions as a methodological device. I thoroughly agree with Carnap’s rendering of the phenomenological reductions and against the mainstream of Husserlian scholars. The fact that Husserl’s views on logic and mathematics expounded in Chapter XI of the ﬁrst volume of his opus magnum, Logische Untersuchungen, remained essentially the same after the so-called transcendental turn is very difﬁcult to reconcile with usual more subjective renderings of the phenomenological reductions. Moreover, Carnap’s rendering has support in a neglected passage of the ﬁrst volume of Ideen. Thus, Husserl says:50 We adhere here, but immediately stress, that the attempt at a universal doubt shall serve us only as a methodological aid, to emphasize certain points…. [Ideen I, p. 64]

Indeed, Carnap is also explicitly Husserlian in another neglected passage of Aufbau on p. 86, where he uses ad nauseam Husserlian technical terminology. Thus, Carnap says:51 49 ‘Die Unterscheidung zwischen wirklichen und nichtwirklichen steht nicht am Beginn des Konstitutionssystems. Für die Basis wird kein Unterschied gemacht zwischen den Erlebnissen, die auf Grund späterer Konstitution als Wahrnehmung, Halluzination, Traum usw. unterschieden werden. Diese Unterscheidung und damit die zwischen wirklichen und nichtwirklichen Gegenständen tritt erst auf einer ziemlich hohen Konstitutionsstufe auf. Zu Beginn des Systems sind die Erlebnisse einfach so hinzunehmen, wie sie sich geben; die in ihnen vorkommenden Realsetzungen und Nichtrealsetzungen werden nicht mitgemacht, sondern ‘‘eingeklammert’’; es wird also die phänomenologische ‘‘Enthaltung’’ (εποχη) im Husserls Sinne ausgeübt.’ 50 ‘Wir knüpfen hier an, betonen aber sogleich, daß der universelle Zweifelsversuch uns nur als methodischer Behelf dienen soll, um gewisse Punkten hervorzuheben ….’ 51 ‘… das Grundgebiet liegt nur im Bewußten (im weiteren Sinne): zu ihm gehören alle Erlebnisse, ob gleichzeitig oder nachträglich auf sie reﬂektiert wird oder nicht. Wir sprechen deshalb lieber vom ‘‘Erlebnisstrom’’. Das Grundgebiet könnte auch als ‘‘das Gegebene’’ bezeichnet werden; doch muß hierbei beachtet werden, daß damit nicht etwas oder jemand

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… the basic domain lies only in consciousness (in the wider sense): to it belong all experiences of consciousness, no matter whether they are immediately or afterwards reﬂected upon. We speak therefore preferably of “stream of consciousness”. The basic domain could also be referred to as “the given”, though one must herein take into account that with it is not presupposed something or someone to which the given is given. The expression “the given” has the advantage with respect to the expressions “autopsychological” and “stream of consciousness” of a certain neutrality. [Der logische Aufbau der Welt, p. 86]

The ﬁrst four lines of the above quotation could very well have been obtained from Husserl. In it technical Husserlian expressions are omnipresent and, moreover, in the sense in which Husserl used them. Let us now hear what Husserl had already said about the same issues. By experiences of consciousness in the broadest sense we understand everything present in the stream of consciousness, thus, not only the intentional experiences of consciousness, the actual and the potential cogitations, [and] these taken in their complete concretion, but whatever of real moments is present in this stream and its concrete parts. [Ideen I, p. 80]52 A unity determined purely by the proper essence of the experiences of consciousness itself is exclusively the unity of the stream of consciousness…. [Ideen I, p. 86]53 The stream of consciousness is an inﬁnite unity, and the form of the stream is a form embracing necessarily all experiences of consciousness of a pure I…. [Ideen I, p. 200]54

Thus, for both Carnap and Husserl, the basic domain, on which all other domains of objects are going to be constituted, is that of consciousness. The basic domain contains only ‘Erlebnisse’ – which I have rendered as ‘experiences of consciousness’ – and no matter whether we presently reﬂect upon them or not – since we can in principle always do it – they are in an ‘Erlebnisstrom’, that is, in a stream of experiences of consciousness.55 The term ‘reﬂection’ in the sense used by Carnap is also not only a Husserlian term, but as well as the terms ‘Erlebnis’ and ‘Erlebnisstrom’, of

vorausgesetzt wird, dem das Gegebene gegeben ist. Der Ausdruck ‘‘das Gegebene’’ hat vor den Ausdrücken ‘‘Eigenpsychisches’’ und ‘‘Erlebnisstrom’’ den Vorzug einer gewissen Neutralität.’ 52 ‘Unter Erlebnissen im weitesten Sinne verstehen wir alles und jedes im Erlebnisstrom vorﬁndliche, also nicht nur die intentionalen Erlebnisse, die aktuellen und potentiellen cogitationes, dieselben in ihrer vollen Konkretion genommen, sondern was irgend an reellen Momenten in diesem Strom und seinen konkreten Teilen vorﬁndlich ist.’ There is a very similar passsage to the above on p. 75 of the same book. In fact, the notions of ‘Erlebnis’ and ‘Erlebnisstrom’ pervade most of that work as well as many other writings of Husserl. 53 ‘Eine rein durch die eigenen singulären Wesen der Erlebnisse selbst bestimmte Einheit ist ausschließlich die Einheit des Erlebnisstromes….’ 54 ‘Der Erlebnisstrom ist eine unendliche Einheit, und die Stromform ist eine alle Erlebnisse eines reinen Ich notwendig umspannende Form….’ 55 Husserl sometimes uses the expression ‘Bewußtseinsstrom’ as synonymous with ‘Erlebnisstrom’, though the latter expression is more frequent in the two Husserlian books that are especially pertinent here, namely, volumes one and two of Ideen.

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fundamental importance in Husserl’s philosophy.56 On the technical Husserlian term ‘reﬂection’, the following passages are especially pertinent. The study of the stream of consciousness is carried out on the other hand in various peculiarly built reﬂective acts, which themselves also belong to the stream of consciousness and could be made and must be made objects of phenomenological analysis in corresponding reﬂections of higher level. [Ideen I, p. 180]57 Reﬂection is, accordingly to what was presently argued, a title for acts, in which the stream of consciousness with all its various occurrences (moments of experiences of consciousness, intentionalities) becomes evidently seizable and analysable. [Ideen I, p. 181]58 Only by means of reﬂective experiencing acts do we know something about the stream of consciousness and about its necessary relationship with the pure I; thus, that it is a ﬁeld of free performances of cogitations of the same pure I…. [Ideen I, p. 184]59

Thus, according to Husserl as well as to Carnap, the stream of consciousness of a consciousness – which we could very well identify with the consciousness itself, as Carnap seems to prefer, so as to avoid any so-called ‘metaphysical connotations’ – contains a manifold of experiences of consciousness ordered in inner time. Most of those experiences of consciousness are not the object present to consciousness at a given time point in inner time. But consciousness has the capability of reﬂecting upon any such experience of consciousness, that is, of making it the object of consideration, for example, an experience of consciousness presently had sometime ago can very well be reﬂected upon and related to that presently given to consciousness. Incidentally, here lies the phenomenological basis of Carnap’s choice of the ‘Ähnlichkeitserinnerung’ – which I render here, following already established terminology, as ‘recollection of similarity’60 – as the basic relation of the constitutional system of Aufbau. Finally, the given is also a technical expression frequently used by Husserl. On this point, Carnap reiterates on pp. 89–90 that he prefers to use the expression ‘the given’ in a more neutral, subject-free manner.

56 To assess the importance of the terms ‘Erlebnis’ and ‘Erlebnisstrom’ in Husserl’s writings, I suggest the reader consult the ‘Sachregister’ (subject index) of Ideen I, pp. 428–9, where the references to the term ‘Erlebnis’ are more than a half page long, and together with those to ‘Erlebnisstrom’ are almost a whole page long. 57 ‘Das Studium des Erlebnisstromes vollzieht sich seinerseits in mancherlei eigentümlich gebauten reﬂektierten Akten, die selbst wider in den Erlebnisstrom gehören und in entsprechenden Reﬂexionen höherer Stufe zu Objekten von phänomenologischen Analysen gemacht werden können und gemacht werden müssen.’ 58 ‘Reﬂexion ist nach dem soeben Ausgeführten ein Titel für Akte, in denen der Erlebnisstrom mit all seinen mannigfachen Vorkommnisse (Erlebnismomenten, Intentionalien) evident faßbar und analisierbar wird.’ 59 ‘Durch reﬂektiv erfahrende Akte allein wissen wir etwas vom Erlebnisstrom und von der notwendigen Bezogenheit desselben auf das reine Ich; also darauf daß er ein Feld freien Vollzuges von Cogitationen des einen und selben reinen Ich ist….’ 60 See, for example, Richardson, op. cit. Another possible translation would be ‘remembrance of similarity’.

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There is a passage on pp. 86–7 of Aufbau immediately following one quoted above and belonging to the remarks on literature written with smaller print, that can serve as an additional perfect example of Carnap’s conscious attempt to mask Husserl’s inﬂuence in Aufbau. Carnap begins his extensive remark with a characterization of his position in Aufbau as methodological solipsism. Thus, he says:61 Since the choice of the autopsychological basis signiﬁes the application of the form and method of solipsism, but not the acknowledgement of its contentual thesis, we can, thus, speak of “methodological” solipsism. [Der logische Aufbau der Welt, p. 86]

He refers then to the following authors as methodological solipsists in some sense: Driesch – to whom he especially refers – and then adds that he also has some afﬁnities with von Schubert-Soldern, Gomperz, Ziehen, Husserl (Ideen, pp. 316– 17), Dingler, Reininger, Jacoby, Volkelt. It would be an interesting task for scholars like Moulines to show that all the authors mentioned by Carnap in such a context used the technical expressions ‘Erlebnis’, ‘Erlebnisstrom’ and ‘reﬂektieren’ in the same sense as Carnap and Husserl. That would be the only way to falsify my thesis that the reference to those authors had the purpose of masking Husserl’s fundamental inﬂuence in Aufbau. On pp. 87–90, Carnap tries to distance himself somehow from Husserl by arguing for a sort of subject free autopsychological basis, as if the experiences of consciousness were somehow to ﬂoat in the air, unrelated to a conscience. Such remarks, probably added both to appease his new partners in Vienna and to mask Husserl’s inﬂuence, are of little value, especially since the basic elements, the elementary experiences of consciousness, as Carnap calls them – see p. 92 – occur, according to him as well as to Husserl, not as a multiplicity of different unrelated and chaotically distributed experiences of consciousness, but as essentially related by being immersed in the stream of consciousness, which is a continuous medium that gives unity to the multiplicity of experiences of consciousness, and which could very well be identiﬁed with the I itself, since experiences of consciousness of different subjects do not occur in the same stream of consciousness. In the above quoted passage from p. 200 of the ﬁrst volume of Husserl’s Ideen I the indissoluble relation of the stream of consciousness to the I is stressed. Moreover, on p. 203 Husserl states:62 … two streams of consciousness (spheres of consciousness for two pure I) of identical essential content are not thinkable … that no completely determined experience of consciousness of one could belong to the other; only experiences of consciousness of identical internal nature could be common to them (though not individually identically

61 ‘Da die Wahl der eigenpsychischen Basis nur die Anwendung der Form der Mehtode des Solipsismus bedeutet, nicht aber die Anerkennung seiner inhaltlicher These, so können wir hier von ‘‘methodischen Solipsismus’’ sprechen.’ 62 ‘… zwei Erlebnisströme (Bewußtseinssphären für zwei reine Ich) von identischer Wesensgehalt undenkbar sind, … daß kein vollbestimmtes Erlebnis des einen je zum anderen gehören könnte; nur Erlebnisse von identischer innerer Artung können ihnen gemein sein (obwohl nicht individuell identisch gemeinsam) nie aber zwei individuell bestimmte Erlebnisse, die zudem einen absolut gleichen ‘‘Hof’’ haben.’

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Hence, one could conclude that even the reﬂection on past experiences of consciousness and, therefore the similarity recollection between a present experience of consciousness and a past one is possible only because they belong to the same stream of consciousness. Thus, Carnap’s artiﬁcial attempt to free the experiences of consciousness from a conscience is completely misguided. In fact, Carnap very clearly acknowledges on p. 93 of Aufbau the role of the stream of consciousness as a continuous medium in which are immersed the experiences of consciousness, and that is already enough to accept that experiences of consciousness do not ﬂoat in the air but are bounded to a particular stream of consciousness. When the elementary experiences of consciousness are chosen as basic elements, it is not also supposed that the stream of consciousness is composed of determined discrete experiences of consciousness. Rather it will only be presupposed that statements can be made about certain positions in the stream of consciousness of a kind like that such a position is in a determined relation with another determined [position], etc.; but it will not be asserted that the stream of consciousness could be uniquely divided in such positions. [Der logische Aufbau der Welt, p. 93]63

A passage from p. 138 of Aufbau not only offers additional material against Carnap’s ad hoc attempt to render the experiences of consciousness subject free, but it is so Husserlian that Husserl would have subscribed it entirely. Thus, Carnap says:64 The “given” never lies in the conscience as mere, unprocessed material, but always in more or less complicated connections and formations. The synthesis of knowledge, the processing of the given to [form] structurations, to representations of things, of “reality”, occurs mostly without intention, not according to conscious procedures. [Der logische Aufbau der Welt, p. 138]

It is especially pertinent to quote the example given by Carnap to illustrate his point in the above passage. The example concerns Husserl’s fundamental thesis about perception, namely, that we can only really perceive sides of the objects of external experience, and we in some sense anticipate or add the unseen side. Thus, for example, we see the front side (or the back side) of a house, but consider having seen the whole house. Carnapian scholars have once more missed this point, and tried to see here the inﬂuence of Gestalt psychology. However, Husserl obtained 63 ‘Wenn die Elementarerlebnisse als Grundelemente gewählt werden, so wird damit nicht angenommen, der Erlebnisstrom sei aus bestimmten, diskreten Elemente zusammengesetzt. Vielmehr wird nur vorausgesetzt, daß über gewisse Stellen des Erlebnisstromes Aussagen gemacht werden können von der Art, daß eine solche Stelle zu einer bestimmten anderen in einer bestimmten Beziehung stehe und dergl; wird aber nicht etwa behauptet, der Erlebnisstrom könne eindeutig in solche Stellen zerlegt werden.’ 64 ‘Das ‘‘Gegebene’’ liegt im Bewußtsein niemals als bloßes, unverarbeitetes Material vor, sondern immer im mehr oder weniger verwickelten Bindungen und Gestaltungen. Die Erkenntnissynthese, die Verarbeitung des Gegebenen zu Gebilden, zu Vorstellungen der Dinge, der ‘‘Wirklichkeit’’, geschieht meist unabsichtlich, nicht nach bewußten Verfahren.’

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this fundamental result about our perception of external objects ﬁrst, and Gestalt psychologists, as well as Carnap, obtained it from Husserl. Thus, Carnap says:65 When intuiting a house it will be immediately and intuitively perceived as a corporeal object, its not perceived backside will be taken into account, its later existence after looking away will be considered, the determined well known house will be recognized in it, etc., mostly without there being carried out chains of inference in expressive thought. [Der logische Aufbau der Welt, p. 138]

Husserl would have completely subscribed that passage. On the ﬁrst issue mentioned by Carnap, namely, the intuition of external objects, I will quote only the following passage:66 To the perception of things belongs also, and that is an essential necessity, a certain inadequacy. A thing can in principle be given only from one side, and that means not only incompletely, not only imperfectly in no matter what sense…. A thing is necessarily given in mere “forms of appearance”, necessarily there is at the same time a nucleus of “actually presented”, comprehensively surrounded by a horizon of improper being given together and more or less vague indetermination…. In this manner, to be imperfect in inﬁnitum belongs to the unremovable essence of the correlation “thing” and “perception of thing”…. In principle always remains a horizon of determinable undetermination, no matter how much further we go in the experience, or how large the continuum of actual perceptions of the same thing we have perused. [Ideen I, p.100]

Thus, the thesis that intuitions of things in the physical world are always inadequate, in the sense of being incomplete, and, hence, that an adequate sense perception is impossible, though it functions as a sort of regulative idea in a Kantian sense, is a fundamental Husserlian thesis. Once more, Carnapian scholars have either ignored Carnap’s allegiance to such a Husserlian thesis, or, as mentioned above, have erroneously asserted that Carnap obtained it from Gestalt psychology. With respect to the attempt at ignoring Carnap’s allegiance to that fundamental Husserlian thesis, it should be mentioned that it was by no means casually mentioned by Carnap but clearly accepted by him, as other passages, for example, from pp. 163 and 170 of Aufbau clearly show. With respect to the attribution of the thesis to the inﬂuence 65 ‘Beim Anschauen eines Hauses wird dieses unmittelbar und intuitiv als körperlichen Gegenstand wahrgenommen, seine nicht wahrgenomenne Rückseite wird mitgedacht, seine Fortexistenz beim Wegblicken wird gedacht, es wird das bestimmte, bekannte Haus in ihm wieder erkannt usw., meist ohne daß dabei Sclußketten in ausdrücklichem Denken vollzogen werden.’ 66 ‘Zur Dingwahrnehmung gehört ferner, und auch das ist eine Wesensnotwendigkeit, eine gewisse Inadequatheit. Ein Ding kann prinzipiell nur ‘‘einseitig’’ gegeben sein, und das sagt nicht nur unvollständig, nicht nur unvollkommen in einem beliebigen Sinne…. Ein Ding ist notwendig in bloßen ‘‘Erscheinungsweisen’’ gegeben, notwendig ist dabei ein Kern von ‘‘wirklich Dargestelltem’’ auffassungsmäßig umgeben von einem Horizont uneigentlicher ‘‘Mitgegebenheit’’ und mehr oder minder vager Unbestimmtheit…. In dieser Weise in inﬁnitum unvollkommen zu sein, gehört zum unaufhebbaren Wesen der Korrelation ‘‘Ding’’ und ‘‘Dingwahrnehmung’’…. Prinzipiell bleibt immer ein Horizont bestimmbarer Unbestimmtheit, wir mögen in der Erfahrung noch so weit fortschreiten, noch so große Kontinuum aktueller Wahrnehmungen von demselben Dinge durchlaufen haben.’

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of Gestalt psychology, it should be pointed out that (i) Husserl obtained it ﬁrst, (ii) Carnap was well acquainted with Husserl’s main publications up to that point, (iii) Carnap was taking part in Husserl’s seminars while writing Aufbau, and (iv) Gestalt psychologists were most surely also inﬂuenced by Husserl on this point. Finally, it should be stressed that in Aufbau Carnap follows Husserl in considering phenomenology as a fundamental science. He even goes so far as expressing that his constitutional system presupposes in some sense the results from phenomenology. Thus, on pp. 119–20, Carnap states:67 In case that the real sciences (and indeed for the lower constitutional levels especially the phenomenology of perception and psychology) arrive at the result that the relations between the objects are different as they are here presupposed, then these other relations have to be expressed, on the basis of the same methodological principles, in the corresponding constitutional forms. [Der Logische Aufbau der Welt, pp. 119–20]

A similar passage occurs on p. 148 of Aufbau. Thus, Carnap says:68 The content [of the exhibited constitutional system] is dependent on the contentual results of the real sciences, and indeed for the lower levels especially [those] of the phenomenology of perception and psychology. [Der logische Aufbau der Welt, p. 148]

It is of special importance to understand Carnap’s objectives in Aufbau to take into account two very similar passages on pp. 139 and 141 on the nature of the constitutional system. Since the passages are very similar, I quote just the ﬁrst one. Carnap states on p. 139:69 The constitutional system is a rational reconstruction of the whole structuring of reality carried out in knowledge predominantly in an intuitive way. [Der logische Aufbau der Welt, p.139]

Hence, combining the last quotes, one can very well conclude that the most basic part of the task of the constitutional system shall be the rational reconstruction of what has been already obtained in a more intuitive way in phenomenology. It should by now be no surprise why Carnap leans so much on Husserl’s results. What is by no means completely clear is why he does not explicitly acknowledge the great extent of Husserl’s inﬂuence but, on the contrary, tries to mask it. However, the extent of Husserl’s inﬂuence is much greater than has been shown up to this point. That was just the tip of the iceberg. 67 ‘Falls die Realwissenschaften (und zwar für die unteren Konstitutionsstufe vor allem die Wahrhehmungsphänomenologie und die Psychologie) zu dem Ergebnis kommen, daß die Verhältnisse der Gegenstände andere sind, als hier angenommen wird, so werden diese anderen Verhältnisse nach denselben methodischen Grundsätzen in den entsprechenden Konstitutionsstufen auszudrücken sein.’ 68 ‘Der Inhalt [des dargestellten Konstitutionssystems] ist von den inhaltlichen Ergebnissen der Realwissenschaften, und zwar für die unteren Stufen insbesondere der Phänomenologie der Wahrnehmung und der Psychologie abhängig.’ 69 ‘Das Konstitutionssystem ist eine rationale Nachkonstruktion des gesamten in der Erkenntnis vorwiegend intuitiv vollzogenen Aufbaus der Wirklichkeit.’

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5 A Permutation of Terminology Relatively early in Aufbau Carnap is concerned with the establishment of a fundamental distinction between two very different sorts of relations connected with the notion of a sign. A sign, for example, a word, can refer to an object – following Frege, Carnap uses the verb bedeuten in this special sense. On the other hand, gestures and movements of the body of a person can serve as signs of psychic processes of that person. Moreover, words also can serve to ‘express’ such psychic processes. Thus, in communication the two different functions of signs occur together, though the difference between the two relations by no means disappears. It is convenient for the following discussion to quote Carnap extensively on this point. We are capable of recognizing, from the voice, facial expressions and other movements of a human being, what happens in him, hence, from physical processes [we] arrive at a conclusion about [the] psychical. The relation taken here as basis between a movement etc. and the psychic processes, of which it is “expression”, we call [the] relation of expression. To its domain belong almost all movements of the body and its members, especially the involuntary. [Der logische Aufbau der Welt, p. 24]70 The relation of expression must surely be distinguished from the relation of [being a] sign. This [relation] exists between those physical objects that “refer” and what they refer to, for example, between the written sign “Rome” and the city “Rome”. Since all objects, in case they are objects of conceptual knowledge, are designated or in principle can be designated, thus, to the counterdomain of the relation of [being a] sign belong the objects of all sorts of objects. [Der logische Aufbau der Welt, p. 24]71 In some cases the same physical object is in an expression relation and in a relation of [being a] sign with the psychical. At the same time the relations can and must be most surely maintained separately. Spoken words are, for example, in each case expression of something psychical, no matter with what are they contentually concerned; since by means of the sound of the voice, the tempo, rhythm etc., but also by means of the choice of the single words and the style, they reveal something about the momentary psychical state of the speaker. But the words also have a reference; the difference [between] their expressive content and their referential content is especially easy to recognize if the reference concerns something other than psychic processes in the speaker. [Der logische Aufbau der Welt, pp. 24–5]72 70 ‘Wir vermögen aus Stimme, Mienen und anderen Bewegungen eines Menschen zu erkennen was ‘‘in ihm vorgeht’’, also aus physischen Vorgängen einen Schluß auf Psychisches zu ziehen. Die hier zugrundeliegende Beziehung zwischen einer Bewegung usw. und dem psychischen Vorgang, dessen ‘‘Ausdruck’’ sie ist, nennen wir ‘‘Ausdrucksbeziehung’’. Zu ihrem Vorbereich gehören fast alle Bewegungen des Leibes und seiner Glieder, besonders auch die unwillkürlichen.’ 71 ‘Die Ausdrucksbeziehung muß wohl unterschieden werden von der Zeichenbeziehung. Diese besteht zwischen denjenigen physischen Gegenständen, die etwas ‘‘bedeuten’’ und dem was sie bedeuten, z.B. zwischen dem Schriftzeichen ‘‘Rom’’ und der Stadt ‘‘Rom’’. Da alle Gegenstände, sofern sie Gegenstände begrifﬂicher Erkenntnis sind, irgendwie bezeichnet sind oder doch grundzätzlich bezeichnet werden können, so gehören zum Nachbereich der Zeichenbeziehung die Gegenstände aller Gegenstandsarten.’ 72 ‘In manchen Fällen steht derselbe physische Gegenstand zugleich in einer Ausdrucksbeziehung und in einer Zeichenbeziehung zu Psychischem. Dabei können und

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A few points need to be stressed here, which will be important for the discussion in the remaining part of this chapter and the next. Firstly, it should be mentioned that already at this early stage of his exposition, on pp. 26–7, Carnap stresses the importance of what he has called the ‘expression relation’ for the problem of intersubjectivity. On this issue, I will say much more below. A second point that I would like to stress is that Carnap adheres to the Frege-Husserl distinction between sense and reference. This is especially important, since if we adhere to that theory, Carnap’s sign relation is really a three-termed relation. The following passage not only makes perfectly clear Carnap’s commitment to that distinction, but also, due to its use of the word ‘Bedeutung’ in Frege’s sense, shows Fregean inﬂuence, whereas the usage of the Husserlian technical expression ‘intentional objects’ attests to an inﬂuence of Husserl. It is also pertinent to state that he uses the verb ‘ausdrücken’ in this context – as Husserl – for the relation of having a sense. Carnap says:73 From the signs themselves we distinguish, on the one hand, the “sense” that it expresses, on the other hand, the “referent”, that it refers to….by the sign itself we understand the written (or spoken etc.) ﬁgure; 7, vii, 5+2 are different, as signs; hence … “7”, “vii”, “5+2” are different objects. By the sense of a sign we understand what is common in the intentional objects of those representations, thoughts etc., which is the objective of the sign to awaken; 7 and vii have the same sense; hence, <7> is the same as , but <5+2> is something different. Similarly is <der Abendstern> the same as , is something different…. By the referent of a sign we understand the object that it refers to; 7, vii and 5+2 have the same referent, namely, the number seven; [7], [vii] and [5+2] are the same, moreover, [the evening star] and [the morning star] are identical…. [Der logische Aufbau der Welt, pp. 60–61]

More is to be said later on Carnap’s adoption of the sense-reference distinction. Another related point that needs stressing for further purposes is that in the passage of p. 24 quoted above, in which he characterizes the sign relation, he uses the verbs ‘bedeuten’ and ‘bezeichnen’ – that is: to designate – as synonyms. müssen die Beziehungen aber sehr wohl auseinander gehalten werden. Gesprochene Worte sind z. B. in jedem Fall Ausdruck für etwas Psychisches, mögen sie inhaltlich betrefffen, was sie wollen; denn durch Klang der Stimme,Tempo, Rhythmus usw., aber auch durch Wahl der einzelnen Worte und des Stils verraten sie etwas von dem augenblicklichen psychischen Zustand des Sprechenden. Außerdem aber haben die Worte eine Bedeutung; der Unterschied ihres Ausdruckgehaltes und ihres Bedeutungsgehaltes ist besonders dann leicht zu erkennen wenn die Bedeutung Anderes betrifft als psychische Vorgänge des Sprechenden.’ 73 ‘Von dem Zeichen selbst unterscheiden wir einerseits den ‘‘Sinn’’, den es ‘‘ausdrückt’’, andererseits die ‘‘Bedeutung’’, die es bedeutet….unter dem Zeichen selbst verstehen wir die schriftliche (oder sprachliche usw. ) Figur; 7, vii, 5+2 sind verschieden, was die Zeichen selbst anbetrifft; also … “7’’, ‘‘vii’’, ‘‘5+2’’ sind verschiedene Gegenstände. Unter dem Sinn eines Zeichens verstehen wir das Übereinstimmende an den intentionalen Gegenständen derjenigen Vorstellungen, Gedanken oder dgl., die hervorzurufen der Zweck des Zeichens ist; 7 und vii haben denselben Sinn: also <7> ist dasselbe wie , aber <5+2> ist etwas anderes. Ebenso ist <der Abendstern> dasselbe wie , <der Morgenstern> ist etwas anderes…. Unter der Bedeutung eines Zeichens verstehen wir den Gegenstand, den es bedeutet; 7, vii und 5+2 haben dieselbe Bedeutung, nämlich die Zahl Sieben; [7], [vii] und [5+2] sind dasselbe, ferner sind [der Abendstern] und [der Morgenstern] identisch….’

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Let us return, however, to the issue that I want to discuss in this section. The distinction mentioned above between what Carnap called the ‘expression relation’ and the (three-termed) sign relation has also a counterpart in Husserl’s writings. This time, however, the similarities are not with either of the ﬁrst two volumes of Ideen, but with the First Logical Investigation of Husserl’s opus magnum, Logische Untersuchungen – a book included in the bibliography of both Der Raum and Aufbau. Of course, there is no explicit reference in the above passages or in any part of Aufbau to Husserl’s Logische Untersuchungen. The ensuing quotations – in which the word Bedeutung is translated, as is usual in non-Fregean English, as ‘meaning’ – make it clear that Carnap should have referred to that book. Every sign is sign of something, but not every sign has a “meaning”, a “sense”, that is expressed with the sign…. Namely, signs in the sense of marks … express nothing, except in case that they, besides the indicative function, fulﬁll a meaning function. [Logische Untersuchungen II, U. I, p. 23]74 In the proper sense something is called a mark solely when and where it serves a thinking creature as indication for something whatever…. Now, in them we ﬁnd as this common the circumstance that some objects or states of affairs, about whose existence someone has actual knowledge, indicate to him the existence of other objects or states of affairs in the sense that the conviction about the being of the ﬁrst is experienced by him as motivation (and certainly not as an evident motivation) for the conviction or suspicion about the being of the others. [Logische Untersuchungen II, U. I, pp. 24–5]75 We distinguish from the indicative signs the meaningful, the expressions…. For the provisional understanding we stipulate that every discourse or part of a discourse, as well as any essentially similar sign is an expression, in which case it shall not depend on whether the discourse is actually spoken, thus, directed with communicative purpose at some person, or not. On the contrary, we exclude the play of facial expressions and gestures, with which we involuntarily and in any case without communicative purpose accompany our discourse, or in which also without a collaborating discourse, the state of the soul of a person obtains an “expression” understandable for the surroundings. Such externalizations are not expressions in the sense of discourse…. Brieﬂy, such expressions have properly no meaning. Nothing changes in it by the fact that a second [person] is capable of interpreting our involuntary externalizations (for example, the “expressive movements”), and that she experiences by such means something about our thoughts and emotions. [Logische Untersuchungen II, U. I, pp. 30–31]76 74 ‘Jedes Zeichen ist Zeichen von etwas, aber nicht jedes Zeichen hat eine ‘‘Bedeutung’’, einen ‘‘Sinn’’, der mit dem Zeichen ausgedrückt ist…. Nämlich Zeichen im Sinne von Anzeichen … drücken nichts aus, es sei denn, daß sie neben der Funktion des Anzeigens noch eine Bedeutungsfunktion erfüllen.’ 75 ‘Im eigentlichen Sinn ist etwas nur Anzeichen zu nennen, wenn es und wo es einem denkenden Wesen tatsächlich als Anzeige für irgendetwas dienen…. In ihnen ﬁnden wir nun als dieses Gemeinsame den Umstand, daß irgendwelche Gegenstände oder Sachverhalte, von deren Bestand jemand aktuelle Kenntnis hat, ihm den Bestand gewisser anderer Gegenstände oder Sachverhalte in dem Sinne anzeigen, daß die Überzeugung von dem Sein der einen von ihm als Motiv (und zwar als nicht einsichtiges Motiv) erlebt wird für die Überzeugung oder Vermutung vom Sein der anderen.’ 76 ‘Von den anzeigenden Zeichen unterscheiden wir die bedeutsamen, die Ausdrücke…. Zur vorläuﬁgen Verständigung setzen wir fest, daß jede Rede und jeder Redeteil, sowie jedes

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Thus, Husserl – as well as Carnap – distinguishes between the meaning relation of some signs that express a Bedeutung in Husserl’s usage (and by these means could refer to a Bedutung in Frege’s usage) and the indication relation, which Carnap opted to call instead ‘expression relation’. With respect to what Carnap called the ‘sign relation’ the difference is only of emphasis, since though in the passage on p. 24 of Aufbau quoted above the sense is omitted, in view of Carnap’s adherence on p. 60 – also quoted – to the sense-reference distinction, to have a Bedeutung in Frege’s usage, a sign needs to have a sense, that is, a Bedeutung in Husserl’s usage. With respect to the other relation, the difference is only a terminological one, namely, contrary to Husserl, Carnap uses the terminology ‘expression relation’ for that indicating or manifesting relation distinguished by Husserl, but the characterization of their meaning is essentially the same. Moreover, as will be clear from the following passages, the situation in which both relations are present and the distinction therein are essentially the same. In particular, the following passage should be compared with the passage on pp. 24–5 of Aufbau quoted above. If one examines this connection, one recognizes immediately that all expressions in communicative discourse play the role of marks. They serve the hearer as signs for the “thoughts” of the speaker, i.e. for his psychic experiences of consciousness that confer sense, which belong to the communicative intention. This function of linguistic expressions we call the manifestation function. The psychic experiences of consciousness that manifest form the content of the manifestation. We can take the sense of the predicate manifested in a broad or a narrow sense. We restrict the narrow [sense] to the acts of conferring sense, whereas the broader can include all acts of the speaker that are attributed to him by the hearer on the basis of his discourse (and eventually by the fact that it [the discourse] says [something] about them…. We immediately observe that the usual mode of expression permits to designate the manifested experiences of consciousness as [being] expressed. [Logische Untersuchungen II, U. I., pp. 33–4]77 wesentlich gleichartige Zeichen ein Ausdruck sei, wobei es darauf nicht ankommen soll, ob die Rede wirklich geredet, also in kommunikativer Absicht an irgendwelche Person gerichtet ist oder nicht. Dagegen schließen wir das Mienenspiel und die Geste aus, mit denen wir unser Reden unwillkürlich und jedenfalls nicht in mitteilender Absicht begleiten, oder in denen auch ohne mitwirkende Rede, der Seelenzustand einer Person für ihre Umgebung verständlichen ‘‘Ausdrücke’’ kommt. Solche Äußerungen sind keine Ausdrücke im Sinn der Reden…. Kurz, derartige Ausdrücke haben eigentlich keine Bedeutung. Daran wird nichts geändert dadurch, daß ein zweiter unsere unwillkürlichen Äußerungen (z. B. die ‘‘Ausdrucksbewegungen’’) zu deuten, und daß er durch sie über unsere inneren Gedanken und Gemütsbewegungen mancherlei zu erfahren vermag.’ 77 ‘Wenn man diesen Zusammenhang durchschaut, erkennt man sofort, daß alle Ausdrücke in der kommunikativen Rede als Anzeichen fungieren. Sie dienen dem Hörenden als Zeichen für die ‘‘Gedanken’’ des Redners, d. h. für die sinngebenden psychischen Erlebnisse desselben, sowie für die sonstigen psychischen Erlebnisse, welche zur mitteilenden Intention gehören. Diese Funktion der sprachlichen Ausdrücke nennen wir die kundgebende Funktion. Den Inhalt der Kundgabe bilden die kundgegebenen psychischen Erlebnisse. Den Sinn des Prädikates kundgegeben können wir in einem engeren oder weiteren Sinne fassen. Den engeren beschränken wir auf die sinngebenden Akte, während der weitere alle Akte des Sprechenden befassen mag, die ihm auf Grund seiner Rede (und eventuell dadurch, daß sie von ihnen aussagt) von dem Hörenden eingelegt werden…. Wir merken gleich an, daß es die

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But also in the life of the soul not relating communicatively, an important role is assigned to the expressions. It is clear that the changed function does not affect what makes an expression an expression. [Logische Untersuchungen II, U. I, p. 35]78 From this it seems clear that the meaning of the expression and anything else that also belongs essentially to it cannot coincide with the manifesting performance. [Logische Untersuchungen II, U. I, pp. 35–6]79 In the monologue the words certainly cannot serve us in the function of marks for the existence of psychical acts, because such indications would be completely without purpose. [Logische Untersuchungen II, U. I, pp. 36–7]80

Hence, it should be clear by now that also with respect to the characterization and distinction between the sign as indicator or mark of something, more speciﬁcally, between the relation of pointing to the psychic activities of the speaker in communicative discourse, and the relation of conveying a meaning to a sign and through it referring to an object, Carnap’s Aufbau has a decisive Husserlian inﬂuence. Indeed, as the above quoted passages show, Carnap’s treatment of those issues in Aufbau amounts essentially to a permutation of Husserl’s terminology. Once more, he should have acknowledged Husserl’s inﬂuence. But he did not. In the next section I will consider some minor points, which nonetheless will serve to round up Carnap’s procedure in Aufbau. In particular, I will be concerned with the famous sense–reference distinction, to which Carnap pledged allegiance in the passage quoted from pp. 60–61. 6 An Unsuspected Ambivalence As we saw in the preceding section, in the quoted passage of pp. 60–61 of Aufbau, Carnap pledged his allegiance to the sense-reference distinction. On p. 61, he makes it apparently clear that his allegiance is to the Fregean version of that distinction, which has two distinctive features, namely, that the referent of an assertive sentence (or statement) is a truth-value and that the referent of what Frege calls a ‘conceptual

gewöhnliche Sprechweise erlaubt, die kundgegebenen Erlebnisse auch als ausgedrückte zu bezeichnen.’ 78 ‘Aber auch in dem sich im Verkehr nicht mitteilenden Seelenleben ist den Ausdrücken eine große Rolle beschieden. Es ist klar, daß die veränderte Funktion nicht das trifft, was die Ausdrücke zu Ausdrücken macht.’ 79 ‘Hiernach scheint es klar, daß die Bedeutung des Ausdruckes und was ihm sonst noch wesentlich zugehört, nicht mit seiner kundgebenden Leistung zusammenfallen kann.’ 80 ‘In der monologischen Rede können uns die Worte doch nicht in der Funktion von Anzeichen für das Dasein psychischer Akte dienen, da solche Anzeige hier ganz zwecklos wäre.’

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word’ is not the extension of the concept but the concept itself.81 Thus, Carnap states on p. 61 of Aufbau:82 The sense of a statement is the thought expressed by it; the referent of the statement is the truth-value that it has, either the True or the False. [Der logische Aufbau der Welt, p. 61]

Thus, contrary to Husserl, who considered that the referents of statements were states of affairs, Carnap most explicitly pledges allegiance to Frege’s version of the sensereference distinction by stating that the referents of statements are truth-values. Indeed, on pp. 65–6 Carnap attempts to identify states of affairs with thoughts, when he declares that they are expressed by sentences or propositional functions. Carnap states:83 … the individual states of affairs are to be expressed by sentences, the general states of affairs by propositional functions. [Der logische Aufbau der Welt, pp. 65–6]

However, Carnap is not completely faithful to Frege’s version of the sense-reference distinction, and once in a while seems to side with Husserl. Thus, not only did he use the distinctive Husserlian terminology of ‘intentional object’ in the passage of pp. 60–61 quoted above, but on pp. 190 and 191 of Aufbau there are some passages in which Carnap forgets the Fregean version of the sense-reference distinction and explicitly states that states of affairs are designated by statements in a similar manner to that in which a word designates an object. The following passage is especially revealing. A fruitful form results from the circumstance that the words form statements and that the statements designate states of affairs. A conferment of a sign, that forms a whole statement, thus, that designates a state of affairs, we call an “assertion”. The relation of assertion (between an assertion and its state of affairs) is to be constituted together with the relation of conferring a sign (between a word and the designated object), since both constitutions relate to each other and support each other. [Der logische Aufbau der Welt, p. 190]84

81 For Husserl, the referent of what Frege called ‘conceptual word’ is the extension of the concept, whereas the concept is its sense. On the other hand, for Husserl the referent of an assertive statement is a state of affairs, which has a sort of referential basis called by Husserl a ‘situation of affairs’. Hence, the path from a statement to its truth value has in Husserl two more steps than in Frege, whereas the path from a conceptal word – or universal name, in Husserl’s terminology – to the extension is in Husserl one step shorter than in Frege. 82 ‘Der Sinn eines Satzes ist der von ihm ausgedrückte Gedanke; die Bedeutung eines Satzes ist der Wahrheitswert, den er hat, entweder das Wahre oder das Falsche.’ 83 ‘… die individuellen Sachverhalte sind durch Aussagen, die generelllen Sachverhalte durch Aussagefunktionen auszudrücken.’ 84 ‘Eine fruchtbare Form ergibt sich aus dem Umstand, daß die Worte Sätze bilden und die Sätze Sachverhalte bezeichnen. Eine Zeichengebung, die einen ganzen Satz bildet, also einen Sachverhalt bezeichnet, nennen wir eine ‘‘Angabe’’. Die Angabebeziehung (zwischen einer Angabe und ihrem Sachverhalt) ist zusammen mit der Zeichengebungsbeziehung (zwischem einem Wort und dem bezeichneten Gegenstand) zu konstituieren, da die beiden Konstitutionen aufeinander Bezug nehmen und sich gegenseitig unterstützen.’

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Carnap’s commentaries immediately following in Aufbau the above quoted passage leave no doubt about Carnap’s unofﬁcial contention that assertive sentences refer to states of affairs. Indeed, in a concrete example, he speaks of a state of affairs as being a relation between two objects. Moreover, such assertions are clearly incompatible with the passage quoted above from pp. 65–6, according to which states of affairs are ‘expressed’ by sentences and propositional functions, where ‘to express’ is clearly meant in Husserl’s usage, namely, as expressing a sense. Therefore, though Carnap ofﬁcially adheres to the Fregean version of the sense-reference distinction, the ghost of Husserl’s version plays him a trick. We will see in Chapter Four that it continued to play tricks on Carnap two decades later. Moreover, Carnap’s ambivalence between Frege’s and Husserl’s theories of sense and reference played him some additional tricks in Aufbau that deserve being mentioned. The most glaring example of Carnap’s ambivalence concerns not the referent of statements, but the theory of compositionality of both sense and referent propounded by Frege in ‘Über Sinn und Bedeutung’.85 According to Frege, the sense of a statement is completely determined by the senses of its constituent parts, and the referent of a statement is completely determined by the referents of its constituent parts. Moreover, a statement can very well have a sense without having a referent. This occurs when one of its constituent parts lacks a referent. Carnap, however, states on p. 16 of Aufbau the following: ‘A scientiﬁc statement has a sense only when the referent [Bedeutung] of the occurring names of objects can be given.’86 If we render Bedeutung as we have done in the translation, that is, in Frege’s unusual use of that word, Carnap’s assertion is clearly incompatible with Frege’s views on compositionality. However, if we use the word Bedeutung as Husserl did – and as is usual in German – that is, as a partial synonym of the word ‘Sinn’, that is, sense, Carnap’s assertion turns out to be not only perfectly compatible with Frege’s views on compositionality, but even a somewhat careless formulation of the principle of compositionality for senses. Of course, this last rendering of the word Bedeutung is inconsistent with Frege’s usage. Hence, on the basis of Frege’s theory of compositionality of sense and his usage of the word Bedeutung, Carnap’s assertion is not only false, but even has a ﬂair of paradoxicality. It is compatible with Frege’s views on compositionality if and only if it is incompatible with Frege’s usage of the word Bedeutung and is rendered according to Husserl’s usage. Nonetheless, Carnap’s confusions about sense and reference are still more astonishing, and it is incredible that Carnapian scholars have ignored them. First of all, we have seen in the last quote that Carnap uses the German word Aussage in its usual meaning of ‘statement’. We have also seen in other passages from Aufbau that he uses the German verb bezeichnen in its usual meaning of ‘to designate’. There is, however, a passage on p. 25 of Aufbau that deﬁes any interpretation. Thus, Carnap says: 85 For Frege’s compositionality thesis, see Kleine Schriften, edited by Ignacio Angelleli (Hildesheim, Georg Olms 1967, revised edition 1990), pp. 148–51. 86 The German text reads: ‘Eine wissenschaftliche Aussage hat nur dann einen Sinn, wenn die Bedeutung der vorkommenden Gegenstandsnamen angegeben werden kann.’ [Der logische Aufbau der Welt, p. 16]

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The Young Carnap’s Unknown Master We can divide the (linguistic) signs accordingly [to the criterion of] whether they have an independent referent [Bedeutung] only in combination with other signs or standing alone. In the strictest sense only those signs (for the most part compound) have an independent referent that designate a statement, thus, sentences. [Der logische Aufbau der Welt, p. 25]87

Thus, according to that ignored passage of Aufbau, sentences designate, or refer to, statements. On the basis of Frege’s views, only when we quote the words of someone else do we refer to his statements. But to say that in the normal usage of language sentences refer to statements is a sign of grotesque elementary confusions. In this case, there is no Husserlian cure for such a patient. For Husserl, statements [Aussagen] refer to states of affairs. In fact, I have been charitable by translating the word Satz as ‘sentence’ and not as ‘proposition’. For Husserl, the sense of a statement [Aussage] is a proposition [Satz], that is, he uses the word Satz as a synonym of Gedanke, that is, thought. That usage is perfectly compatible with the usage of the word Satz in mathematical contexts, meaning ‘proposition’ or ‘theorem’. On the basis of such a general usage, which should have been familiar to Carnap, one would have to render Carnap’s last statement as saying that a proposition designates (or refers to) a statement. Such preposterous assertion deﬁes any interpretation, no matter how generous it could be, and simply does not deserve any additional commentary. It should ﬁnally be pointed out that there are many other passages in Aufbau, in which Carnap’s usage of the words Bedeutung and bedeuten should be rendered in Husserl’s, not in Frege’s usage. However, the above quotations are enough as examples of Carnap’s lack of clarity. Indeed, the quotations in this section will probably take by surprise analytic philosophers accustomed to see in Carnap at least the paradigm of expository clarity. However, those quotations seem to point to his conﬂict in the late twenties between a Husserlian inﬂuence he was so eager to hide from his new partners, especially, Schlick and Neurath, and his desire to adopt Frege’s semantic views. What resulted was a semantic monster. 7 On the Constitutional System and Phenomenology As we already observed above, Carnap acknowledges that the basis of his constitutional system is not independent from phenomenology. Interestingly enough, he explicitly acknowledges on pp. 200–204 that the top of the constitutional building, namely, the constitution of the cultural or spiritual objects, is also dependent on phenomenology. Thus, it is pertinent to quote some passages here. The constitution of the spiritual objects on the basis of their manifestations is in a certain analogy with the constitution of the physical things on the basis of the experiences of consciousness, in which they are perceived. That these constitutions cannot be given here in detail has its roots [in the fact] that the psychology (or phenomenology) of cultural 87 ‘Wir können die (Sprach) Zeichen danach einteilen, ob sie nur in Verbindung mit anderen Zeichen oder auch schon für sich allein eine selbständige Bedeutung haben. Im strengsten Sinne haben nur diejenigen (meist zusammengesetzten) Zeichen, die eine Aussage bezeichnen, also die Sätze, eine selbständige Bedeutung.’

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knowledge has not been investigated and systematically expounded as much as that of perceptions. [Der logische Aufbau der Welt, pp. 200–201]88 Which objects of the different cultural regions are to be constituted as primary spiritual objects should be researched by a logic of the cultural sciences; and a phenomenology of the cultural sciences should then establish for the singular primary cultural object on the basis of which physical objects as its manifestations and in which manner is it to be constituted. [Der logische Aufbau der Welt, p. 201]89 In details the nature of the value experiences of consciousness of the diverse kinds of values is studied by the phenomenology of values…. The characteristic properties of the diverse value experiences of consciousness can be constitutionally expressed, once the phenomenological analysis is carried out, with the help of the already constituted qualities of the autopsychological and their components, in particular those of sentiments and desires. By this means it is then possible to exhibit the constitutions of the diverse kinds of values on the basis of those constitutions. That does not mean any psychologization of values, so little as the constitution of the physical objects on the basis of sensory qualities means more or less a psychologization of the physical. [Der logische Aufbau der Welt, pp. 203–4]90

Incidentally, the last sentence of the above quotation makes it clear that Carnap in Aufbau did not conceive of Husserl’s phenomenology and phenomenological foundation of science – as some analytic philosophers ignorant of Husserl’s views have done – as a return to psychologism. There are many other remarks scattered through the whole book that could be interpreted as referring either directly or indirectly to Husserl and phenomenology. Some of the comments seem to amount to a criticism of Husserl’s views, others, however, seem to weaken such criticisms. Some especially interesting examples of this ambivalence build Carnap’s commentaries on the so-called ‘problem of essence’

88 ‘Die Konstitution der geistigen Gegenstände auf Grund ihrer Manifestationen steht in einer gewissen Analogie zur Konstitution der physischen Dinge auf Grund der Erlebnisse, in denen sie wahrgenommen werden. Daß diese Konstitutionen hier nicht ausführlich angegeben werden können, liegt daran, daß die Psychologie (oder Phänomenologie) der Kulturerkenntnis noch nicht in dem Maß durchforscht und systhematisch dargestellt ist wie die der Wahrhehmungen.’ 89 ‘Welche Gegenstände der verschiedenen Kulturgebiete als primäre geistige Gegenstände zu konstituieren sind, müßte von einer Logik der Geisteswissenschaften untersucht werden; und eine Phänomenologie der Geisteswissenschaften müßte dann für den einzelnen primären geistigen Gegenstand feststellen, auf Grund welcher physischen Gegenstände als seiner Manifestationen und in welcher Art er zu konstituieren ist.’ 90 ‘Im einzelnen wird die Beschaffenheit der Werterlebnisse der verschiedenen Wertarten von der Wertphänomenologie untersucht…. Die charakteristischen Eigenschaften der verschiedenen Werterlebnisse lassen sich dann, wenn die phänomenologische Analyse durchgeführt ist, mit Hilfe der früher konstituierten Qualitäten des Eigenpsychischen und der Komponenten von solchen, insbesondere der der Gefühle und der Wollungen, konstitutional ausdrücken. Dadurch ist es dann möglich, die Konstitutionen der verschiedenen Wertarten auf Grund jener Konstitutionen aufzustellen, Das bedeutet keine Psychologisierung der Werte, so wenig wie die Konstitution der physischen Gegenstände aus Sinnesqualitäten etwa eine Psychologisierung des Physischen bedeutet.’

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[in German: Wesensproblem]. Thus, on pp. 25–6 Carnap refers to the problem of essence and to the problem of an essential relation as metaphysical problems. Later it will be shown that the problem of the essential relation, as well as the problem of the essence of a relation, can neither be solved in (rational) science, nor can it be in general formulated. It belongs to metaphysics. [Der logische Aufbau der Welt, p. 26]91

Nonetheless, much later in the book – pp. 221–2 – Carnap distinguishes between a constitutional and a metaphysical problem of essence, and the characterization of the metaphysical problem is such that it is at least very questionable that it is directed against Husserl, though it probably applied to some phenomenologists more inclined to a sort of realism, like Max Scheler. The question about the constitutional essence of an object wants to know how it ﬁnds itself in the constitutional connection of the system, particularly, how it is obtained from the basic objects. On the contrary, the question about the metaphysical essence wants to know what the object concerned is in itself. That it presupposes that the object is given not only as a determined constitutional form, but also as “object in itself”, precisely characterizes the question as belonging to metaphysics. [Der logische Aufbau der Welt, pp. 221–2]92

Immediately after making that distinction, Carnap goes on – on p. 222 – to try to dissolve the constitutional essence in the notion of reference by attempting to reduce statements concerned with the constitutional essence of an object to statements that are true or false in virtue of what happens with the most basic states of affairs. The indication of the essence of an object, or what is the same, the indication of the referent of a sign, consists therefore in the indication of criteria of the truth of those statements in which the sign of that object can occur…. Thus the criterion consists … in a reduction of all statements about the object, about whose constitutional essence is asked, to such statements, that admit being shown to be true or false by means of the most basic states of affairs. [Der logische Aufbau der Welt, p. 222]93

91 ‘Später wird sich zeigen, daß das Problem der Wesensbeziehung ebenso wie das Wesensproblem einer Beziehung innerhalb der (rationalen) Wissenschaft weder gelöst, noch überhaupt gestellt werden kann. Es gehört zur Metaphysik.’ 92 ‘Die Frage nach dem konstitutionalen Wesen eines Gegenstandes will wissen, wie er im konstitutionalen Zusammenhang des Systems steht, insbesondere, wie er sich aus den Grundgegenständen herleitet. Die Frage nach dem metaphysichen Wesen will wissen, was der betreffende Gegenstand an sich sei. Daß sie voraussetzt, es gebe den Gegenstand nicht nur als bestimmte Konstitutionsform, sondern auch als ‘‘Gegenstand an sich’’, charakterisiert gerade diese Frage, als zur Metaphysik gehörig.’ 93 ‘Die Angabe des Wesens eines Gegenstandes, oder, was dasselbe ist, die Angabe der Bedeutung des Zeichens eines Gegenstandes, besteht deshalb in der Angabe von Kriterien der Wahrheit derjenigen Sätze, in denen das Zeichen dieses Gegenstandes auftreten kann…. so besteht also das Kriterium … in einer Zurückführung aller Sätze über den Gegenstand, nach dessen konstitutionalen Wesen gefragt wird, auf solche Sätze, die sich durch die UrSachverhalte als wahr oder falsch erweisen lassen.’

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I am not going to digress into a critique of Carnap’s contention, but have mentioned this passage just to stress Carnap’s struggle in Aufbau with the notion of essence. Incidentally, the reference to states of affairs and the contention that statements are true or false depending on what happens with some corresponding states of affairs can be seen as one more example of Carnap’s unofﬁcial use of Husserl’s version of the sense-reference distinction. Carnap has similar struggles with the Husserlian notions of “the I”, “intentionality” and “intentional object”. Thus, on p. 226, he characterizes the I as the class of the experiences of consciousness, not a mere sum of the experiences of consciousness. According to Carnap’s own constitutional system, the I is then an object of a higher level than the experiences of consciousness and, thus, clearly different from them. Husserl would in principle agree with such a contention. Immediately thereafter – on the same p. 226 – however, Carnap tries to minimize such a commitment to Husserl’s views by pointing out that the I can only be constituted much later in the system, namely, after the constitution of the other. That assertion is not even true for Carnap’s constitutional system. If the I is just the class of experiences of consciousness in the stream of consciousness, it can be constituted immediately in the ﬁrst step of nonbasic objects. On this point, Carnap seems to be confusing – not because he did not understand the difference, but probably to appease Schlick and Neurath – the I as the class of experiences of consciousness in the stream of consciousness with the embodied I as a person (human being). On pp. 226–8, Carnap makes similar ambivalent comments with respect to the notions of intentional object and intentionality. He does not reject such notions, but tries to show – see pp. 227–8 – that the intentional relation is deﬁnable in the theory of relations. The following passage is especially pertinent to understand Carnap’s attitude towards intentionality. But when someone says that it lies in the essence of an experience of consciousness to intentionally point towards something, even when not in the case of every experience of consciousness its intentional object becomes conscious, then that is valid in general from the standpoint of the constitutional theory: it is essential for every object that it belongs to certain ordering connections, since if not it could not in general be constituted, thus, could not exist as an object of knowledge. [Der logische Aufbau der Welt, p. 228]94

Thus, on the one hand, Carnap acknowledges the role of intentionality but, on the other hand, tries to dissolve its peculiarity by simply reinterpreting it as a special case of an ordering connection. I am not going to consider here more passages of Aufbau, in which Carnap struggles with Husserlian technical notions, trying to save their ‘essential’ features, by means of interpreting them in terms more palatable to his new friends in Vienna – Schlick and Neurath – while rejecting the ‘inessential’ overtones. There are also some Husserlian slips, like the use of the word ‘essential’ in the last passage quoted, 94 ‘Wenn man aber sagt, es liege im Wesen eines Erlebnisses auf irgend etwas intentional hinzuweisen, auch wenn nicht bei jedem Erlebnis sein intentionales Objekt bewußt werde, so gilt auch dies vom Gesichtspunkt der Konstitutionstheorie aus allgemein: es ist für jeden Gegenstand wesentlich, daß er gewissen Ordnungszusammenhängen angehört, sonst könnte er überhaupt nicht konstituiert sein, also nicht als Erkenntnisgegenstand bestehen.’

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or the use of the expression ‘extensive wholes’ [in German: extensive Ganzen] on pp. 48–9, while contrasting them with classes, in the same sense, in which Husserl had used it in the Third Logical Investigation,95 but I will refrain from considering them here. The relatively large number of quotations from Aufbau in this chapter – together with the quotations from three different writings of Husserl – are more than enough to prove my contention that the inﬂuence of Husserl on Carnap’s book is by far the most signiﬁcant philosophical inﬂuence. The discussion in the next chapter of the problem of intersubjectivity in Aufbau and in Husserl’s writings will also contribute to establish that Carnap’s book is without much doubt at least a neo-Husserlian book. What Carnap did in Aufbau – besides trying to cover the origin and inﬂuence of the book – is to build a constitutional system based on the groundwork of Husserl’s phenomenology and using the logical tools of the logic of Frege, Russell and Whitehead, especially, Russell’s theory of relations. Carnap wanted to show that the tools of the theory of relations could be especially fruitful to systematize Husserl’s constitutional theory, based on the experiences of consciousness. In some sense, Carnap saw himself as a continuator or disciple of the master, though he probably already suspected that the master would not necessarily agree with such a deviant reinterpretation of his constitutional system, in which intuitive insights were replaced by deﬁnitions. Still less would the master agree in seeing that a disciple had presented a constitutional system particularly similar to his, but with almost no explicit acknowledgement of its origin. Husserl had already had a similar experience with regard to some of his manuscripts on time, which presumably his former assistant Heidegger had used and reformulated for other purposes in Sein und Zeit.96 Thus, after all, Carnap and Heidegger had something more in common than having studied with neo-Kantian professors and having being Husserl’s postdoctoral students.97

95 See Logische Untersuchungen II, U. III, § 17, where Husserl introduces the notion of extensive whole and offers as examples of extensive wholes space and time, as does Carnap on p. 48 of Aufbau. 96 Sein und Zeit (1927, ninth edition, Tübingen, Max Niemeyer 1967). Husserl asked Heidegger to publish his investigations on inner time, which dated from 1905 on. Thus, part of the manuscripts was published the next year, edited by Heidegger, with the title Vorlesungen zur Phänomenologie des inneren Zeitbewußtseins (1928, Husserliana X, Den Haag, M. Nijhoff 1966). 97 Some would say that they also had in common being opponents of traditional metaphysics. Such a contention, however, does not deserve any consideration, since the antimetaphysician Carnap and the ultra-metaphysician Heidegger were opposed to traditional metaphysics on the basis of diametrically different reasons. In fact, such a contention is as void of any rationality as a contention that would see similarities in the opposition to liberalism from anarchists, on the one hand, and fascists, on the other hand. Incidentally, I have used informally in discussions the pair (Carnap, Heidegger) as a falsiﬁer of historical-materialist and sociological interpretations of the history of philosophy. Born in the same country, in the same social class, with two years difference, having both studied under neo-Kantian inﬂuence at the university, both somewhat interested in Frege’s writings during their formative years, and having being Husserl’s post-doctoral students in Freiburg, nonetheless, they developed philosophical views as far apart as there have been in the history of philosophy.

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8 On Carnapian Scholarship In view of the conclusions of the past section and the vast documentation on which they are based, a few words should be said about the assessment of Aufbau in the almost eighty years since its publication. Without any doubt, the prejudices so strongly held in the circles of analytic philosophy have played a decisive role. First of all, most analytic philosophers are perfectly ignorant with respect to Husserl’s philosophical views. Few of them, if any, have heard about Husserl’s views in his youth work Philosophie der Arithmetik and of Frege’s criticisms in his review of 1894, a review that, caricatures aside, came too late to have an inﬂuence on Husserl’s development. They are perfectly ignorant of Husserl’s superior criticism of psychologism in logic, of his philosophy of mathematics, his more reﬁned semantics of sense and reference, his theory of meaning categories, his theory of parts and wholes, his epistemology of mathematics, and many other themes of his opus magnum, Logische Untersuchungen. They know even less that Husserl maintained basically the same views on those issues after his ‘transcendental turn’ of 1907. Finally, they, of course, have no idea about Husserl’s transcendental phenomenology, and if at all try to assimilate it to Kantian or neo-Kantian views, though Husserl already in Logische Untersuchungen98 sharply criticized Kant’s views as a sort of relativism to the human species, thus, an anthropologism, and diverged from Kant and the neoKantians on many important philosophical issues. In some cases, instead of reading Husserl, analytic philosophers rely on questionable writings of Dagﬁnn Føllesdal, plagued by their same prejudices.99 Secondly, there is a related prejudice in analytic circles as far as Carnap and the so-called logical empiricists are concerned. According to such a prejudice, Carnap must have been an empiricist all his life. Thus, since he most clearly builds his constitutional system in Aufbau from an autopsychological basis, he was either following Russell’s empiricism or Mach’s also empiricist phenomenalism. Other interpretations would have broken the bridge that goes from the old empiricist tradition to their ‘culmination’ in Quine. Of course, this prejudice is a special case of the big and harmful prejudice of putting the valuable tools of logic, mathematics and linguistic analysis in philosophy at the almost exclusive service of empiricist and naturalist views. On the other hand, the recent trend to render Carnap’s early work as strongly inﬂuenced by Kant and the neo-Kantians – a trend parallel and equally wrong as that of trying to make Frege a Kantian or neo-Kantian – is clearly an understandable reaction both to the diverse empiricist renderings of Carnap’s Aufbau and to the prevalent Quinean naturalism and radical empiricism, which taken up to its ﬁnal consequences made possible present post-modern scepticism and relativism. But

98 See Logische Untersuchungen I, Chapter VII. 99 Thus, for example, Føllesdal teaches analytic philosophers that Husserl’s notion of ‘noema’ in Ideen I is a generalization of Frege’s notion of sense, when it is, if at all, a generalization of his own notion of sense – that happened to coincide with Frege’s – and the generalization had already begun in the Fifth Logical Investigation with the distinction between the notions of matter and quality of the acts of conscience.

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Kantian interpreters of the young Carnap are as ignorant of Husserl’s views as are their rival empiricists. The fact that Carnap propounded a sort of synthetic a priori for the statements about intuitive space in Der Raum and built a constitutional system in Aufbau was for such scholars a clear indication of a sort of allegiance to Kant and neo-Kantianism. Both contentions of the Kantianisers of Carnap were clearly wrong, since, ﬁrstly, it was Husserl, not Kant, who inspired the synthetic a priori nature of statements about intuitive space in Der Raum, and, secondly, Carnap’s notions of constitution and constitutional system were taken from Husserl, and had nothing to do with Kant. The other usual ‘argument’ of those scholars is the circumstance that Carnap wrote his dissertation under the neo-Kantian Bruno Bauch and also visited courses of the neo-Kantian Heinrich Rickert in Freiburg. They forget that Carnap was not given the dissertation’s theme by Bauch, but selected it himself, and was by far more knowledgeable of the most recent developments in logic, mathematics and physics than any of the neo-Kantians, with the possible exception of Cassirer. The circumstantial ‘argument’ could have, in the best of cases, some plausibility in the case of lesser minds, which usually work on themes chosen by their professors and see themselves as mere continuators of their thesis director. In the phenomenological circles, the situation is not much better. Very few phenomenologists have the proﬁciency in analytic philosophy and the logicalmathematical tools to understand Carnap’s writings, and simply do not even bother trying to read his writings. In fact, one of the problems that has confronted the legacy of Husserl is that most phenomenologists are not even capable of fully understanding Husserl’s Logische Untersuchungen and, thus, are not in a position to appreciate either the important contributions made in that work or its relevance for analytic philosophy. The fact of the matter is that Husserl’s disciples and followers up to this date have been usually too far behind their master in philosophical capabilities both to completely and critically assess his importance for contemporary and future philosophy, and to make solid contributions of their own. Nonetheless, there are a few scholars that have already seen the importance of Husserl’s inﬂuence on Carnap. The by far most decisive contribution is that of Verena Mayer, who in two important pioneering papers on Husserl’s inﬂuence on Carnap’s Aufbau some ﬁfteen years ago, namely, ‘Die Konstruktion der Erfahrungswelt: Carnap und Husserl’ of 1991 and ‘Carnap und Husserl’ of 1992 has stressed many of the astonishing similarities between Carnap’s Aufbau and Husserl’s writings discussed in this chapter, and has also mentioned very brieﬂy the similarity between their respective constitutions of – what in Carnap’s terminology is– the heteropsychological.100 Those writings, however, have not received their due consideration by mainstream scholars. In any case, they should be seen without doubt as precursors of the present chapter and more remotely of the following one. 100 See her ‘Die Konstruktion der Erfahrungswelt: Carnap und Husserl’, in Wolfgang Spohn (ed.), Erkenntnis Orientated, Dordrecht, Kluwer 1991, pp. 287–303, and ‘Carnap und Husserl’, in David Bell and Wilhelm Vossenkuhl (eds), Wissenschaft und Subjektivität, Berlin, Akademie Verlag 1992, pp. 185–201. An even earlier precursor is Frederik Schipper’s book Intuitie en Constructie in de Filosoﬁe van Husserl en Carnap (Amsterdam: Rodopi 1980), a book written in Dutch and, as far as I know, still not translated either into English or German.

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Although I have been fully conscious of Husserl’s inﬂuence on Carnap’s Aufbau, as well as on an important Carnapian distinction in Logische Syntax der Sprache for almost forty years, due to the fact that Mayer’s writings anticipated this book by some ﬁfteen years, she deserves her due credit as a pioneer on this issue. Thus, though my treatment of Husserl’s inﬂuence on Carnap’s Aufbau in this chapter is much more detailed and daring than hers, it should be seen as a completion of her pioneering work on this somewhat delicate issue. However, the same cannot be said of the next chapter, since Mayer barely touches the problem, whereas my examination of Husserl’s and Carnap’s respective constitutions of the heteropsychological is immensely more thorough. Another especially important contribution is that of Sahotra Sarkar in a recent paper,101 in which he studies Husserl’s inﬂuence in Der Raum and arrived at very similar conclusions to those expounded in Chapter 1, and to which I had also independently arrived in a recently published extensive critical review of Der Raum in Spanish, on which Chapter 1 is based.102 At the end of that paper, Sarkar announced that he had plans to write a paper on Husserl’s inﬂuence on Aufbau. Thus, it is very possible that he has arrived at similar conclusions as Verena Mayer and the present author. Moreover, a recent book by Thomas Ryckman, namely, The Reign of Relativity,103 also mentions brieﬂy the similarities of Carnap’s Aufbau with Husserl’s writings, though its most important contribution to the trend of ﬁnally acknowledging Husserl’s inﬂuence on current philosophical discussions outside of ofﬁcial phenomenology is without doubt his treatment of Husserl’s inﬂuence on Hermann Weyl. In another recent paper, Jean-Michel Roy also has discussed the relation between Husserl and Carnap’s Aufbau, though I disagree with his analyses on most points.104 A careful reading of the present chapter can very well serve to counter many of Roy’s misunderstandings and contentions. It is unnecessary to emphasize that I feel much nearer to the investigations of Mayer and Sarkar on the relation between Husserl and Carnap than to those of Roy. The next chapter will discuss one of the most profound and concrete inﬂuences of Husserl on Carnap, which can also be seen as another argument against the Kantian rendering of Aufbau.

101 See his ‘Husserl’s Role in Carnap’s Der Raum, in Thomas Bonk (ed.), Language, Truth and Logic, Dordrecht, Kluwer 2003, pp. 179–90. 102 ‘Releyendo al Joven Carnap’, Manuscrito 29, no. 1, 2006, pp. 259–96. See also my recently published ‘La Relevancia de Carnap’, Principia 10, n. 2, 2006, pp. 209–35, which is a critical study of Ramón Cirera, Andoni Ibarra and Thomas Mormann (eds), El Programa de Carnap, Barcelona, C.L.E. 1996. 103 The Reign of Relativity (Oxford et al., 2005), especially p. 142. 104 See his paper ‘Carnap’s Husserlian Reading of the Aufbau’, in Steve Awodey and Carsten Klein (eds), Carnap Brought Home (Chicago et al., 2004), pp. 41–62.

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Chapter 3

Carnap and Husserl on Intersubjectivity 1 The Problem of Intersubjectivity The problem of intersubjectivity, that is, the problem of my knowledge of the existence of other subjects similar to me, is a very special philosophical problem. In particular, such a problem can only arise for a philosophy that in some sense or another has – using Carnap’s terminology – an autopsychological basis. Thus, for example, the problem does not arise for philosophers that propound a sort of naïve realism, accepting as given the existence of a real world, with its objects and events, and with different human beings equally equipped in principle to discover the laws of the physical world. Neither does it arise for materialist, physicalist or naturalist philosophers, for which the existence of the physical world and its inhabitants is not under scrutiny. In particular, such a problem would not have had the same pressing importance for Carnap nor had he taken it so seriously, had he opted for a physicalist basis of his constitutional system. Moreover, even for many philosophies of an idealist or of a psychologistic ﬂavour, the problem of intersubjectivity does not arise. For example, contrary to Frege’s caricatures of his psychologistic rivals, they did not propound a sort of relativism to the individual human subject, but one to the human species. Hence, the inference made by Frege from the psychologistic theses to a relativism of the truth of logical and arithmetical laws to the individual subject is a non sequitur. On the contrary, as Husserl clearly explained,1 psychologism was not a sort of individual relativism, but of relativism to a species, an important distinction that Frege completely overlooked in his critique of psychologism, ﬁrst in arithmetic, and then in logic.2 Psychologism propounded a relativization of the truths of logic and mathematics to the psychic constitution of the human species, while questioning their validity for other possible rational beings, and presupposed that human beings are in principle equally equipped for obtaining knowledge. Psychologism even identiﬁed logical laws with the normative application of some psychological laws valid for every normally endowed human being.3 Thus, for psychologism, the problem of intersubjectivity does not have much importance, since they explicitly presupposed that there are other human beings essentially equally equipped for obtaining knowledge as the psychologist author, be it Benno Erdmann, Sigwart or any other. Indeed, as a matter of fact, the problem of intersubjectivity is non-existent for the immense majority of philosophers. 1 In Logische Untersuchungen I, Chapter VII. 2 With respect to arithmetic, see Die Grundlagen der Arithmetik, and with respect to logic, see the preface to Grundgesetze der Arithmetik. 3 See once more Husserl’s Logische Untersuchungen I.

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The problem of intersubjectivity probably is taken seriously for the ﬁrst time in modern philosophy by Descartes’ universal doubt, in which the existence of the whole world, with all its inhabitants – including human beings – the existence of God and the truth of mathematical statements all disappear under the tsunami of that universal doubt.4 Nonetheless, after he obtained the absolute certainty of his existence as cogito, Descartes went on to ‘prove’ the existence of God and, thanks to the benevolence of le bon Dieu, he believed that he had also ‘proven’ the existence of the world and, in particular, of other human beings. However, the rigour of the radical philosophical doubt of the beginning of his meditations had been weakened after he had obtained the certainty of his cogito and completely abandoned by the time he tried to reconquer the physical world and its inhabitants, including other human beings. The fact that the problem of intersubjectivity has arisen so rarely in the history of philosophy can serve us to disentangle a little bit more the confusions concerning the philosophical inﬂuences in Aufbau. It is especially pertinent to examine whether Kant considered the problem of intersubjectivity. The answer to this question is clearly negative. Kant did not see the problem of intersubjectivity as a problem at all. Only in the third paralogism of the Dialectic of his Kritik der reinen Vernunft is the problem barely touched, not examined.5 Although some scholars would like to see a strict relation between Husserl’s transcendental phenomenology and Kant’s transcendental idealism, notwithstanding some coincidences, there are major differences. One of them lies precisely in this issue. Kant did not even consider Descartes’ universal doubt, nor can his system be at all considered as autopsychological. Kant accepted the truth of the fundamental sciences, namely, traditional essentially Aristotelian logic, arithmetic, non-abstract school algebra, Euclidean geometry and Newtonian physics. He never questioned their validity, but set himself the task of offering a philosophical foundation, or better, justiﬁcation, of classical Newtonian mechanics and Euclidean geometry. Thus, he was not interested in examining whether knowledge in mathematics and physics was possible, but presupposed their existence and wanted to determine the conditions in the knowing subject that make it possible that we have such knowledge. His answer that mathematical knowledge, as well as that of the foundations of physics, is neither empirical nor analytic – in the very limited and unclear understanding of analyticity that he had – but synthetic a priori, on the basis of the constitution of the knowing subject, not only never questioned that knowledge, but presupposed it. On the other hand, Kant was, of course, also interested in showing that metaphysical theoretical knowledge is not possible, since it does not fulﬁl the conditions of possibility of knowledge. In his attempt at disclosing the conditions of possibility of knowledge, he not only presupposed the existence of the geometrical and physical knowledge he wanted to justify, but made explicit use in the table of categories of the classiﬁcation of judgements in traditional logic. Thus, it is perfectly clear that the revolutions in logic, geometry, mathematics, in general, and physics left nothing standing of Kant’s justiﬁcation of the fundamental sciences existing in 4 5

Meditationes de prima philosophia 1641, English translation (Indianapolis, 1951). Kritik der reinen Vernunft, A 362–3.

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his day, and that neo-Kantianism at the beginning of the twentieth century, as well as present neo-neo-Kantianism (of Friedman, Richardson and others) has had to tackle a very difﬁcult task of saving some – already multiply transformed – features of Kantian views. Returning to the problem of intersubjectivity, it should be said that the problem is virtually non-existent for Kant, because he presupposed that the conditions of possibility of scientiﬁc knowledge that he was examining were not the conditions of possibility of knowledge of the individual subject, but of all subjects similarly endowed, more speciﬁcally, of all human beings. That is the reason why Husserl, in his Logische Untersuchungen, rightly classiﬁed Kant’s views together with those of psychologists as a speciﬁc relativism or, more precisely, as an anthropologism, that is, a speciﬁc relativism to the human species. Kant was examining the conditions of possibility of knowledge by normally constituted human subjects. On this point, one should not forget that Kant contrasted many times our human sensible intuition with a sort of intellectual intuition that he attributed to God.6 If we were to use Carnap’s distinction between a physicalist, an autopsychological and a heteropsychological basis, both Kant and psychologism would have to be classiﬁed as presupposing a heteropsychological basis, one that – contrary to the physicalist basis or other autopsychological alternative bases – was in any case not feasible for Carnap. Indeed, as made explicitly clear in Aufbau more than once, the heteropsychological has its epistemological foundation in the physical.7 Let us now see what Carnap had to say about the problem of intersubjectivity. On pp. 90–91, Carnap stresses the extreme importance of intersubjectivity, especially for a system of knowledge like his, based on an autopsychological basis. The emphasis on his thesis that science is concerned strictly with structure or form, not with content, is clearly linked by Carnap to the requirement of obtaining objective knowledge. In particular, he underscores that though his basis is an autopsychological one, based on experiences of consciousness, he is not concerned with the particular experiences of consciousness of an individual subject, which are incomparable with the particular experiences of consciousness of other subjects. It seems pertinent to quote Carnap on this issue: Particularly for scientiﬁc knowledge … intersubjectivity is one of the most important requirements … certainly the material of the individual streams of consciousness is totally different, moreover, in general, incomparable, since a comparison of two impressions or two sentiments from different subjects in the sense of their immediate quality of givenness is absurd: but certain structural properties coincide for all streams of consciousness. Science must limit itself to the statements about such structural properties, since it shall be objective. And it can limit itself to structural statements … since all objects of knowledge are not content, but form and can be presented as structural formations. [Der logische Aufbau der Welt, pp. 90–91]8 6 See Kritik der reinen Vernunft , especially, B 72, but also, for example, B 148. 7 See, for example, Aufbau, pp. 78–9 , 82. 8 ‘Besonders für die wissenschaftliche Erkenntnis ist … die Intersubjektivität eine der wichtigsten Forderungen … zwar das Material der individuellen Erlebnisströme völlig verschieden, vielmehr überhaupt inkomparabel ist, da eine Vergleichung zweier Empﬁndungen

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The Young Carnap’s Unknown Master Only on the basis of this knowledge, that science, according to its essence, is structural science and that because of that there is a path beginning in the individual stream of consciousness to constitute [something] objective, is the system form with autopsychological basis acceptable. From the ignorance of this fact and of this path it is possible to explain some of the resistance until now against the autopsychological basis (or the “methodological solipsism”); and maybe also some other formulations for the subject [as] starting point, as for example, “transcendental subject”, “epistemological subject”, “supraindividual conscience”, “conscience in general”, that maybe are to be interpreted as emergency solutions, since one saw no path from the natural starting point in the sense of the epistemological order of the objects, namely, from the autopsychological to the suprasubjective. [Der logische Aufbau der Welt, p. 91]9

Incidentally, besides clearly Husserlian expressions like ‘according to its essence’ and the general attempt to revindicate expressions like ‘transcendental subject’ and ‘conscience in general’, which occur – among others – in Husserl’s writings, I should like to point out that the use of the expressions ‘structure’ and ‘form’ probably responds to an attempt to avoid the (for his new friends in Vienna) less palatable term ‘essence’, though a conscientious study of Husserl’s analyses would make it perfectly clear that he also is not interested in the individual peculiarities of his experiences of consciousness and the individual peculiarities of its intentional objects, but in the structural properties both of the experiences of consciousness and of its intentional objects. In fact, Husserl’s transcendental subject is not even a general human subject, like Kant’s, but precisely a conscience in general. Returning to the comparison with Kant, it should by now be perfectly clear that the importance assigned by Carnap to the problem of intersubjectivity is another undisputable trait of the non-Kantian nature of his constitutional project. If it were necessary after the discussion in the preceding chapters still to offer arguments against the Kantian or neo-Kantian renderings of the young Carnap’s views, the diametrically opposed attitude with respect to the problem of intersubjectivity or, more precisely, of the constitution of other subjects from an autopsychological basis, puts the nail on the cofﬁn of those misinterpretations. On the other hand, as we will see in the present oder zweier Gefühle verschiedener Subjekte im Sinne ihrer unmittelbaren Gegebenheitsqualität widersinnig ist: aber gewisse Struktureigenschaften stimmen für alle Erlebnisströme überein. Auf die Aussagen über solche Struktureigenschaften muß sich die Wissenschaft beschränken, da sie objektiv sein soll. Und sie kann sich auch auf Strukturaussagen beschränken….da alle Erkenntnisgegenstände nicht Inhalt, sondern Form sind und als Strukturgebilde dargestellt werden können.’ 9 ‘Nur auf Grund dieser Erkenntnis, daß Wissenschaft ihrem Wesen nach Strukturwissenschaft ist und daß es daher einen Weg gibt, vom individuellem Erlebnisstrom ausgehend Objektives zu konstituieren, ist die Systemform mit eigenpsychischer Basis annehmbar. Aus der Unkenntnis dieser Tatsache und dieses Weges dürfen manche der bisherigen Widerstände gegen die eigenpsychische Basis (oder den ‘‘methodischen Solipsismus’’) zu erklären sein; und vielleicht auch manche andere Formulierungen für das Ausgangssubjekt, wie z.B. ‘‘tranzendentales Subjekt’’, ‘‘erkenntnistheoretisches Subjekt’’, ‘‘überindividuelles Bewußtsein’’, ‘‘Bewußtsein überhaupt’’, die vielleicht als Notbehelfe zu deuten sind, weil man vom natürlichen Ausgangspunkt im Sinne einer erkenntnismäßigen Ordnung der Gegenstände, nämlich vom Eigenpsychischen aus keinen Weg zum Übersubjektiven sah.’

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chapter, with Husserl the situation is exactly the opposite as with Kant. Husserl conceded an extreme importance to the problem of intersubjectivity, so decisive that, besides the Fifth Cartesian Meditation of his late Cartesianische Meditationen,10 and the second volume of Ideen, there are, for example, three very thick volumes of the Husserliana edition, namely, volumes XIII–XV concerned exclusively with this problem.11 Moreover, it will be shown in the following sections that Husserl’s and Carnap’s solutions to the problem of intersubjectivity are essentially the same. That solution to the problem of intersubjectivity is, however, not totally compelling. Thus, the exposition will be followed by a critique of the solution, and a subsequent attempt to offer an alternative based on a small but important correction of their solution.12 2 Carnap’s Solution to the Problem of Intersubjectivity Already relatively early in Aufbau, while discussing the distinction between what he called the sign relation and the expression relation, Carnap asserted the importance of the latter relation for the problem of our knowledge of intersubjectivity – that is, in Carnap’s more frequent terminology, the problem of the constitution of the heteropsychological. Thus, he says on pp. 26–7: The expression relation is relatively little investigated, though it is certainly very important for practical life. Since from [our] acquaintance with it in fact depends all understanding of other human beings. But we possess and value this knowledge not explicitly in a theoretical [fashion], but only intuitively (“empathy”). [Der logische Aufbau der Welt, pp. 26–7]13

A similar, though somewhat long, passage occurs on pp. 78–9: We have to add here to the expression relation in the strict sense also the relation that one could more or less designate as “verbal expression”. Hereunder is understood the relation between a body movement and a psychical process, if the movement expresses the presence and the nature of a psychical process by means of speaking, writing or any other conferment of a sign…. The expressive movements, including such verbal expressions, are the only indications from which we can get acquainted [with] the psychic processes in other human beings, the “heteropsychological” processes. Now, every psychic process, if it presents itself as heteropsychological, is in principle knowable, namely, either as inferable 10 Cartesianische Meditationen (1928, Husserliana I, Den Haag, 1963). 11 The three volumes have the same title Zur Phänomenologie der Intersubjektivität (Husserliana XIII, XIV and XV Den Haag, 1973), and amount to some 1,800 pages. 12 When critically discussing Husserl’s and Carnap’s attempts at a solution to the problem of intersubjectivity and, especially, when offering an alternative solution in § 4, I will be presupposing – for the sake of the argument – a somewhat orthodox transcendental phenomenological standpoint, though my approach both to Husserl’s phenomenology and to analytic philosophy, for example, as a Fregean scholar, has always been somewhat heterodox and consciously alienated from the hard core trends. 13 ‘Die Ausdrucksbeziehung ist verhältnismäßig wenig untersucht, obschon sie doch für das praktische Leben sehr bedeutsam ist. Denn von ihrer Kenntnis hängt ja alles Verstehen der anderen Menschen ab. Wir besitzen und verwerten diese Kenntnis aber nicht theoretischexplizit, sondern nur intuitiv (‘‘Einfühlung’’).’

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The Young Carnap’s Unknown Master from the expressive movements or capable of being questioned (capable of being declared). Thus, every sentence about a psychic object can be transformed in a sentence about those indications. From this it follows that the psychic objects are reducible to the expressive movements, thus, to physical objects. [Der logische Aufbau der Welt, pp. 78–9]14

In order to avoid any misunderstandings, Carnap makes it clear on p. 79 that in the last two sentences of the last quoted passage, psychic objects are to be understood as heteropsychological, since the autopsychological objects do not need any mediation of the physical objects to be constituted. We should remind ourselves here of the epistemic order that guides Carnap’s constitutional system: the physical domain is grounded on the autopsychological one, not the other way around. An especially important step in the constitutional system previous to the constitution of the heteropsychological on the basis of the physical, is the constitution of a very peculiar object of the material world, namely, the body of the constitutional subject, constituted on an autopsychological basis. Carnap determines this peculiar object of the physical world by means of ﬁve characteristics in an extensive passage on p. 171, followed by a more informal explanation of each of the ﬁve characteristics. I will quote from the introduction to the ﬁrst passage, and then the ﬁve explanations from the second one, since they are more illuminating than their counterparts. There is a determinate visual thing L that satisﬁes the following conditions. It is constitutionally univocally characterized by means of these determinations, and also already by means of an appropriate part of them. This visual thing is called “my body”. [Der logische Aufbau der Welt, p. 171]15 1. My body is always near my eye. 2. There is no body, whose whole surface can be simultaneously seen; the part of the surface of a body seen at once is because of that never a closed surface. But now, for some bodies the complete surface is visible, thus, the visible surface [is] a closed surface. On the contrary, in the case of my body the visible surface in general is an open [one],

14 ‘Zur Ausdrucksbeziehung im engeren Sinne müssen wir hier noch die Beziehung hinzunehmen, die man etwa als ‘‘Angabebeziehung’’ bezeichnen könnte. Hierunter ist die Beziehung zwischen einer Körperbewegung und einem psychischen Vorgang verstanden, wenn die Bewegung durch Sprechen, Schreiben oder sonstige Zeichengebung das Vorhandensein und die Beschaffenheit des psychischen Vorganges angibt…. Die Ausdrucksbewegungen einschließlich solcher Angaben sind die einzigen Kennzeichen, aus denen wir die psychischen Vorgänge in anderen Menschen, die ‘‘fremdpsychischen’’ Vorgänge, erkennen können. Nun ist jeder psychische Vorgang, wenn er als fremdpsychischer auftritt, prinzipiell erkennbar, nämlich entweder aus Ausdrucksbewegungen erschließbar oder erfragbar (angebbar). Also kann jede Aussage über einen psychischen Gegenstand umgeformt werden in eine Aussage über jene Kennzeichen. Daraus folgt, daß alle psychischen Gegenstände auf Ausdrucksbewegungen (im weiteren Sinne), also auf physische Gegenstände zurückführbar sind.’ I have translated the word ‘Angabe’ in the above passage as ‘verbal expression’, not as ‘assertion’ as in some quotations on § 6 of the preceding chapter, because the context requires a more general translation than one restricted to statements. 15 ‘Es gibt ein bestimmtes Sehding L, daß die folgenden Bedingungen erfüllt. Es ist durch diese Bestimmungen, und auch schon durch einen geeigneten Teil von ihnen, eindeutig konstitutional gekennzeichnet. Dieses Sehding heißt ‘‘mein Leib’’.’

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since some parts of its surface, for example, the eyes and backside, are not visible. 3. To the positions of the surface of my body correspond the qualities (or local signs) of the tactile sense, in such a way that a tactile impression of a determined quality is lived when the corresponding position in the skin is touched by another body or by another part of my body. 4. The qualities of the kinaesthesial impressions correspond to different sorts of movements of my body. 5. The remaining senses are connected in a determined manner with certain parts of my body, namely, the organs of sense. [Der logische Aufbau der Welt, p. 171]16

Hence, the body is a very peculiar material object, especially near to me, that receives sense impressions, some of which are related to its movements, for example, when it touches or is touched by other bodies, and that has some parts – like the eyes and the backside – that can never be seen by the subject. This impossibility is clearly distinguished from the other impossibility already discussed in the previous chapter, and which Carnap obtained from Husserl, of not simultaneously seeing all sides of a material object. This very peculiar object that is the body [Leib] of the subject will play a decisive role in uncovering the realm of the heteropsychological. At the beginning of his discussion of the problem of intersubjectivity, Carnap stresses once more – on pp. 183–4 – two already mentioned points, namely, the importance of the problem of intersubjectivity and the role of what he called the ‘expression relation’. The last point has already been emphasised here with some quotations, and the passage on pp. 183–4 does not add anything essentially new. The passage concerned with the ﬁrst point, however, is worth quoting, because it also mentions the importance of the ﬁrst step in the constitution of the heteropsychological, namely, the constitution of the other human beings ﬁrst as physical things, bodies in the sense of Körper in our entourage. Their constitution as 16 ‘1. Mein Leib ist immer in der Nähe meines Auges. 2. Bei keinem Körper kann die ganze Oberﬂäche gleichzeitig gesehen werden; der auf einmal gesehene Teil der Oberﬂäche eines Körpers ist daher nie eine geschlossene Fläche. Wohl aber ist für manche Körper die ganze Oberﬂäche sichtbar, also die sichtbare Fläche eine geschlossene. Bei meinem Leib dagegen ist auch die überhaupt sichtbare Fläche eine offene, da einige Teile seiner Oberﬂäche, z. B. Auge und Rücken, nicht sichtbar sind. 3. Den Stellen der Oberﬂäche meines Leibes enstsprechen die Qualitäten (oder Lokalzeichen) des Drucksinnes derart, daß eine Druckempﬁndung von bestimmter Qualität erlebt wird, wenn die entsprechende Hautstelle durch einen anderen Körper oder durch einen anderen Teil meines Leibes berührt wird. 4. Die Qualitäten der kinästhetischen Empﬁndungen entsprechen bestimmten Arten von Bewegungen meines Leibes. 5. Die übrigen Sinne hängen in bestimmter Weise mit gewissen Teilen meines Leibes, nämlich den Sinnesorganen zusammen.’ It shoud be observed that in the English translation above two important distinctions of the German language are lost. Firstly, I have translated both Fläche and Oberﬂäche as ‘surface’, though the ﬁrst one has a more geometrical, maybe even abstract usage, whereas the second is the everyday word. More importantly, I have rendered both Leib and Körper as ‘body’. The word Körper is the more general one, whereas the word Leib is restricted to (possibly) animated bodies, usually of persons. That is why Carnap always uses the word Leib to refer to the body of the subject.

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something heteropsychological will be grounded on the physical. Carnap states the importance of this step for the constitutional system as follows: Besides the thing “my body”, the “other human beings” belonging (as physical things) to this class [of human beings] form a sort of object that is of particular importance for the constitutional system. To it will adhere the constitution of the heteropsychological and with it of all higher objects. [Der logische Aufbau der Welt, p. 183]17

After this preliminary step of the constitution of physical things, among which are the still not as such constituted bodies of other human beings, Carnap begins properly the constitution of the heteropsychological. Some physical processes are observed in some of those things, namely, those that are to be constituted as other human beings, with the aid of the expression relation and the sign conferment. It is pertinent here to quote two important passages: Firstly, on the basis of determined processes in the already as physical things constituted “other human beings” will be constituted the heteropsychological objects with the aid of the expression relation. Determined processes in the other human beings will moreover be conceived as “sign conferment”; with their aid will be constituted the “world of the other”. [Der logische Aufbau der Welt, p. 185]18 … the constitution of the psychic of the other human being, of the “heteropsychological”, will be taken care for the ﬁrst time now. This constitution consists in [the procedure] that on the basis of the physical processes in another human being, with the help of the already constituted relation expression, to this human being will be assigned psychic processes. Besides the expression relation, the “sign conferment” will also be useful, that is, the expressions, that the other human being directs to me. [Der logische Aufbau der Welt, pp. 185–6]19

On p. 186, Carnap makes two observations directed at avoiding possible misunderstandings, namely, that in the above-sketched process of constitution of the heteropsychological, the attribution made to the other is to the other’s body [Leib] not to his soul, which can only be constituted as a result of such an assignment or attribution of psychic processes by means of the expression relation and the sign conferment, and, secondly, that the psychic processes that are attributed to the other are autopsychological, since no other psychic processes have been constituted 17 ‘Die außer dem Ding ‘‘mein Leib’’ zu dieser Klasse [der Menschen] gehörenden ‘‘anderen Menschen’’ (als physische Dinge) bilden eine Gegenstandsart, die für das Konstitutionssystem von ganz besonderer Bedeutung ist. An sie werden die Konstitutionen des Fremdpsychischen und damit aller höheren Gegenstände anknüpfen.’ 18 ‘Zunächst werden auf Grund bestimmter Vorgänge an den als physischen Dingen schon konstituierten ‘‘anderen Menschen’’ mit Hilfe der Ausdrucksbeziehung die fremdpsychischen Gegenstände konstituiert. Bestimmte Vorgänge an den anderen Menschen werden weiterhin als ‘‘Zeichengebung’’ aufgefaßt; mit ihrer Hilfe wird die ‘‘Welt des Anderen’’ konstituiert.’ 19 ‘… die Konstitution des Psychischen der anderen Menschen, des ‘‘Fremdpsychischen’’, wird erst jetzt vorgenommen. Diese Konstitution besteht darin, daß auf Grund der physischen Vorgänge an einem anderen Menschen mit Hilfe der früher konstituierten Ausdrucksbeziehung diesem Menschen psychische Vorgänge zugeschrieben werden. Außer der Ausdrucksbeziehung wird auch noch die ‘‘Zeichengebung’’ verwertet, d.h. die Angaben, die der andere Mensch mir macht.’

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besides autopsychological. Thus, a sort of transference or analogy based on the autopsychological is at the basis of the constitution of the heteropsychological. Although the experiences of consciousness of the other need not coincide with the constitutional subject’s, their constituent parts do coincide. As Carnap puts it; These whole series of experiences of consciousness of the other human being consists in nothing other than a reordering of my experiences of consciousness and its constituent parts. For the other can in any case experiences of consciousness be constituted that do not coincide with any of my experiences of consciousness. But the constituent parts of the novel experience of consciousness must occur as constituent parts of my experiences of consciousness…. [Der logische Aufbau der Welt, p. 186]20

Moreover, in complete analogy with the constitution of the autopsychological, the heteropsychological will not be restricted to the presently conscious, but will be extended to the presently unconscious experiences of consciousness. In this way will be constituted the ‘soul’ of the other in analogy with mine. On this last point, it is pertinent to quote Carnap’s Aufbau. The so constituted psychic of the other will be the class of the “psychic states of the other” called in analogy with “my soul” “the soul of the other”. The general region of the “heteropsychological” comprises the psychical of all other human beings that (that is, whose bodies) are present as physical things in the constituted physical world. [Der logische Aufbau der Welt, p. 187]21

Another important point stressed by Carnap is that in his constitutional system the constitution of the heteropsychological is not possible without the mediation of the body of the other. Thus, in particular, the soul of the other is constitutionally grounded on its body [Leib]. Thus, says Carnap: From the indicated sort of constitution of the heteropsychological follows: there is no heteropsychological without body. Since (in constitutional language) heteropsychological can only be constituted by means of the mediation of the body, and certainly of such, in which are present certain processes (the “processes of expression”), which are similar to those of my body…. [Der logische Aufbau der Welt, p. 187]22

20 ‘Diese ganze Erlebnisreihe des anderen Menschen besteht dabei in nichts anderem als einer Umordnung meiner Erlebnisse und ihrer Bestandteile. Für den Anderen können allerdings Erlebnisse konstituiert werden, die mit keinem meiner Erlebnisse übereinstimmen. Aber die Bestandteile des neuartigen Erlebnisses müssen als Bestandteile meiner Erlebnissen vorkommen.’ 21 ‘Das so konstituierte Psychische des Anderen wird die Klasse der ‘‘psychischen Zustände des Anderen’’ analog ‘‘meiner Seele’’ ‘‘die Seele des Anderen’’ genannt. Das allgemeine Gebiet des ‘‘Fremdpsychischen’’ umfaßt das Psychische aller anderen Menschen, die (d.h. deren Leiber) als physische Dinge in der konstituierten physikalischen Welt vorkommt.’ 22 ‘Aus der angegebenen Art der Konstitution des Fremdpsychischen folgt: es gibt kein Fremdpsychisches ohne Leib. Denn (in konstitutionaler Sprache) Fremdpsychisches kann nur durch Vermittlung eines Leibes konstituiert werden, und zwar eines solchen, bei dem gewisse Vorgänge (die ‘‘Ausdrucksvorgänge’’) vorkommen, die denen meines Leibes ähnlich sind….’

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Carnap also stresses the importance for the constitution of the heteropsychological of what he called ‘sense conferment’, that is the linguistic manifestations of the other human being. On this point, Carnap says on p. 188: Besides the processes of expression, there are still certain other physical processes in the other human being as physical thing of very particular importance for the extension of our knowledge, and because of it also for the continuation of the constitutional process. These are the sign conferring expressions, especially spoken and written words; we call them “sign conferments”. They make possible the dissemination of the constitutional system, an increase of the number of objects capable of being constituted of nearly all kinds. [Der logische Aufbau der Welt, p. 188]23

Carnap sees some complications with the constitution of the relation between sign conferment and the object designated by the sign, that is, with the referent [Fregean Bedeutung]. I am not going to dwell on this issue. In any case, he stresses on pp. 191–2 the dependence of any possible understanding of the heteropsychological on both the sign conferment and the expressive movements. Moreover, he says: But still more: the comprehensible and comprehended content is in its whole consistency conditioned by the consistency of the intervening manifestation. In other words: heteropsychological is (also intuitively) only recognizable as referent of a manifestation (expressive movement or sign conferment); the referent of a manifestation is a univocal function of the physical consistency of the manifestation…. [Der logische Aufbau der Welt, p. 192]24

Since before the constitution of the other human beings, the constitutional subject had been concerned with only one psychic object, namely, with himself as a stream of consciousness or, in any case, as a class of experiences of consciousness, the constitution of the experiences of consciousness of another human being can only proceed, by analogy, with the constitutional subject’s constitution, by means of the same constitutional forms as before. In particular, a similarity relation between elementary experiences of consciousness analogous to the basic relation in the autopsychological level will play an analogous role at the heteropsychological level. Thus, Carnap states:

23 ‘Außer den Ausdrucksvorgängen sind noch gewisse andere physische Vorgänge an den anderen Menschen als physischen Dingen von ganz besonderer Bedeutung für die Erweiterung der Erkenntnis, und daher auch für die Weiterführung des Konstitutionssystems. Es sind dies die zeichengebenden Äußerungen, vor allem gesprochene und geschriebene Worte; wir nennen sie ‘‘Zeichengebungen’’. Sie ermöglichen eine Verbreitung des Konstitutionssystems, eine Vermehrung der Anzahl der konstituierbaren Gegenstände beinahe aller Arten.’ 24 ‘Aber noch mehr: der verstehbare und verstandene Inhalt ist in seiner ganzen Beschaffenheit bedingt durch die Beschaffenheit der vermittelnden Äußerung. Mit anderen Worten: Fremdpsychisches ist (auch intuitiv) nur erkennbar als Bedeutung einer Äußerung (Ausdrucksbewegung oder Zeichengebung); die Bedeutung einer Äußerung ist eine eindeutige Funktion der physischen Beschaffenheit der Äußerung….’

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More precisely: the former constitutional steps taken with basic relation Er will now be taken with an analogous relation ErM, existing between the experiences of consciousness of M. [Der logische Aufbau der Welt, p. 194]25

Carnap stresses that the constitution of the other human beings and of their respective worlds, being constitutional objects based on the autopsychological domain, can be seen as the result of ramiﬁcations of the constitutional subject’s constitutional system. Two passages on the same p. 194 make this dependence clear. … all “objects of M” are certainly objects of one constitutional system and because of it remit ﬁnally to its basic object, thus, to a relation existing between the elementary experiences of consciousness (my experiences of consciousness!). In any case, one can in a certain sense talk about “constitutional system of M”; but with it nothing else is to be understood than a certain branch “of the” (or “of my”) constitutional system, which ramiﬁes at a higher level. [Der logische Aufbau der Welt, p. 194]26 From the indicated sort of constitution of the “world of M” results that there exists an analogy between this and “my world”; more precisely; between the whole constitutional system (S) and the “constitutional system of M” (SM). But at the same time, SM is only a partial system inside S; the world of M is constituted inside my world, it shall not be thought as structured by M; but structured by me for M. [Der logische Aufbau der Welt, p. 194]27

Furthermore, Carnap stresses on p. 196 of Aufbau that once the constitutional subject constitutes the other human being as a heteropsychological object – that is, not merely as a physical thing – one has to acknowledge that the other human being also constitutes the world, including the constitutional subject. Thus, there exists a correspondence between the physical things constituted by the constitutional subject S and the physical things constituted by the heterosubject SM, and between the psychic objects constituted by both subjects. This correspondence is not affected by the differences that remain, for example, that between the experiences of consciousness of my stream of consciousness as constituted in my stream of consciousness and the experiences of consciousness of my stream of consciousness as constituted analogically in the stream of consciousness of the other human being. A decisive next step is the generalization of this correspondence to three subjects and to an unlimited number of possible human subjects. The possibility of such a 25 ‘Genauer: die früher mit der Grundrelation Er vorgenommenen Konstitutionsschritte werden jetzt mit einer zwischen den Erlebnissen des M bestehenden, analogen Relation ErM vorgenommen.’ 26 ‘… alle ‘‘Gegenstände des M’’ sind doch Gegenstände des einen Konstitutionssystems und gehen daher schließlich auf dessen Grundgegenstand zurück, also auf eine Relation, die zwischen den Elementarerlebnisse (meinen Erlebnissen!) besteht. Man kann allerdings in einem gewissen Sinne von ‘‘Konstitutionssystem des M’’ sprechen; aber darunter ist dann nichts anderes zu verstehen als ein gewisser Zweig ‘‘des’’ (oder ‘‘meines’’) Konstitutionssystem, der auf höher Stufe abzweigt.’ 27 ‘Aus der angedeuteten Art der Konstitution der ‘‘Welt des M’’ ergibt sich, daß zwischen dieser und ‘‘meiner Welt’’ eine gewisse Analogie besteht; genauer: zwischen dem ganzen Konstitutionssystem (S) und dem ‘‘Konstitutionssystem des M’’ (SM). dabei ist aber SM nur ein Teilsystem innerhalb S; die Welt des M ist innerhalb meiner Welt konstituiert, sie ist nicht zu denken als von M aufgebaut; sondern als von mir für M aufgebaut.’

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correspondence is a conditio sine qua non for intersubjectivity. It is pertinent here to quote an extensive passage on this issue. Now, if there exists a biunivocal correspondence between SM and S and also between S and SN, then there is also a given biunivocal correspondence between SM and SN, that has the same constituency as those [ones]. Thus, there exists a general biunivocal correspondence between all such systems, thus, [between] the worlds of all those normal human beings known to me, the I included. By “intersubjective correspondence” we want from now on to understand this general correspondence, not more the correspondence between two determined systems. In corresponding fashion, we understand now by “intersubjectively transferable properties” and “intersubjectively transferable statements” such that remain valid, if instead of their object the intersubjectively corresponding object of no matter which other system presents itself. [Der logische Aufbau der Welt, pp. 198–9]28

Carnap concludes his discussion of the problem of intersubjectivity with the obtainment of objects that are objective in the sense of being intersubjective. They are obtained very easily from the fact that the biunivocal correspondence between the objects constituted by all normal human beings is an equivalence relation. He then obtains the intersubjective objects as equivalence classes – he uses the expression ‘abstraction classes’ – of the intersubjective correspondence. Of course, the intersubjective world, that is, the world consisting of all those objects built as equivalence classes, is precisely the realm of objects studied by science. In order to ﬁnish the exposition of Carnap’s solution to the problem of intersubjectivity, it is pertinent to insert here two brief quotations. The intersubjective objects are the abstraction classes of the intersubjective correspondence. We call the world of these objects the “intersubjective world”. [Der logische Aufbau der Welt, p. 199]29 The intersubjective world (in the sense of the just given constitution) forms the proper region of objects of science…. the aspiration of science goes there, to reach a constituency of only intersubjective statements. [Der logische Aufbau der Welt, p. 200]30

It is now time to succinctly discuss Husserl’s solution to the problem of intersubjectivity. 28 ‘Besteht nun eine eineindeutige Zuordnung zwischen SM und S und auch zwischen S und SN, so ist damit eine eineindeutige Zuordnung zwischen SM und SN gegeben, die dieselbe Beschaffenheit hat wie jene. So besteht also eine allgemeine eineindeutige Zuordnung zwischen allen solchen Systemen, also den Welten aller mir bekannten, normalen Menschen, das Ich eingerechnet. Unter ‘‘intersubjektiver Zuordnung’’ wollen wir fortan diese allgemeine Zuordnung verstehen, nicht mehr die Zuordnung zwischen zwei bestimmten Systemen. In entsprechender Weise verstehen wir jetzt unter ‘‘intersubjektiv übertragbaren Eigenschaften’’ und ‘‘intersubjektiv übertragbaren Aussagen’’ solche, die gültig bleiben, wenn an Stelle ihres Gegenstandes der intersubjektiv zugeordnete Gegenstand eines beliebig anderen System tritt.’ 29 ‘Die intersubjektiven Gegenstände sind die Abstraktionsklassen der intersubjektiven Zuordnung. Die Welt dieser Gegenstände nennen wir die ‘‘intersubjektive Welt’’.’ 30 ‘Die intersubjektive Welt (im Sinne der soeben gegebenen Konstitution) bildet das eigentliche Gegenstandsgebiet der Wissenschaft…. das Bestreben der Wissenschaft geht dahin, zu einem Bestande von nur intersubjektiven Aussagen zu gelangen.’

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3 Husserl’s Solution to the Problem of Intersubjectivity As already mentioned, Husserl was especially concerned with the problem of intersubjectivity, as attested by the bulk of material on this issue already published in the still-in-progress edition of his complete works. In the present context it is impossible to try to examine the whole material or even a signiﬁcant part of it. Hence, I will mostly restrict my exposition to the more accessible material, namely, to Ideen II and Cartesianische Meditationen, though I will also brieﬂy refer to the three volumes of Zur Phänomenologie der Intersubjektivität. As was the case with Carnap, I will begin the discussion by considering this particular material object that is the body of the subject. As the whole physical world, it is constituted on the basis of the experiences of consciousness of the constitutional transcendental subject. Thus, as any other physical thing, it is grounded on the autopsychological, to use Carnap’s terminology. However, among all those objects, all those ‘bodies’ in the geometrical-physical sense of the German word Körper, the body [Leib] of the constitutional subject has, as Husserl puts it,31 besides the speciﬁc physical properties, new properties that it does not share with the remaining physical objects, namely, properties of a soul, be they sensitive or strictly psychic. Thus, the body of the constitutional subject – as well as the bodies of other subjects still to be constituted – is a souled or animated body, and as such, it is, on the one hand, grounded on the physical or material and, on the other hand, is not reducible to the material, but supervenes it. As Husserl says on p. 130 of the ﬁrst volume of Ideen: ‘The whole world is not merely physical, but psychophysical.’32 The speciﬁc souled properties of the (living) body are not divisible like everything material, though they are spatio-temporally localized.33 In a passage of the ﬁrst of the three volumes on the phenomenology of intersubjectivity, Husserl tries to make especially precise his distinction between the two German words Leib and Körper, usually rendered in English simply as body. Husserl says there: “Animated body” differentiates itself from body by being a double-layered unity. The body is an apperceptive unity of the comprehensive type “spatial thing”; spatial-temporal unity is constituted, substantial-causal unity of the material thing…. The hand, the member of the animated body, is (as the whole animated body) a unity grounded on it, once more a comprehensive unity of a new type…. [Zur Phänomenologie der Intersubjektivität I, pp. 48–9]34

It is, thus, reasonable to render the word Leib as ‘animated body’ when translating Husserl – at least in contexts in which a possible confusion should be avoided – in 31 See Ideen II, pp. 32–3. 32 The German text reads: ‘Die volle Welt ist ja nicht bloß physische, sondern psychophysische’. 33 See ibid., p. 33. 34 ‘‘‘Leib’’ unterscheidet sich von Körper dadurch, dass es eine doppelschichtige Einheit ist. Der Körper ist eine apperzeptive Einheit des apprehensiven Typus ‘‘Raumding’’; räumlichzeitliche Einheit konstituiert sich, substantial-kausale Einheit des materiellen Dinges…. Die Hand, das Leibesglied, ist (wie der ganze Leib) eine darin fundierte Einheit, wieder eine apprehensive Einheit eines neuen Typus….’

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order to emphasize the contrast with the more general word Körper, that is, physical or geometrical body – which I will render simply as body – though in German the word Leib is also used to refer to the body of a dead person. The preceding basically terminological precision brings us to an especially important peculiarity of my – that is the constitutional subject’s – body. It serves as a sort of point zero of the coordinates of my world, in the sense that it deﬁnes the here and now from which the constitutional subject looks at the world. Hence, it is perfectly clear that, as Carnap said – see the preceding section – the body of the constitutional subject is near to his eye. Some quotations seem pertinent here. And also the distinction is here clearly connected with [the fact] that the animated body becomes the bearer of the orientation point zero, of the here and now, from which the pure I looks at the space and the whole world of senses. In this way, thus, each thing that appears has eo ipso a relation of orientation to the animated body, and not only the actually appearing, but each thing that could possibly appear. [Ideen II, p. 56]35 At the same time are constituted the things of the senses in the subjective manner of the “orientation” and for us … in such a way that a distinguished thing of the senses “animated body” is given as permanent bearer of the centre of orientation. [Ideen II, p. 65]36

The preceding passages explain in a much clearer way than Carnap did the ﬁrst of the ﬁve properties of the body of the constitutional subject enumerated by him in Aufbau and quoted in the preceding section. The following passage of the same book is concerned with the second of those properties, namely, with the incompleteness of the direct constitution of the body of the constitutional subject. Whereas I have with respect to all other things the liberty of arbitrarily changing my position relative to them and at the same time to arbitrarily vary the manifolds of appearances, in which they are given to me, I do not have the possibility to distance myself from my body or it from me, and correspondingly the manifolds of appearances of my body are limited in a determined manner: I can see certain parts of the body only in a peculiarly perspectivist contraction, and others (for example the head) are in general not visible for me. The same animated body that serves me as means of all perceptions hinders me in the case of its own perception and is a remarkably incompletely constituted thing. [Ideen II, p. 159]37 35 ‘Und auch die Auszeichnung hängt offenbar hiermit zusammen, daß der Leib zum Träger der Orientierungspunkte Null wird, des Hier und Jetzt, von dem aus das reine Ich den Raum und die ganze Sinnenwelt anschaut. So hat also jedes Ding, das erscheint, eo ipso Orientierungsbeziehung zum Leib, und nicht nur das wirklich erscheinende, sondern jedes Ding, das soll erscheinen können.’ 36 ‘Dabei konstituieren sich die Sinnendinge in der subjektiven Weise der ‘‘Orientierung’’ und für uns … derart, daß ein ausgezeichneter Sinnending ‘‘Leib’’ als beständiger Träger des Zentrums der Orientierung gegeben ist.’ 37 ‘Während ich allen anderen Dingen gegenüber die Freiheit habe, meine Stellung zu ihnen beliebig zu wechseln und damit die Erscheinungsmannigfaltigkeiten, in denen sie mir zur Gegebenheit kommen, beliebig zu variieren, habe ich nicht die Möglichkeit, mich von meinem Leibe oder ihn von mir zu entfernen, und dem entsprechend sind die Erscheinungsmannigfaltigkeiten des Leibes in bestimmter Weise beschränkt: gewisse Körperteile kann ich nur in eigentümlicher perspektivischer Verkürzung sehen, und andere

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At the beginning of the Fifth Cartesian Meditation, which is especially concerned with the problem of intersubjectivity, Husserl offers a detailed characterization of the body [Leib] of the constitutional subject. As will be seen immediately, the characterization covers the properties 3–5 of Carnap’s characterization mentioned above, whereas, as already pointed out, property 1 was already tacitly covered in the characterization of the body as the zero point of a system of coordinates of the constitutional subject, which serves as the basis for an orientation relation in space, and property 2 was explicitly mentioned by Husserl in the passage quoted immediately above. Husserl characterizes the body of the constitutional subject, brieﬂy, ‘my body’ in Cartesianische Meditationen as follows: Among the properly grasped bodies [Körpern] of this nature, I ﬁnd then with unique distinction my animated body, namely, as the only one that is not a mere body [Körper], but precisely animated body, the only object of my abstractive world layer, to which I attribute, in virtue of experience, ﬁelds of impressions, though in different manners of belonging (ﬁeld of tactual impressions, ﬁeld of warm-cold and so forth), the only one in which I immediately act freely, and particularly govern in all its organs. I perceive, kinethesially touching with the hands, as well as seeing with the eyes and so forth, can at any time so perceive, in which case the kinaesthesia of the organs occur in the I do and obey my I can; moreover, I can, putting these kinaesthesia into action, strike, push and so forth and by these means immediately and then mediately actuate with my body. By being active perceiving, I experience (or can experience) the whole nature, including my proper bodyliness that is in this [case] related to itself. That becomes possible each time that I can perceive by means of one hand the other, [can perceive] by means of a hand an eye and so forth, in which [case] acting organ must become object and object acting organ. [Cartesianische Meditationen, p. 128]38

Husserl also refers to these characteristics of the animated body of the constitutional subject on pp. 159–60 of Ideen II and in a very detailed fashion on pp. 328–30 of the second volume of Zur Phänomenologie der Intersubjektivität.

(z.B. der Kopf) sind überhaupt für mich unsichtbar. Derselbe Leib, der mir als Mittel aller Wahrnehmung dient, steht mir bei der Wahrnehmung seiner selbst im Wege und ist ein merkwürdig unvollkommen konstituiertes Ding.’ 38 ‘Unter den eigentlich gefaßten Körpern dieser Natur ﬁnde ich dann in einziger Auszeichnung meinen Leib, nämlich als den einzigen, der nicht bloßer Körper ist, sondern eben Leib, das einzige Objekt innerhalb meiner abstraktiven Weltschicht, den ich erfahrungsmäßig Empﬁndungsfelder zurechne, obschon in verschiedenen Zugehörigkeitsweisen (Tastempﬁndungsfeld, Wärme- und Kälte-Feld usw.), das einzige in dem ich unmittelbar schalte und walte, und insonderheit walte in jedem seiner Organe. Ich nehme, mit den Händen kinästhetisch tastend, mit den Augen ebenso sehend usw. wahr, kann jederzeit so wahrnehmen, wobei die Kinäthesen der Organe im Ich tue verlaufen und meinem Ich kann unterstehen; ferner kann ich, diese Kinästhesen ins Spiel setzend, stoßen, schieben usw. und dadurch unmittelbar und dann mittelbar leiblich handeln. Wahrnehmend tätig erfahre ich (oder kann ich erfahren) alle Natur, darunter die eigene Leiblichkeit, die darin auf sich selbst bezogen ist. Das wird dadurch möglich, daß ich jeweils mittelst der einen Hand die andre, mittelst einer Hand ein Auge usw. wahrnehmen kann, wobei fungierendes Organ zum Objekt und Objekt zum fungierenden Organ werden muß.’

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However, my body, though the ﬁrst animated body, is not the only animated body that I – the constitutional subject – encounter in the (physical) world. There are other such bodies that appear in the sensory ﬁeld of the constitutional subject, bodies that move in a similar fashion as my body, but on whose sensory movements the constitutional subject does not govern. In the coordinate system of the constitutional subject, whose zero point is his own body, which determines the here and now, any other animated body appears as occupying a different position, a there. Nonetheless, as Husserl puts it on pp. 145–6 of Cartesianische Meditationen, it is always in principle possible that by means of a free displacement of his body, the constitutional subject can occupy the place in space formerly occupied by another body, making the there into a here, a zero point of his coordinate system. Thus, Husserl says: My corporeal animated body has, remitted to itself, its manner of givenness of the central here; each other body and so the body of the other has the mode of there. This orientation of the there is subjected thanks to my kinaesthesia to the free change. In my primordial sphere in the change of orientation is constituted the one spatial nature, and certainly constituted in intentional relation to my as perceiving performing bodyliness. I can change in such a way my position by means of free transformation of my kinaesthesia and especially of the promenade that I can transform each there in a here, that is, I could occupy with my body any spatial place. [Cartesianische Meditationen, pp.145–6]39

The constitution of other bodies as animated bodies [Leiber], similar to ‘my body’, the body of the constitutional subject, that is, not as a mere physical body [Körper], brings us directly to the problem of the constitution of the other psyche. Contrary to what happens with the other body, that is perceived in physical space, the constitutional subject does not have direct access to the other psyche, and not only factually does not have access to it, but cannot have any access. It is a priori impossible to have access to the contents of a stream of consciousness different from my own consciousness. The constitution of the other psyche has to be mediated, through a sort of analogy. First of all, the other body behaves in a similar way as mine. It has similar kinaesthesia as mine, it pushes other objects as mine does, it can move from his place there in space and occupy another place in space, including the place that I now call ‘here’, where my body is presently located. Moreover, the other body has bodily expressions similar to those of my body. The terrain for the constitution of the other psyche is, thus, prepared, though one cannot properly speak of a direct constitution. The procedure of constitution involves what Husserl calls an ‘apresentation’ by analogy. The other animated body is perceived, whereas the other psyche is not perceived but apperceived by the constitutional subject. This procedure

39 ‘Mein körperlicher Leib hat, als auf sich selbst zurückbezogen, seine Gegebenheitsweise des zentralen Hier; jeder andere Körper und so der Körper des Anderen hat den Modus Dort. Diese Orientierung des Dort unterliegt vermöge meiner Kinästhesen den freien Wechsel. Dabei ist in meiner primordinalen Sphäre im Wechsel der Orientierung konstituiert die eine räumliche Natur, und zwar konstituiert in intentionaler Bezogenheit auf meine als wahrnehmend fungierende Leiblichkeit. Ich kann meine Stellung durch freie Abwandlung meiner Kinästhesen und in besondern des Herumgehens so ändern, daß sich jedes Dort in ein Hier verwandeln, d. i. jeden räumlichen Ort leiblich einnehmen könnte.’

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is similar to the one already present when I considered having perceived a physical object, for example, a house, while really perceiving only the front side. I simply complete the perception by a sort of apresentation in an apperception of the unseen part of the physical object. A similar procedure is present in the constitution of the other psyche. I perceive a body different from mine, but very similar to mine in its form and its behaviour in physical space, and I assign such a body by means of an apperception a psyche similar to mine, that is, to that of the constitutional subject. There is, however, a not negligible difference between the two apperceptions. In the case of physical objects, I can in principle see any other side of the physical object in successive perceptions, though I could never perceive the whole object in one perception. In the case of the other psyche, I can never perceive the other psyche, no matter how many perceptions of its body I have. A direct constitution of the other psyche is a priori excluded. On the other hand, though the procedure functions as a sort of analogy, this analogy should not be understood as a sort of reasoning. The following passages should help the reader understand better Husserl’s procedure of the constitution of the other psyche as a sort of empathy [Einfühlung]. A certain mediation of the intentionality must be present here…. Thus, it is a sort of making present together, a sort of apresentation. [Cartesianische Meditationen, p. 139]40 One such [apresentation] is present already in the external experience, since the properly seen front side of a thing always and necessarily apresents a backside of the thing and delineates it a more or less determined content. On the other hand, it cannot be exactly this kind of the already co-constitutive apresentation of the primordial nature, since to it belongs the possibility of corroboration by means of corresponding fulﬁlling presentations (the back side becomes the front side), whereas that must be a priori excluded for that apresentation which shall drive [us] into another original sphere. [Cartesianische Meditationen, p. 139]41 … it presents itself a body in the perceptual domain of my primordial nature, which as primordial naturally is a mere piece of determination of my (immanent transcendence). Since in this nature and world my animated body is the only body that is originally constituted and can be constituted as animated body (actuating organ), so the body there, which certainly is conceived as animated body, obtains this sense from an apperceptive transference of my animated body, and then in a manner that excludes an actually direct and, thus, primordial identiﬁcation of the predicates of the speciﬁc bodyliness, an identiﬁcation by means of proper perception. It is from the beginning clear that only a connecting similarity of that body there with my animated body inside of my primordial

40 ‘Eine gewisse Mittelbarkeit der Intentionalität muß hier vorliegen…. Es handelt sich also um eine Art Mitgegenwärtig-machens, eine Art Appräsentation.’ 41 ‘Eine solche liegt schon in der äußeren Erfahrung vor, sofern die eigentlich gegebene Vorderseite eines Dinges stets und notwendig eine dingliche Rückseite appräsentiert und ihr einen mehr oder minder bestimmten Gehalt vorzeichnet. Andrerseits kann es gerade diese Art der schon die primordinale Natur mitkonstituierenden Appräsentation nicht sein, da zu ihr die Möglichkeit der Bewährung durch entsprechende erfüllende Präsentation gehört (die Rückseite wird zur Vorderseite), während das für diejenige Appräsentation, die in eine andere Originalsphäre hineinleiten soll, a priori ausgeschlossen sein muß.’

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The following passage on p. 141 expresses most clearly Husserl’s contention that such an analogy is not reasoning at all. It would, thus, be a certain comparative apperception, but because of it by no means an inference by analogy. Apperception is no inference, no act of thought. [Cartesianische Meditationen, p. 141]43

The apperception is both a grounded and an indirect constitution of the other psyche. It is grounded because it presupposes and builds on the direct perception of the other body, with its purely physical properties and with the properties that supervene the physical and make that body an animated body similar to that of the constitutional subject, a body that moves without having to be pushed by another body, a body with expressions and gestures that seem to point out to some psychic states. It is indirect because, as already mentioned, the constitutional subject cannot have direct access to the psychic life of the other psyche, to its experiences of consciousness. Nonetheless, the similarity in the physical and especially in the souled properties of both bodies, that is, the body of the constitutional subject and the other animated body, is sufﬁcient for the constitution of the other psyche by means of an analogical apperception. As Husserl puts it: That which I actually see is not a sign and is not the other; and what is therein apprehended in actual originality, this bodyliness there (and even one side of its surface), that is properly the body of the other, precisely only seen from my position and from this side, and in accord with the sensory constitution of the experience of the other corporeal animated body of a for me in principle not originally accessible soul, both in the unity of a psychophysical reality. [Cartesianische Meditationen, p. 153]44

42 ‘…es tritt im Wahrnehmungsbereich meiner primordinalen Natur ein Körper auf, der als primordinaler natürlich bloß Bestimmungsstück meiner selbst (immanente Transzendenz) ist. Da in dieser Natur und Welt mein Leib der einzige Körper ist, der als Leib (fungierendes Organ) ursprünglich konstituiert ist und konstituiert sein kann, so muß der Körper dort, der als Leib doch aufgefaßt ist, diesen Sinn von einer apperzeptiven Übertragung von meinem Leib her haben, und dann in einer Weise, die eine wirklich direkte und somit primordinale Ausweisung der Prädikate der speziﬁschen Leiblichkeit, eine Ausweisung durch eigentliche Wahrnehmung ausschließt. Es ist von vornherein klar, daß nur eine innerhalb meiner Primordinalsphäre jenen Körper dort mit meinem Körper verbindende Ähnlichkeit das Motivationsfundament für die analogisierende Auffassung des ersteren als anderer Leib abgeben kann.’ 43 ‘Es wäre also eine gewisse verähnlichende Apperzeption, aber darum keineswegs ein Analogieschluß. Apperzeption ist kein Schluß, kein Denkakt.’ 44 ‘Das was ich wirlich sehe, ist nicht ein Zeichen und nicht Andere; und das dabei in wirklicher Originalität Erfaßte, diese Körperlichkeit dort (und sogar die eine Oberﬂäche derselben), das ist der Körper des Anderen selbst, nur eben von meiner Stelle und von dieser Seite gesehen und gemäß der Sinneskonstitution der Fremderfahrung körperlicher Leibes einer prinzipiell für mich nicht originaliter zugänglichen Seele, beide in der Einheit einer psychophysichen Realität.’

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Husserl’s constitutional process of the other psyche on the autopsychological basis by means of the analogical apperception immediately based on the perception of the other animated body culminates in the constitution of another psyche, another I with an animated body playing for him the role of the zero point of a coordinate system similar to that determined by my body. Husserl says on p. 146: Moreover, the other is apresentatively apperceived as I of a primordial world, respectively, of a monad, in which his body is originally constituted and experienced in the modus of the absolute here, precisely as centre of function for his dominion. [Cartesianische Meditationen, p. 146]45

In a passage on pp. 156–7 Husserl sums up his procedure, stressing the importance of the constitution of the other human beings for an intersubjective world. That the others are constituted in me as others is the only imaginable manner [in] which they can have sense and validity for me as existing and so existing…. Certainly, they are in reality separated from mine, since no real connection transfers from their experiences of consciousness to my experiences of consciousness and so in general from their essentially proper to my [essentially proper]. To that corresponds the real separation, the worldly, of my psychophysical existence from that of the other that presents itself as spatial in view of the spatiality of the objective animated bodies. On the other hand, this original community is not [simply] a nothing…. It is a principally peculiar link, a real community, and precisely such that makes transcendentally possible the being of a world, of a world of humans and things. [Cartesianische Meditationen, pp. 156–7]46

From my exposition thus far, it would seem that, similarities aside, there exists an important difference between Carnap’s constitution of the heteropsychological and Husserl’s constitution of the heteropsychological, namely, that in Carnap’s constitutional process the facial expressions, gestures and verbal utterances of the other animated body play a decisive role for the procedure of transferring it a psyche by analogy, whereas in Husserl it seems as if the bodily movements, the kinaesthesia were already enough for the analogical apperception. This, however, is false. Certainly, in his exposition in Cartesianische Meditationen and even in Ideen II Husserl did not stress sufﬁciently the role of gestures and verbal utterances as a fundamental part of the basis for the analogical apperception. Nonetheless, it is only because Husserl in some sense took it for granted in his exposition that he meant 45 ‘Ferner, der Andere ist appräsentativ apperzipiert als Ich einer primordinalen Welt bzw. einer Monade, in der sein Leib im Modus des absoluten Hier, eben als Funktionszentrum für sein Walten ursprünglich konstituiert und erfahren ist.’ 46 ‘Daß die Anderen sich in mir als Andere konstituieren, ist die einzig denkbare Weise, wie sie als seiende und soseiende für mich Sinn und Geltung haben können…. Zwar sind sie reell von der meinen getrennt, sofern keine reelle Verbindung von ihren Erlebnissen zu meiner Erlebnissen und so überhaupt von ihren Eigenwesentlichen zu dem meinen überführt. Dem entspricht ja die reale Trennung, die weltliche, meines psychophysischen Daseins von dem des Anderen, die sich als räumliche darstellt vermöge der Räumlichkeit objektiver Leiber. Andererseits ist diese ursprüngliche Gemeinschaft nicht ein Nichts…. Es ist eine prinzipiell eigenartige Verbundenheit, eine wirkliche Gemeinschaft, und den die, die das Sein einer Welt, einer Menschen- und Sachenwelt, transzendental möglich macht.’

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also gestures and verbal utterances, and, thus, did not need to especially stress their relevance. In other writings, however, he was more explicit, leaving no doubt as to whether facial expressions, gestures and verbal utterances were especially important for the similarity basis of the analogical apperception. I will now quote passages from each of the three volumes of Zur Phänomenologie der Intersubjektivität, in order to eliminate any possible doubt about the inclusion of facial expressions, gestures and verbal utterances in the basis for the analogical apperception. In empathy one shall distinguish: 1) The understanding of the animated body as the comprehended zero point of an oriented surrounding. 2) The understanding of bodily “exteriorizations”, “expressions” of the states of the other, attitudes, behavioural forms, intentions and so forth, or even of the manifesting character. As expression in the play of facial expressions, in the gestures. [Zur Phänomenologie der Intersubjektivität I, p. 435]47 The verbal utterances, then the intentionally spoken discourse “belong” to the external bodyliness…. Certainly that can also be apperceived as external effect. But as exteriorizations they express internality and belong to the internal bodyliness, that is, to the region of the “I generate”. “I move”, “I actuate”. [Zur Phänomenologie der Intersubjektivität II, p. 327]48 To the latter, to consider them now, belong the non-arbitrary expressions of the experiencing that which one can properly observe in them, that is, “the others” in their bodily behaviour and apperceptively attribute them, as well as the mediate expressions of their lives …. But further [belong] the intentional and in particular linguistic communications. [Zur Phänomenologie der Intersubjektivität III, p. 220]49

Those passages – from 1913, 1924 and 1931, respectively – are sufﬁcient to make it clear that for Husserl gestures, facial expressions and verbal utterances are an important part of the background that makes possible the analogical apperception of the other psyche, and it seems unnecessary to insert new quotations. Other especially relevant passages occur, for example, on pp. 435–6 of the ﬁrst volume (from 1918), and on pp. 83 (from 1930), 664 and 664–5 (from 1935) of the third volume of Zur Phänomenologie der Intersubjektivität.

47 ‘In der Einfühlung ist wohl zu unterscheiden: 1) Das Verstehen des Leibes als des eingefühlten Nullobjekts in einer orientierten Umwelt. 2) Das Verstehen leiblicher ‘‘Äusserungen’’, ‘‘Ausdrücke’’ der fremdlichen Zustände, Stellungnahmen, Verhaltensweisen, Absichten etc. oder gar des sich bekundenden Charakters. Als Ausdruck im Mienenspiel, in der Geste.’ 48 ‘Die Lautäusserungen, dann die absichtlich gesprochene Rede ‘‘gehören’’ zur Aussenleiblichkeit…. Doch kann das auch schon als äussere Wirkung apperzipiert werden. Als Äusserungen aber drücken sie Innerlichkeit aus und gehören zur Innerleiblichkeit, bzw, zum Gebiet des ‘‘ich erzeuge’’, ‘‘ich bewege’’, ‘‘ich wirke’’.’ 49 ‘Zu den letzteren, um nun auf sie einzugehen, gehören die unwillkürlichen Ausdrücke des Erfahrens, das, was man ihnen “scil. Den Anderen” in ihren leiblichen Gehaben selbst ansehen kann und apperzeptiv ihnen einlegt, ebenso wie die mittelbaren Ausdrücke ihres Lebens…. Dazu aber die absichtlichen und im besonderen sprachlichen Mitteilungen.’

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The similarities between Carnap’s and Husserl’s treatments of intersubjectivity are now perfectly evident. They both grounded the constitution of subjectivity, ﬁrstly, on the constitution of the body of the constitutional subject, assigning the animated body the same characteristics, and, secondly, on the constitution of another body, the body of the other, having a similar behaviour as that of the body of the constitutional subject, including not only kinaesthesia, but also facial expressions, gestures and verbal utterances. The constitution of the other psyche, the heteropsychological, occurs in both cases not directly – I cannot have any ﬁrst hand contact with the experiences of consciousness of another I – but by means of a sort of empathy based on the observed similarities, an empathy that conduces the constitutional subject to assign a psyche to the other animated body similar to his own psyche. It is very difﬁcult to think that the young Carnap, who, besides Logische Untersuchungen, had already read the ﬁrst volume of Ideen, and who was studying with Husserl in the years 1924–25, while writing Aufbau, did not receive Husserl’s inﬂuence on most, if not all the points that I have brought in this and the preceding chapter. Moreover, the fact, attested by the then assistant to Husserl, Ludwig Landgrebe, that they – that is he and Carnap – used to have philosophical discussions in those days, and the fact that Landgrebe was then working on the manuscripts for the second volume of Ideen – whose subtitle in English translation is: Phenomenological Investigations on Constitution – make it highly probable that Carnap was seriously inﬂuenced by Husserl’s not only published but especially still unpublished work on all those points. Indeed, as I have shown in the preceding chapter, Carnap viewed his constitutional system as dependent or founded on phenomenological research. Whereas Husserl used the phenomenological approach directly in the constitution of the hierarchy of objects belonging to different strata, Carnap presupposed the results of phenomenology in the constitution of the same hierarchy of stratiﬁed objects, while using the tools from logic, especially, Russell’s theory of relations. And though Husserl would probably had disagreed with Carnap over that utilization of his results, the young Carnap probably conceived Aufbau in those years, and until his arrival in Vienna, as a continuation and application of Husserl’s work done by one of his disciples, and probably would have had no misgivings in giving Husserl the proper acknowledgement. His immediate contact with Schlick and Neurath after his arrival in Vienna, the hostility of both of them to Husserl’s views, together with the extremely strong personality of Neurath and the fact that Schlick was an academically very powerful full professor in a rigid hierarchical university system and in very difﬁcult post-war years probably made Carnap ‘forget’ his especially important intellectual debt to Husserl, the young Carnap’s unknown master. Nonetheless, after Neurath’s death in 1945, Carnap still had some twenty-ﬁve years to acknowledge Husserl’s decisive inﬂuence on Aufbau and elsewhere, but opted to remain silent. In particular, Carnap’s autobiography in the Schilpp volume represented a golden opportunity to amend such conscious oblivion, but it turned out to be one more chapter of his selective amnesia.

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4 A Critical Assessment of the Husserl-Carnap Solution Husserl’s and Carnap’s attempts at a solution to the problem of intersubjectivity had an epistemological objective, as well as ethical implications. The epistemological objective was to offer a rigorous foundation of objective scientiﬁc knowledge in the sense of intersubjective knowledge. The ethical implications are not made explicit in the texts I have been considering, but are concerned with the acknowledgement of other human beings as constitutional subjects in their own right, in principle, equally endowed as the original constitutional subject, and capable of building together a community of equals. However, the very similar argumentations of Husserl and Carnap are not completely compelling. The problem lies essentially in giving equal weight to the different sorts of ‘psychic’ manifestations of the animated body of the other, without calibrating their important differences. Surely, the kinaesthesia of other bodies different from the already constituted animated body of the constitutional subject could justify the assignment of some sort of psychic principle to that body. The constitutional subject can very well observe that bodies of very different shapes and sizes seem to move on their own, for example, the bodies of ants, of dogs or crocodiles, and could assign those bodies some sort of psychic principle. Nonetheless, there is no reason to assign them the status of an embodied constitutional subject equally endowed as the original constitutional subject, that is, the status of another human being. Moreover, even if the animated bodies observed were much more similar to the body of the constitutional subject, he is not compelled, on the basis of pure kinaesthesia, to assign those bodies via empathy the status of other human beings. Furthermore, even in the case where the other animated bodies make expressions of anger or fear, or other gestures that could be subjectively interpreted by the constitutional subject as similar to his own expressions of anger, fear or whatever, that would not be compelling for the assignment of the status of another human being, but in the best of cases could only serve to acknowledge some sort of psychic principle guiding the behaviour of those animated bodies. In fact, a monkey could very well mimic the facial expressions and gestures of the constitutional subject, without the latter being compelled to assign the monkey the status of another human being. Incidentally, a robot or some sort of machine could be so endowed as to mimic both the movements and the gestures of the constitutional subject, but the latter would still not be compelled to assign it the status of another human being. Indeed, Husserl was conscious of similar difﬁculties and in Zur Phänomenologie der Intersubjektivität tried to distinguish between normal others and abnormal others, including in the last category animals and children. This brings us to the core of the problem under consideration. The situation is completely different when we consider the linguistic expressions. The constitutional subject could have encountered an animated body that looks very similar to his own body, capable of similar kinaesthesia as his animated body, and capable of facial expressions and gestures similar to those of his own body. But he is still not compelled to assign via empathy the status of another human being, that is, of another embodied constitutional subject completely similar to the embodied I, to the psychic principle governing his animated body. However, when the other animated body makes verbal utterances that the constitutional subject understands,

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when the other animated body can verbally communicate with the constitutional subject, the latter immediately understands that, the phenomenological reductions and the suspension of judgement notwithstanding, the language that he understands has not been generated or created in the stream of consciousness of the constitutional subject, but is a language he shares with the psychic principle of the other animated body – and of each similarly endowed psychic principle of an animated body. Hence, it is an intersubjective language. Even if the constitutional subject had added some technical terminology to that language with the purpose of better grasping his phenomenological distinctions, the core of the language is intersubjective, not created by the constitutional subject. Hence, the constitutional subject is compelled to assign the status of an equally endowed embodied constitutional subject to any psychic principle of animated body, with which he can communicate by means of this intersubjective language. Thus, is built the community of constitutional subjects, each acknowledging that they share a language not created by any of them, and in principle capable of sharing intersubjective knowledge. This knowledge and, especially, scientiﬁc knowledge of nature could then be conceived, as Carnap already pointed out,50 as concerned with equivalence classes of the objects objectiﬁed by the different psychic principles of animated bodies. Furthermore, since each constitutional subject, now with the status of human beings, is, in principle, capable of learning any human language, the community of, in principle, equally endowed human constitutional subjects can be extended to include all psychic principles of animated bodies capable of communicating in any human language. In this way is built a world community of human subjects, equally endowed in principle, to learn any human language and bounded by the intersubjective chain of those human languages, which is the immediate ground of their equal humanity and the foundation of an intersubjective acquisition of science and knowledge. Although I cannot dwell on this issue here, it is clear that the present solution to the problem of intersubjectivity has ethical consequences. The constitutional subject, by acknowledging the intersubjectivity of his own language, as a language he shares with others, is compelled also to acknowledge the existence of other human beings, equally capable of constituting their common world, including the original constitutional subject. The grounds for any principled or essential difference between the constitutional subjects disappear. Each human being is a constitutional subject in his own right and in principle equal to each other. An autonomous equalitarian ethics can be founded on the solution to the problem of intersubjectivity, an ethics grounded on rationality – not on the dogmas and irrational fears of traditional religions or the obscurantism of a self-proclaimed ‘scientiﬁc materialist’ secular religion – and capable of serving as a rigorous foundation for the claim for equality and justice in all those aspects of the lives of all human beings that depend exclusively on what is essential or substantial for human existence. Hence, the solution to the problem of intersubjectivity could serve both as a non-Kantian autonomous foundation of ethics and as an ethical foundation of a genuine equalitarian society and community of societies of all human beings. Such issues, however, are not the concern of this work.

50 See the passage of Aufbau, p. 199 quoted on p. 86, footnote 29.

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Finally, in order to avoid any misunderstandings of my trend of thoughts, it must be pointed out that in the above approach to a solution to the problem of intersubjectivity I am not pretending that the point of departure of Husserl and Carnap of the methodological suspension of judgement was faulty from the very beginning because the constitutional subject was already in some sense a prisoner of language.51 On the contrary, my attempt at a solution presupposes the acceptance of the legitimacy of the problem and of Husserl’s methodological standpoint. I am convinced that if the constitutional subject were never to encounter any other psychic principle of another animated body, who communicated in a language understood by the constitutional subject, the latter probably could not even distinguish the language used from the conceptual distinctions for which the language is used, and, of course, would never have had to acknowledge that his language is an intersubjective language, not his own creation or, more generally, not a constitutive trait of his own subjectivity. Only through the encounter with another psychic principle of an animated body that speaks the same language does the embodied constitutional subject acknowledge the intersubjectivity of language and is compelled to recognize the existence of other similarly embodied and equally endowed constitutional subjects, that is, of other human subjects. Hence, this proposal of a solution to the intersubjectivity problem should by no means be understood as an attempt at dissolving the problem by charging it of being based on confusions or of being trivial, or whatever. On the contrary, it takes the problem of intersubjectivity very seriously and tries to amend the HusserlCarnap solution. It builds on the shoulders of the Husserl-Carnap solution, and has nothing to do with ordinary language sophistry.

51 In particular, my critique of the Husserl-Carnap solution to the problem of intersubjectivity should be clearly distinguished from Suzanne Cunningham’s Wittgensteinian critique of Husserl’s approach to the problem of intersubjectivity in her Language and the Phenomenological Reductions of Edmund Husserl (Den Haag, 1976).

Chapter 4

Carnap, Husserl and Analytic Philosophy 1 Trails of Husserl’s Inﬂuence in Carnap’s Middle Period After the publication of Aufbau Carnap moved away from Husserlian inﬂuence, adopting the views for which he is mostly known, namely the views usually associated with the names ‘logical empiricism’ or ‘logical positivism’. Of course, from 1928 until the end of his life Carnap’s views experienced important changes, but none so decisive as that which separates his ﬁrst from his middle period. One should not underestimate his extension of logical syntax to semantics, or his struggles with the criteria of meaning, nor his pioneering work in the semantics of modal logic, nor his attempts at building an inductive logic. But all those changes occur under the general assumptions of logical empiricism, namely, that all knowledge about the world is empirical, that non-empirical statements about the world are senseless and, thus, there do not exist any statements that are both synthetic and a priori, that logic and mathematics are completely devoid of meaning but serve the important purpose of establishing the formal deductive relations between empirical statements, and, ﬁnally, that the role of philosophy is the logical analysis of language or (and) the logical analysis of science. Some of those traits of logical empiricism – which were completely absent in Der Raum – were already present in Aufbau, though not in as sharp a form as in Carnap’s post-Aufbau philosophy, and certainly not all of them were present. Incidentally, it is very difﬁcult to render what Carnap does in Aufbau as logical analysis either of science or of language. Indeed, it is much more adequate to say that what Carnap does in Aufbau is a logical reconstruction, especially with the tools of Russell’s theories of relations and classes, of Husserl’s phenomenological theory of constitution. Nonetheless, it should be stressed that in comparison with former empiricist philosophies the views of Carnap and most logical empiricists – with the exception of Neurath – were relatively moderate, due to the acknowledgement of the importance of logic and mathematics and the characterization of their statements as analytic. It had afﬁnities with Hume and with Russell, but was clearly very dissimilar to the more radical empiricisms of Locke and Mill. However, though by 1930 Carnap had distanced himself radically from Husserl’s views, there still remained a few traces of Husserl’s distinctive views in some of Carnap’s writings of the middle period of the 1930s. I will point to two especially clear cases without attempting to be exhaustive. The ﬁrst one is the distinction made by Carnap in ‘Überwindung der Metaphysik durch logische Analyse der Sprache’1 1 ‘Überwindung der Metaphysik durch logische Analyse der Sprache’, 1932, reprint in Scheinprobleme in der Philosophie und andere metaphysikkritische Aufsätze, Thomas Mormann (ed.), (Hamburg, 2004), pp. 81–109.

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between two sorts of meaningless sentences, namely those that contain a word devoid of any meaning and those that violate the laws of logical grammar.2 Those distinctions were already clearly made by Husserl more than thirty years before in the Fourth Logical Investigation of his Logische Untersuchungen,3 a book that Carnap seems to have already read before he ﬁnished his dissertation.4 According to Husserl, there are two sorts of meaningless expressions, namely, those that alone do not have any sense – like abracadabra5 – and presumed statements, all of whose constituents have sense, but that violate the rules of logical grammar. Carnap, of course, does not refer to Husserl as the source of that distinction, but that does not weaken in any way my contention that he learned it from Husserl. Another important distinction made by Carnap in his middle period and which became not only one of his standard distinctions, but also part of the most basic nucleus of modern logic, is the distinction between formation rules and transformation rules made at the very beginning of Die logische Syntax der Sprache.6 That distinction was clearly made by Husserl in Chapter Eleven of the ﬁrst volume of Logische Untersuchungen thirty-four years before, and reiterated in the ﬁrst part of his Formale und transzendentale Logik7 of 1929. As pointed out above, Carnap was clearly familiar at least with Husserl’s Logische Untersuchungen. The distinction between formation rules – in Husserl’s terminology, ‘rules that protect against nonsense’ – and transformation rules, rules that allow us to derive sentences from sentences and, as Husserl sometimes said, ‘protect against (formal) countersense’, are neither Carnap’s, nor Frege’s, nor Russell’s or Whitehead’s or Hilbert’s, but Husserl’s. I have already stressed this point in many writings, beginning with my dissertation of 1973,8 but the ﬁrst scholar, so far as I know, who pointed out this issue was Yehoshua Bar-Hillel in his paper ‘Husserl’s Conception of a Purely Logical Grammar’ in 1956.9 In any case, it has been a clear injustice of scholars in the history of logic never to acknowledge that this basic distinction was stated very clearly for the ﬁrst time in Husserl’s Logische Untersuchungen.10 2 On Husserl’s inﬂuence on ‘Überwindung der Metaphysik durch logische Analyse der Sprache’, see also Thomas Mormann’s excellent overview of Carnap’s work in his Rudolf Carnap (Munich, 2000), p. 47. 3 See Logische Untersuchungen II, U. I, § 15. See also U. IV, § 12. 4 Logische Untersuchungen is included in the references of both Der Raum and Der logische Aufbau der Welt. Thus, one can very well assume that Carnap was already acquainted with that book when he wrote his dissertation, though he usually does not refer speciﬁcally to it. 5 It is a triviality that a presumed statement containing such a presumed word does not have any sense and is no statement at all. 6 Die logische Syntax der Sprache (1934, English revised edition 1937, reprint, Chicago et al., 2002). 7 Formale und transzendentale Logik (1929, Den Haag, 1974). 8 Edmund Husserls Philosophie der Logik und Mathematik im Lichte der gegenwärtigen Logik und Grundlagenforschung (1973, Bonn). 9 ‘Husserl’s Conception of a Purely Logical Grammar’, (Philosophy and Phenomenological Research 17, 1956): 362–9. 10 In a recent important paper, namely, ‘Husserl on “the Totality of All Conceivable Arithmetical Operations”’ (History and Philosophy of Logic 27, No. 3, 2006): 211–28, Stefania

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In Carnap’s later period there could still be some traces of Husserl’s inﬂuence but in some cases so diluted that it is far too difﬁcult to really assess whether there was some inﬂuence or not. As an example, I should mention that in Meaning and Necessity11 Carnap correctly sided with Husserl and against Frege with regard to the referent of predicates. Thus, he considered that the referents of predicates are extensions of concepts, whereas the concepts are the senses of those predicates. That was essentially Husserl’s view on that issue, but since Frege’s view that the concepts were the referents of predicates was so questionable, Carnap did not need to take from Husserl what was in any case so clear. A clearer case of Husserl’s inﬂuence in Carnap’s late period has been stressed recently by Michael Beaney in his interesting paper ‘Carnap’s Conception of Explication: from Frege to Husserl?’,12 in which he points out to an acknowledgement made by Carnap – in his peculiar masquerading style – in his Logical Foundations of Probability13 of some possible inﬂuence of Husserl on his notion of explication. In the passage referred to by Beaney, Carnap mentions that his notion of explication has afﬁnities with similar notions present in Langford, Kant and Husserl. Although Schlick and Neurath were already dead, Carnap’s reference to Husserl is similar in style to those of Aufbau, namely, though the most strong afﬁnity is with Husserl, Carnap tries to dilute Husserl’s inﬂuence by inserting his name in a list of authors with vague or remote afﬁnities to his own views. Thus, Beaney points out that Carnap’s notion of explication is much nearer to Husserl’s than to Kant’s.14 Nonetheless, as many Fregean and Carnapian scholars, Beaney is completely ignorant of the true relationships between Husserl and their pet philosophers, and states15 that Carnap learnt about the afﬁnity of his notion of explication with Husserl’s indirectly, namely, from an article that appeared in 1942 in The Dictionary of Philosophy, edited by Dagobert Runes.16 Beaney is completely ignorant of the fact that Carnap was a student of Husserl at least during three semesters in the years 1924–25 and, moreover, that he had already read Logische Untersuchungen and Ideen I when he wrote Der Raum, where references to Husserl are neither omitted nor adulterated, as occurs in his later work. Furthermore, Beaney is also completely ignorant about Carnap’s conscious tendency of masquerading Husserl’s inﬂuence on his views.

Centrone argues that Husserl’s notion of all conceivable operations in his Philosophie der Arithmetik (1891, Den Haag, M. Nijhoff 1970) is extensionally equivalent to the notion of partial recursive function introduced by Kleene some ﬁfty years later. Centrone’s assertions, if correct, will most surely require an important revision of the history of contemporary logic and of the theory of computability. 11 Meaning and Necessity (Chicago, 1947). 12 Michael Beaney, ‘Carnap’s Conception of Explication: From Frege to Husserl?’, in Steve Awodey and Carsten Klein (eds), Carnap Brought Home (Chicago et al., 2004), pp. 117–50. 13 Logical Foundations of Probability (Chicago, 1950), p. 3. 14 Michael Beaney, ‘Carnap’s Conception of Explication: From Frege to Husserl?’, p. 136. 15 Ibid., p.135. 16 Dagobert Runes (ed.), The Dictionary of Philosophy (New York, 1942), p. 105.

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It is clear that Beaney’s understanding of Husserl is very limited. He seems never to have read Logische Untersuchungen, Ideen or Formale und transzendentale Logik. In the references of the paper referred to above only Philosophie der Arithmetik and Erfahrung und Urteil17 are mentioned, and in his selection of Frege’s writings The Frege Reader18 only Husserl’s youth work, Philosophie der Arithmetik is referred to. But Beaney is by no means an exception among analytic philosophers. It is already a sign of progress that in his paper he also refers to Husserl’s Erfahrung und Urteil. To refer exclusively to a youth book of a philosopher – in Husserl’s case, to Philosophie der Arithmetik – while ignoring his most important writings is one of the worst possible sorts of philosophical scholarship. If scholars had referred only to Frege’s Begriffsschrift19 and completely ignored his later writings, he would have been still considered an epoch-making logician, but would have been rightly forgotten as a less than mediocre philosopher. Similarly, if scholars had referred only to Kant’s youth writing De mundis sensibilis atque intelligibilis,20 he would have been completely forgotten a few years after his death. Incidentally, in the Introduction to his The Frege Reader Beaney repeats, as also does Carnap on p. 40 of his Logical Foundations of Probability, one of the two parts of the myth in analytic circles of Frege’s inﬂuence on Husserl, namely, that Husserl abandoned his psychologistic views of Philosophie der Arithmetik under the inﬂuence of Frege, more speciﬁcally, of Frege’s critical review of 1894 of Husserl’s ﬁrst book. The other part of the myth, based on Føllesdal’s writings,21 consists in assigning Husserl’s notion of noema a Fregean origin, namely, as a generalization of Frege’s distinction between sense and referent. As already mentioned, only if it were possible for the future to causally affect the past could Frege had inﬂuenced Husserl on this last point, since Husserl knew of Frege’s distinction in May of 1891, when Frege sent him a copy of his recently published ‘Funktion und Begriff’ and, thus, after he had already made essentially the same distinction in his recently published review of Schröder’s Vorlesungen über die Algebra der Logik I,22 and a year after he 17 Erfahrung und Urteil (1939, sixth edition, Hamburg, 1985) 18 In his collection of Frege’s writings, The Frege Reader (Oxford, 1997) only Philosophie der Arithmetik is referred to or even included in the references. It should be stressed that Beaney’s is not an isolated case, but an example of a general trend among Fregean scholars, who in this sense resemble more Marxist or religious ‘scholars’ than responsible philosophical scholars. Indeed, there is no essential difference between Stalinist reconstructions of pictures of the early bureaucratic (though so-called ‘socialist’) regime in Russia, in which Trotski has been blanked out completely, and the writings of most current Fregean scholars, who treat Husserl as already dead by 1891 – or even earlier – and who only acknowledge that he wrote Philosophie der Arithmetik. 19 Begriffsschrift 1879, reprint (Hildesheim, Georg Olms, 1964). 20 De mundis sensibilis atque intelligibilis 1770, reprint in volume V of Wilhelm Weischedel (ed.), Theorie-Werkausgabe Immanuel Kant (second edition, Frankfurt, 1978), pp. 12–107. 21 See, for example, his MA thesis Husserl und Frege (Oslo, 1958) and ‘Husserl’s Notion of Noema’, Journal of Philosophy 66 (1969): 680–87. 22 ‘Besprechung von E. Schröders Vorlesungen über die Algebra der Logik I’ (1891, reprinted in Edmund Husserl, Aufsätze und Rezensionen: 1890–1910, Den Haag, 1979), pp. 3–43.

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introduced the distinction in his posthumously published ‘Zur Logik der Zeichen’.23 Indeed, it was Frege, the ﬁrst of the two great philosophers, who became acquainted with the fact that the other had already reached the distinction. Precisely in his letter of 24 May 1891 to Husserl, referred to in Beaney’s recent paper, Frege acknowledges that Husserl had made the distinction in his review of Schröder’s book, but Beaney, as does almost every Fregean scholar, usually ignores any evidence that could wake him up from his comfortable mythology. Concerning the other part of the myth, it should ﬁrst be pointed out that Philosophie der Arithmetik, though published at the beginning of 1891, is essentially an expansion of Husserl’s professorship writing Über den Begriff der Zahl of 1887 and presents Husserl’s views up to 1889 or 1890. Already about 1890 the study of Cantor and Riemann on the one hand, and of Bolzano and Leibniz, on the other hand, began to move Husserl away from the Brentanian brand of psychologism of his Philosophie der Arithmetik, which, as a matter of fact, did not have much in common with Frege’s caricature of the young Husserl’s views in his review so dear to Fregeans. The fact that his views were changing was the reason why he did not publish a second volume to that book, which was supposed to follow almost immediately the publication of the ﬁrst. In any case, if one wants to really learn about Husserl’s abandonment of his youth views, it is pertinent to consult the Appendices to the Husserliana edition of Philosophie der Arithmetik, his early studies on the foundations of arithmetic and geometry, published posthumously under the title Studien zur Arithmetik und Geometrie24 and his Aufsätze und Rezensionen: 1890–1910. The fact of the matter is that, as attested in his Introduction to the Logical Investigations,25 his mature philosophy of logic and mathematics – indeed a non-logicist sort of structural Platonism, with afﬁnities to Bourbaki and inﬂuence from Riemann26 – was already arrived at by 1894–95, and his critiques of psychologism were ﬁrst presented in courses of 1895–96. Husserl’s mature views on logic and mathematics are essentially different from Frege’s, having rejected reductionisms of the logicist or set-theoreticist sorts already by 1890.27 Moreover, as I have shown elsewhere,28 Husserl’s critique of psychologism is far more sophisticated than Frege’s, and it is no accident that it was Husserl, much more than Frege, who was responsible for the refutation of psychologism.

23 ‘Zur Logik der Zeichen’ dates from 1890, but was ﬁrst publihed as an Appendix to the Husserliana edition of Husserl’s Philosophie der Arithmetik (Den Haag, 1970), pp. 340–73. See pp. 343–4. 24 Studien zur Arithmetik und Geometrie (Den Haag, 1983). The texts included in that book date from 1886–1901. 25 Introduction to the Logical Investigations (Den Haag, 1975), especially pp. 32–8, where Husserl discusses in detail the development of his thought from Philosophie der Arithmetik to Logische Untersuchungen. 26 On this issue the reader can consult, besides my already mentioned dissertation, my recent paper ‘Husserl’s Philosophy of Mathematics: its Origin and Relevance’ (Husserl Studies 22, 2006): 193–222. 27 See Studien zur Arithmetik und Geometrie, pp. 244–51. 28 See my reconstruction of Husserl’s argumentation in ‘The Structure of the Prolegomena’ (Manuscrito 23, 2, 2000): 61–99.

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It is time for scholars in analytic circles to revise their views on the early history of analytic philosophy and its relation to Husserl’s views. As I see the relation between Frege and Husserl, it has some partial similarities with the relation between Leibniz and Kant, though the latter pair was not one of contemporaries. The possible inﬂuence of Frege on Husserl is not as immediate and direct as Fregeans would want. Husserl made it clear in Philosophie der Arithmetik that his criticism of Frege’s views notwithstanding, he had a very high opinion of Frege’s philosophical capabilities. In some sense, the early writings of Frege set a standard of rigour that was not ignored by Husserl, and the former’s well thought solutions to problems in the philosophy of mathematics probably motivated Husserl to examine those issues more thoroughly and to reﬂect on Frege’s views immediately before and after the publication of Philosophie der Arithmetik. Something similar occurred to Kant with respect to Leibniz. The writings of the latter motivated Kant in his theoretical philosophy, and the mere fact that there had been a Leibniz most probably played a role in the high standards that Kant set himself in his theoretical philosophy. In both cases, the extraordinary logician and very important philosopher set the very high standards for the even greater philosopher. In the case of Frege and Husserl, however, since they were contemporaries, there was some possible inﬂuence in the same sense the other way around. Thus, it is not an accident that late in his life Frege used an example from Husserl’s Logische Untersuchungen to explain the distinction between sense and reference.29 Hence, it seems very probable that Frege read at least part of that work.30 Incidentally, Husserl’s treatment of indexes in the First Logical Investigation has important afﬁnities with Frege’s later treatment in ‘Der Gedanke’,31 though it would not be appropriate to speak of any decisive inﬂuence of Husserl on Frege.32 Most probably, Husserl’s Logische Untersuchungen played the role of a distant echo in the older Frege, in a similar fashion to that which Die Grundlagen der Arithmetik played in Husserl before his transcendental turn. 29 See Frege’s letter to Paul F. Linke, dated 24 August 1919, in Wissenschaftlicher Briefwechsel (Hamburg, 1976), pp.153–6, especially p. 156. I thank Claire O. Hill for having brought this passage to my attention almost a decade ago. 30 Both Husserl’s example and his treatment of indexes mentioned in the next sentence occur in the second volume of Logische Untersuchungen, namely, in Chapter One, § 12 and Chapter Three, § 26. 31 ‘Der Gedanke’ 1918, reprinted in Frege’s Kleine Schriften (Hildesheim, 1967, 1990), pp. 342–62. See especially pp. 349–50. 32 In fact, in what seems to be the sketch of his later paper ‘Der Gedanke’, namely, in his ‘Logik’ of 1897, Frege already brieﬂy considers the problem of the indexes. See his Nachgelassene Schriften (Hamburg,1969, revised edition 1983), pp. 137–63, especially p. 146. Nonetheless, the discussion of indexes in that paper is not only brief and incomplete, but also more distanced from Husserl’s treatment of indexes in Logische Untersuchungen than that of ‘Der Gedanke’. Thus, it is not excluded that Husserl’s analyses exerted some mild inﬂuence on Frege’s discussion of indexes in the latter paper. However, since Husserl’s and Frege’s views on – what Husserl called – ‘the ideality of meanings’– in Frege’s terminology: ‘objectivity but inactuality (that is, lack of physical reality) of sense’ – were so similar, it is possible that Frege’s completion of his brief analysis of indexes in 1897 would have brought him nearer to Husserl’s views in a natural, spontaneous way.

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Finally, it should be mentioned here that there are other issues dear to logical empiricism, like the deductive-nomological model both for the explanation of facts and for the explanation of laws of lower level, that seemed to have been anticipated by some somewhat marginal remarks of Husserl, while contrasting logical-mathematical theories with physical theories, in the ﬁrst volume of Logische Untersuchungen,33 though such issue does not concern Carnap in particular, but especially Hempel and Popper, and could very well be a coincidence. Another related point, in which Husserl’s views have some afﬁnities with an important school of present-day philosophy, though one cannot here speak of any direct inﬂuence, has been discussed by Thomas Mormann in his paper ‘Husserl’s Philosophy of Science and the Semantic Approach’.34 Mormann shows that there are some afﬁnities between Husserl’s scattered views on scientiﬁc theories and the views of current structuralism of Sneed, Stegmüller, Moulines, Balzer and others. It should be stressed here that such a similarity is by no means a surprise, since Bourbaki’s views on mathematics have clearly inﬂuenced the structuralist’s philosophy of science, and Husserl’s views on mathematics are very similar to those of Bourbaki. 2 Carnap’s Later Views and Analytic Philosophy Carnap’s views from the middle of the 1930s on are very well known. His acceptance of Tarski’s semantics brought him some critique by the most radical of all logical empiricists, Otto Neurath. In some sense, Carnap was developing an empiricism that was not empiricist enough to please not only Neurath but also his new partners in the United States of America. Indeed, with Carnap’s and others’ forced emigration to the United States and elsewhere, logical empiricism lost some of its features. The allegiance to empiricism was deﬁnitive, but even then their empiricism was not radical enough for the tastes of some Anglo-American philosophers schooled in American pragmatism and inﬂuenced by the behaviourist trend in psychology. On the other hand, the fact that in his research in philosophy of science from a logical empiricist perspective, Carnap was forced to liberalize more than once his empiricist criteria of (empirical) meaning, but even then at the end all his proposals failed, was clearly seen as an unmistakeable sign of failure of his programme by so diverse philosophers as his radical empiricists critics and non-empiricists like Popper. In fact, during the three decades from 1940 to 1970 Carnap’s views were under siege from very different sides. Their demise is usually attributed either to Quine’s criticism of Carnap’s analytic-synthetic distinction, or to Thomas Kuhn’s views on the history of science – which seemed at ﬁrst sight to collide with Carnap’s unhistorical analysis of empirical science – or to a combination of both. I think that such interpretations of the demise of Carnap’s views, in particular, and of logical empiricism, in general, are completely out of focus. The historical investigations of Kuhn and others – whose historical analyses have been, incidentally, questioned by

33 See Logische Untersuchungen I, Chapter IV, § 23 and Chapter XI, §§ 63, 64 and 72. 34 ‘Husserl’s Philosophy of Science and the Semantic Approach’, (Philosophy of Science 58, 1991): 61–83.

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more than one historian and philosopher of science35 – represented no real menace to Carnap’s systematic investigations. Historical investigations of science can at best be complementary to the systematic investigations of the nature of science, but by no means can they replace them. The very interesting development of the structuralist trend of Sneed, Stegmüller, Moulines, Balzer and others in the philosophy of science,36 as well as the investigations by the school of Veikko Rantala, David Pearce and others,37 the school of the physicist Günther Ludwig,38 and the investigations of Erhard Scheibe39 are clear examples of the fruitfulness and relevance of systematic analysis of science in the post-Kuhnian era. Moreover, as Stegmüller has shown,40 historical and systematic studies of science are not only compatible, but, moreover, it is perfectly possible to incorporate the dynamic components of science in the more systematic investigations of the structure of science. The demise of logical empiricism was mostly due to the straitjacket of empirical meaning to which it adhered. Although the criteria of meaning were successively liberalized, such liberalizations fell extremely short of doing justice to highly developed empirical sciences, especially to the paradigmatic empirical science of physics. Highly developed empirical sciences like physics are fundamentally theoretical, with an almost completely – if not completely – theoretical vocabulary that connects with experience and observation in complicated and mostly indirect ways via interpretations. Already Duhem,41 some decades before the birth of logical empiricism had clearly shown the difference between what a scientist in the natural sciences ‘observes’ when he makes an experiment and what a layman ‘observes’ when watching the same experiment. Moreover, in the ﬁrst volume of Logische Untersuchungen42 Husserl already distinguishes between laws of lower level in the natural sciences, which are generalizations of the empirically given, and theoretical laws vaguely based on experience, which he calls hypotheses cum fundamento in re, and of which there always exists a wide variety compatible with the empirically given. Incidentally, the otherwise very well schooled in physics Moritz Schlick, Hans 35 See, for example, Stephen Toulmin’s ‘Postscript: The Structure of Scientiﬁc Theories’, in Frederick Suppe (ed.), The Structure of Scientiﬁc Theories (Urbana et al., 1977) pp. 609– 14. See also ibid., I. Bernard Cohen’s extensive contribution ‘History and the Philosopher of Science’, pp. 308–49 for historical analyses clearly different from Kuhn’s. 36 See, for example the joint book of Wolfgang Balzer, Carlos Ulises Moulines and Joseph D. Sneed An Architectonic for Science (Dordrecht, 1987), as well as Stegmüller’s Theorie und Erfahrung (I) Theorienstrukturen und Theoriendynamik (Berlin, 1973, 1985) and (II) Die Entwicklung des neuen Strukturalismus seit 1973 (Berlin et al., 1986). 37 See, for example, David Pearce’s book Roads to Commensurability (Dordrecht, 1987). 38 See his Die Grundstrukturen einer Physikalischen Theorie (Berlin et al., 1978). 39 See Zur Reduktion Physikalischer Theorien (Berlin et al., ﬁrst volume 1997, second volume 1999). 40 See, for example, Stegmüller’s The Structuralist View of Theories (Berlin et al., 1979), as well as his books referred to above. 41 See, for example, his paper ‘Quelques réﬂections au sujet der théories physiques’, reprinted and translated into English in his Essays in the History and Philosophy of Science (Indianapolis, 1996), pp. 1–28. 42 See Logische Untersuchungen I, Chapter Four, § 23 and Chapter Eleven, § 63.

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Reichenbach and Carnap were more conscious in their early philosophical analyses of physics of the complexities of that discipline and its systematic analysis, than were the logical empiricists, and especially Carnap, as they settled in countries like the United States of America or Great Britain, with very strong radical empiricist or pragmatist traditions. 3 On Quine, Against Quine and Beyond The case of Quine and his presumed role in the demise of logical empiricism deserves some attention. First of all, it should be mentioned that his critique of the analyticsynthetic distinction,43 even if it were correct, would be applicable only to Carnap’s version of such distinction. If, for example, you understand by analytic, as Frege did, a statement derivable exclusively from logical axioms and deﬁnitions, without the intervention of any non-logical means, then the distinction between analytic and synthetic would be perfectly clear. Moreover, problematic statements like ‘All unmarried men are bachelors’ would not be analytic on the basis of Frege’s deﬁnition of analyticity. A different issue is, of course, whether such a deﬁnition is satisfactory on other grounds, namely, since after the demise of logicism, the acceptance of such a distinction would put (at least most of) mathematics on the side of the synthetic. That would probably force once more a distinction between empirical and synthetic a priori, drawing the division line more or less where Kant had drawn it – with logic being this time analytic per deﬁnitionem, and (most of) mathematics being synthetic a priori – a view that is nowadays completely unacceptable. Of course, if Frege had been right, since he believed in a moderate version of logicism, namely, in the derivation of the whole of non-geometrical mathematics from logical axioms and deﬁnitions, the synthetic a priori would have been restricted to geometry, a view that though incorrect by today’s standards – at least if understood as Frege did, which is much less sophisticated than Carnap’s views in Der Raum – is nonetheless less preposterous than Kant’s views on the whole of mathematics. There is, however, a different sort of deﬁnition of analyticity in the BolzanoHusserl tradition – or more precisely, Husserl’s deﬁnition, most surely inspired by less clear anticipations in Bolzano’s writings – according to which a statement is analytic if it is true and remains true when it is completely devoid of material content. This notion has indeed some afﬁnities with a notion of logical truth discussed by Quine himself in Philosophy of Logic,44 though it is meant to have a much wider application than the latter. Since Husserl’s deﬁnitions of analyticity and related concepts remain completely unknown by analytic philosophers, it is pertinent to quote Husserl on this issue.45

43 See Quine’s classic paper ‘Two Dogmas of Empiricism’, in From a Logical Point of View 1953 (fourth printing, Cambridge, MA., 1980), pp. 20–46. 44 Philosophy of Logic (Englewood Cliffs, New Jersey, 1970), pp. 49–51. 45 The ﬁrst three quotations are from Logische Untersuchungen II, U. III, § 12, whereas the last one is from the recently published Alte und Neue Logik: Vorlesungen 1908/09, (Dordrecht, 2003), p. 30.

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The Young Carnap’s Unknown Master Analytic laws are unconditionally general laws (and, thus, free from any explicit or implicit postulation of individual existence), which contain no other concepts except formal [ones], [and] thus, when we go back to the primitives, nothing other than formal properties. In comparison with the analytic laws, are their particularizations, which originate by means of the introduction of material concepts and eventually of thoughts postulating individual existence…. As in general, particularizations of laws produce necessities, so particularizations of analytic laws [produce] analytic necessities. What one calls “analytic propositions” are usually analytic necessities. [Logische Untersuchungen II, U. III, § 12]46 Analytically necessary propositions, so can we deﬁne them, are such propositions, which are completely independent from the material peculiarity of their objectualities (determined or conceived in undetermined generality) and from the eventual factuality of the case, from the validity of the eventual postulation of existence; thus, propositions, that allow being completely formalised and [being] considered as special cases or empirical applications of the formal or analytic laws validly obtained by means of such a formalisation. In an analytic proposition it must be possible to replace any material content with the void form something, while completely preserving the logical form of the proposition, and eliminate each postulation of existence by means of passing to the corresponding form of judgement of “unconditional generality” or lawfulness. [Logische Untersuchungen II, U. III, § 12]47 When we have the concept of analytic law and of analytic necessity, thus results eo ipso that of the synthetic a priori law and of the synthetic-aprioristic necessity. Any pure law that contains material concepts in such a way that does not allow a formalisation by means of [replacement of] concepts salva veritate (in other words, any such law that is not an analytic necessity) is a synthetic a priori law. Particularizations of such laws are synthetic necessities; therein, of course, empirical particularizations…. [Logische Untersuchungen II, U. III, § 12]48

46 ‘Analytische Gesetze sind unbedingt allgemeine (und somit von aller expliziten oder impliziten Existentialsetzung von Individuellem freie) Sätze, welche keine anderen Begriffe als formale enthalten, also wenn wir auf die primitiven zurückgehen, keine anderen als formale Eigenschaften. Den analytischen Gesetzen stehen gegenüber ihre Besonderungen, welche durch Einführung sachlicher Begriffe und ev. individuelle Existenz setzender Gedanken … erwachsen. Wie überhaupt Besonderungen von Gesetzen Notwendigkeiten ergeben, so Besonderungen analytischer Gesetze analytische Notwendigkeiten. Was man ‘‘analytische Sätze’’ nennt, sind in der Regel analytische Notwendigkeiten.’ 47 ‘Analytisch notwendige Sätze, so können wir deﬁnieren, sind solche Sätze, welche eine von der sachlichen Eigenart ihrer (bestimmt oder in unbestimmter Allgemeinheit gedachten) Gegenständlichkeiten und von der ev. Daseinssetzung völlig unabhängige Wahrheit haben; also Sätze, die sich vollständig formalisieren und als Spezialfälle oder empirische Anwendungen der durch solche Formalisierung gültig erwachsenden formalen oder analytischen Gesetze fassen lassen. In einem analytischen Satze muß es möglich sein, jede sachhaltige Materie, bei voller Erhaltung der logischen Form des Satzes, durch die leere Form etwas zu ersetzen, und jede Daseinssetzung durch Übergang in die entsprechende Urteilsform ‘‘unbedingter Allgemeinheit’’ oder Gesetzlichkeit auszuschalten.’ 48 ‘Haben wir den Begriff des analytischen Gesetzes und der analytischen Notwendigkeit, so ergibt sich eo ipso der des synthetischen Gesetzes a priori und der synthetisch-apriorischen Notwendigkeit. Jedes reine Gesetz, das sachhaltige Begriffe in einer Weise einschließt, die eine Formalisierung durch Begriffe salva veritate nicht zuläßt (m. a. W. jedes solche Gesetz, das keine analytische Notwendigkeit ist) ist ein synthetisches Gesetz a priori. Besonderungen

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A deductive inference is then an analytic-logical or formal-logical if the rise to form and law can be carried out so purely that no term with material content remains not-formalised. [Alte und Neue Logik: Vorlesungen 1908/09, p. 30]49

The Bolzano-Husserl50 notion of analyticity is not only immune to Quine’s criticism, but also not vulnerable to the difﬁculties that make very implausible the Fregean deﬁnition of analyticity. In particular, it is completely independent of a logicism that Husserl never propounded and, on the other hand, on its basis statements like ‘All unmarried men are bachelors’ are not analytic, since their truth depends on its material content. But the point that I am trying to emphasize here is that Quine’s argumentation, even if correct with respect to Carnap’s deﬁnition of analyticity, has a parochial nature, and would not apply either to Frege’s or to Husserl’s notions of analyticity. Certainly, the Bolzano-Husserl approach to analyticity is much more promising than Frege’s. However, one could possibly ask Husserl to make his notion of ‘formalization’ more precise, since even if logic and foundational mathematical theories were completely formalizable, in the sense of remaining true after all nonlogical constants have been replaced by variables, someone could still argue that at ﬁrst sight theories like, for example, the theory of rings or that of metric spaces, and, of course, real analysis – which are part of abstract mathematics but not foundational theories, like set theory or category theory – could not be completely formalized in that sense. Such an objection, however, is not totally compelling. Nonetheless, the situation is more serious with respect to results in the (more concrete) number theory, which seem not to be completely formalizable in the sense of Husserl’s deﬁnition of analyticity. I will return brieﬂy to this issue later, but will in any case opt to take another route to the problem of deﬁning analyticity, and distinguish between logical truth and analyticity. Indeed in the second volume of his outstanding recent book Logical Forms51 the Brazilian philosopher Oswaldo Chateaubriand characterized logical truth in terms very similar to Husserl’s characterization of analytic law and, moreover, instances of logical laws in terms very similar to Husserl’s analytic necessities. I think that Chateaubriand’s terminology is more adequate than Husserl’s, since it allows for a different use of the term ‘analytic’.52 Thus, I will offer a deﬁnition solcher Gesetze sind synthetische Notwendigkeiten; darunter natürlich auch empirische Besonderungen ….’ 49 ‘Ein deduktiver Schluss ist dann ein analytisch-logischer oder formal-logischer, wenn der Rückang auf Form und Gesetz so rein zu vollziehen ist, dass kein sachhaltiger Terminus unformalisiert bleibt.’ 50 For Bolzano’s related, but also less clear views, see the excellent book by Jan Sebestik, Logique et Mathématiques chez Bernard Bolzano (Paris, 1992), pp. 216–18. See also § 148 of Bolzano’s Wissenschaftslehre, reproduced in Friedrich Kambartel’s selections from volumes I and II of that work, under the title Grundlegung der Logik (Hamburg, 1963, revised edition 1978), pp. 230–35. 51 Logical Forms I and II (Campinas, 2001, 2005). See II, Chapter 18, especially pp. 254–5 and 262. 52 On the issue of logical truth one should also take into account Tarski’s posthumously published paper ‘What are Logical Notions?’ (History and Philosophy of Logic 7, 1985): 143–

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of analyticity that, though vaguely inspired by the Bolzano-Husserl approach, is essentially different from Husserl’s in having a model-theoretic ﬂavour. Let us call a statement ‘analytic’ if it satisﬁes the following conditions: (i) it is true in at least one structure, and (ii) if true in a structure M, then it is true in at least any structure M* isomorphic to M. Here of course, the word ‘isomorphic’ is used in its wider sense, that is, it is not restricted to algebraic structures, and includes homeomorphisms between topological structures as well. In fact, it simply means ‘having the same structure’. It should be perfectly clear that such a deﬁnition of analyticity does not exclude that an analytic statement be true in structures not isomorphic to a structure where it is true, for example, in non-standard models – as happens with the ﬁrstorder Peano Axioms, which are true not only in all structures isomorphic to the intended model, but also in Skolem’s non-standard (denumerable) model, as well as in all non-denumerable elementary extensions both of the standard and of the non-standard model. It also does not exclude that an analytic statement be false in a structure not isomorphic to a structure in which it is true. Thus, analytic statement, as deﬁned above, does not coincide with the intuitive notion of logical truth or logical validity, no matter how such a notion is made precise. What is important is that when the statement is true in a structure M, it is true in all structures M* isomorphic to M, and it is so in virtue only of its form. Clearly, if the truth of a statement depends on experience, it is not invariant under isomorphic transformations, that is, it does not have to be true in structures isomorphic to a structure in which it is true. On the other hand, even if one acknowledges the existence of synthetic a priori statements in Husserl’s or the young Carnap’s sense – in Kant’s sense there are no such statements – the synthetic a priori statements would be concerned with what Husserl called material essences and general features of material regions in Husserl’s terminology, and would presuppose the material existence of such general features in a sense in which mathematical and logical statements do not. Incidentally, it is possible to deﬁne the notion of a synthetic a priori statement in a way perfectly compatible with the above deﬁnition of analyticity. Thus, a statement is synthetic a priori if (i) it is true in at least one physical world, and (ii) if true in a physical world W, it is true in any possible physical world. Thus, contrary to analytic statements, synthetic a priori statements would presuppose the existence of a physical world. On the other hand, if they are true in a physical world, they have to be true in any physical world. Hence, they should be concerned with the most general features of physicality. Thus, according to such a deﬁnition, statements expressing either the three-dimensionality or, in general, the n-dimensionality of space are not synthetic a priori, nor are synthetic a priori the statements that assert that space is Euclidean, locally Euclidean or Riemannian, or that time is one-dimensional, or that it is noncircular. On the other hand, the statement that asserts that a physical world must have at least one dimension, as well as the statement that asserts that anything coloured must have an extension would be synthetic a priori statements. Whether on the basis of the above deﬁnition there are more interesting examples of synthetic a priori statements is not clear. 54, reprinted in Stewart Shapiro (ed.), The Limits of Logic (Cambridge: Dartmouth, 1996), pp. 119–30. It would take us, however, too far away to discuss this issue here in more detail.

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Returning to analyticity, there are some possible objections to the proposed deﬁnition of analyticity that come immediately to mind. The ﬁrst one is related precisely to the already mentioned case of non-standard models of a theory. For example, one could ask whether the new statement that postulates – in the proof of Skolem’s theorem – the existence of a number greater than any natural number, and which is valid in a non-standard model of arithmetic but not valid in the standard models, is analytic or not. The answer would be that it also is analytic, since it is true in all models isomorphic to the non-standard model in which it is true, notwithstanding the fact that it is not true in the standard models of arithmetic. Indeed, it should be stressed that the notion of an analytic statement deﬁned above does not coincide with the categoricity of the theory that has such a statement as its only axiom. In the same vein, in non-abelian groups the dyadic operation is not commutative, though it is commutative in each and every abelian group and, hence, the commutative law for groups is analytic, being true in any isomorphic structure to a structure in which it is true. In the case of Skolem’s theorem, what is decisive is that the Skolem statement is true in its non-standard model in virtue of its form, being also true in any other structure having the same ‘form’ as that non-standard model. Thus, its truth does not depend on any ‘material’ features of its model, be they of an empirical or even synthetic a priori nature. Another possible objection that comes immediately to mind is in some sense dual to the former. One could ask whether the deﬁnition of analyticity would blur the distinction between statements true in a class of isomorphic structures and a statement true in all structures. First of all, one should observe that a statement true in all structures – whatever that means – would also be true in all structures isomorphic to a given structure in which it is true. Thus, it would fulﬁl the criterion of analyticity and would, of course, be classiﬁed as analytic. Whether one could deﬁne a stronger notion, for example, of logical truth, that would apply only to statements true in all structures, that is another issue, and has its own difﬁculties, namely, that it is not invariant with respect to languages of different strength. In fact, that could be a problem for Chateaubriand’s approach considered above. Thus, for example, the notions of logical truth for propositional logic, ﬁrst-order logic and second-order logic are extensionally different, depending directly on the expressive power of the logic being considered. Someone could try to ‘solve’ the difﬁculties by stipulating that logical truths are only those of ﬁrst-order logic, considering with Quine that extensions of ﬁrst-order logic are not logic any more, or one could even restrict logical truth to the tautologies of propositional logic. A more reasonable and less arbitrary candidate would be simple type theory, which is the most natural extension of ﬁrst-order logic. Nonetheless, any such choice contains some arbitrariness, and intuitionists and others could ask for an even more reduced circle of logical truths than those of ﬁrst-order logic. Moreover, in abstract model theory the notion of logic is deﬁned in such a broad manner that allows many unorthodox extensions of ﬁrst-order logic to be considered logics in their own right. Therefore, the problem of producing a satisfactory deﬁnition of a more restrictive notion than analyticity as deﬁned above to apprehend the intuitive notion of a language-invariant logical truth turns out to be dependent on our view of logic. Nonetheless, for any logic the notion of logically

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valid – relative to that logic – is perfectly clear and in principle deﬁnable as soon as one is able to deﬁne the notion of a model for a set of axioms for that logic. Incidentally, it should be pointed out that the distinction between full models and Henkin models in second- and higher-order logic does not represent any problem for the deﬁnition of logical validity for such logics. Logical validity in second-order logic is simply truth in every principal (or full) model. Of course, there are parallel notions to those of logical validity and its cognates for Henkin (or general) models. However, one should not forget that since Henkin proved a semantic Completeness theorem for second- and higher-order logic with general models – from which both the Compactness Theorem and the Löwenheim-Skolem Theorem are derivable – in virtue of such a proof and Lindström’s well-known characterization theorem of ﬁrstorder logic, according to which any extension of ﬁrst-order logic for which are valid both the Löwenheim-Skolem Theorem and the Compactness Theorem collapses to ﬁrst-order logic, second-order logic with the Henkin semantics essentially reduces to ﬁrst-order logic. It is, ironically to paraphrase Quine, ﬁrst-order logic in secondorder clothes. Thus, genuine second- and higher-order logic is that with full models, though its semantic richness surpasses by far its syntax. Another issue that could originate some misunderstanding concerns the particular properties of natural numbers in the natural number sequence, for example, those of the number ‘2’ of being the ﬁrst even number as well as the ﬁrst prime number, and, of course, of being the only even prime number. However, statements true in the structure of the natural numbers are true in all structures isomorphic to that of the natural numbers. Moreover, if we are concerned with the adequate second-order DedekindPeano axiom system, this is categorical, that is, all its models are isomorphic. Incidentally, Paul Benacerraf has tried to extract some anti-Platonist philosophical juice precisely from this metamathematical fact, though his argumentation is based on a fundamental confusion. It is pertinent to say a few words on this issue. Benacerraf argued53 against Frege that arithmetic is concerned with ω-sequences, in general, and not with the particular ω-sequence built by our familiar natural numbers. His objective was, of course, to deny numbers any ontological status. Since I have dealt with Benacerraf’s argumentation elsewhere,54 I just want to point out here that the properties considered by Benacerraf at the beginning of his already classic paper are not properties of natural numbers. He considers two different set-theoretic deﬁnitions of the natural numbers, the one given by Zermelo and the one given by von Neumann, and he observes that in those different set-theoretic formulations numbers have different properties. Thus, for example, in one of those set-theoretic foundations each number is the unit set of its predecessor in the natural number series, whereas in the other set-theoretic foundation it is not so. However, those are not properties of 53 See his paper ‘What Numbers could not be?’ 1965, reprinted in Paul Benacerraf and Hilary Putnam, Philosophy of Mathematics (second revised edition, Cambridge: Cambridge University Press 1983), pp. 272–94. 54 See my paper ‘On Antiplatonism and its Dogmas’ 1996, reprinted as Chapter 15 in Claire O. Hill and Guillermo E. Rosado Haddock, Husserl or Frege?: Meaning, Objectivity and Mathematics (Chicago et al., Open Court 2000, 2003), as well as my recent book A Critical Introduction to the Philosophy of Gottlob Frege (Aldershot: Ashgate, 2006).

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the natural numbers but only properties of a speciﬁc set-theoretic representation of the natural numbers. Indeed, no natural number n+1 is the unit set of its predecessor n, in the same vein in which the fact that the roman numeral that refers to the number ‘7’ is a name formed by three signs – whereas the Arabic sign that refers to the same number is not a composed sign – is completely irrelevant to the nature of the number ‘7’ and by no means expresses any property of that number. They are simply different representations of the same number, and the property of being a composed sign concerns one of its representations, not the number itself. Thus, since they do not express properties of the numbers, but only of their particular representations, a fortiori they cannot represent any property of natural numbers not invariant under isomorphisms and deﬁnitions. The different set-theoretic representations of numbers are simply different ways to mimic in the language of set theory the natural number series. If any lesson is to be extracted from the example discussed by Benacerraf is simply that there is a sort of inherent inadequacy or artiﬁciality of any set-theoretic foundation of the natural numbers. Natural numbers can be mimicked in different ways in set theory, but that does not necessarily mean that they are less fundamental mathematical entities than sets. It is pertinent to observe that there are different possible directions of foundation. In usual set theory, relations are deﬁned in terms of sets, and functions of n arguments are deﬁned as relations of n+1 arguments uniquely determined in the last one. However, following Frege, one could very well deﬁne relations as special cases of functions, whereas one can also deﬁne sets in terms of relations, or, following current category theory, one can simply deﬁne both sets and relations in terms of categories, which are essentially generalized functions called ‘morphisms’ together with some undetermined objects. Another point should be stressed here before continuing the discussion of Quine. It concerns the possible misunderstanding of rendering the deﬁnition of analyticity as in some obscure sense advocating some sort of conventionalism. First of all, it should be pointed out that such conventionalist renderings of logic and mathematics are usually concerned with elementary parts of those disciplines, in which there could be a sort of resemblance of conventionalism. However, that is just not more than a mere resemblance. Once a collection of axioms is given, the totality of possible structures that are models of that set of axioms, be they isomorphic or not to an intended interpretation, if any, cannot be foreseen by the mathematician. Those models are not the result of any convention, or construction, that could preﬁgure them in advance. Moreover, the mathematician cannot foresee the sometimes especially rich features of the structures, expressed by the unlimited number of theorems following from the axioms. This brute objectivity of mathematical facts that does not admit any control by the mathematician is especially clear, as Gödel has pointed out,55 for metamathematical properties of the theories, for example, whether the theory deﬁned by the axioms is decidable, or is syntactically (that is, deductively) or semantically complete. Another example has been pointed out by the distinguished 55 See his paper ‘Some basic theorems on the foundations of mathematics and their implications’, in Volume III of his Collected Works (Oxford, 1996, pp. 304–32). For a detailed discussion of similar arguments against antiplatonist views, see the present author’s forthcoming paper ‘Why and How Platonism?’.

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logician Wilfrid Hodges in his survey essay titled ‘Elementary Predicate Logic’ in the ﬁrst volume of the Handbook of Philosophical Logic,56 as an answer to a comment by Hilary Putnam in his undeservedly famous paper ‘Models and Reality’. Hodges correctly observes that many major theorems of model theory, for example, the so-called Upward Löwenheim-Skolem Theorem – really a theorem of Tarski – that asserts that if a ﬁrst order theory has an inﬁnite model of cardinality α, it has models of any cardinality β≥α, show the falsity of Putnam’s contention that we in some sense construct the models, in which case we would have a sort of control over them.57 Especially decisive on this issue are also the already mentioned results of the mathematical equivalence, that is, interderivability, of the Axiom of Choice with Tychonoff’s Theorem and with about a hundred other results in the most varied areas of mathematics.58 That, for example, a result from general topology is interderivable with a result from the theory of vector ﬁelds is a metamathematical fact that cannot be assessed by any mathematical conventionalism, as it cannot be assessed by any sort of constructivism, formalism or any other philosophy of mathematics except Platonism. Such metamathematical results as the equivalence of the Axiom of Choice and some hundred other mathematical statements from very diverse areas of mathematical research allow only the interpretation that there exist mathematical structures with their properties and interconnections that are completely independent of our will, our symbolism, our manipulations, constructions or conventions. From those three sorts of examples, one can conclude that the mathematician, with his axiom systems and logical tools is able only to discover some features of the mathematical realm, while most probably other features and other mathematical structures will remain forever off limits for our ﬁnite and clearly limited capabilities, even those of the greatest mathematicians. Finally, it could be interesting to consider the possible relation between Husserl’s more syntactically inclined deﬁnition of analyticity and the more ‘semantic’ one that I have sketched above. It is clear that both deﬁnitions attempt at a rendering of ‘analyticity’ as true in virtue of its form or in virtue of its structure. I would venture to say that the extension of Husserl’s notion of analyticity is a proper subset of the scope of the deﬁnition of analyticity given above. Thus, for example, number-theoretic statements like ‘13+23+33+43=100’ are not analytic in virtue of Husserl’s deﬁnition, since they are not formalizable salva veritate, but are analytic 56 ‘Elementary Predicate Logic’, in D.M. Gabbay and F. Guenthner (eds), Handbook of Philosophical Logic I (Dordrecht, 1983), pp. 1–131. The passage is on p. 34, where Hodges says: ‘Unfortunately this claim [Putnam’s – see next footnote] is in ﬂat contradiction to about half the major theorems of model theory (such as the Upward Löwenheim-Skolem Theorem…)’. 57 For Putnam’s unfortunate assertion, see his ‘Models and Reality’ in Journal of Symbolic Logic 45, 1980, pp. 464–82, where he asserts on p. 482: ‘Models are … constructions within our theory itself, and have names from birth’. 58 The classic books on this issue are the book by Herman Rubin and Jean E. Rubin Equivalents of the Axiom of Choice, II (Amsterdam, 1985) and Gregory H. Moore’s Zermelo’s Axiom of Choice (New York et al., 1982). There is also a book titled Equivalents of the Axiom of Choice (Amsterdam, 1963) by Herman Rubin and Jean E. Rubin, which is not a ﬁrst volume, but a ﬁrst edition of the more complete book referred to above.

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in virtue of the above deﬁnition, since a number-theoretic statement is true in any structure isomorphic to that of the natural numbers. Moreover, in virtue of Husserl’s deﬁnition of analyticity, metatheorems, like the Löwenheim-Skolem theorem, the Completeness theorem for ﬁrst-order predicate logic, Lindström’s characterization theorem or the Incompleteness theorems will not be analytic, whereas, if we consider logical languages as linguistic structures, all those metatheorems are clearly analytic in virtue of the above deﬁnition, since when true in a linguistic structure L, they are true in at least any linguistic structure L* isomorphic to L. That is the reason why I prefer to render Husserl’s deﬁnition as an attempt to deﬁne the notion of logical truth, as Chateaubriand – who does not seem to have been acquainted with Husserl’s deﬁnition – has done. Whether one could make precise such a notion of logical truth in a satisfactory way is a different issue, and a very difﬁcult one, as argued above. 4 Against Quine’s Inscrutability of Meaning After such an extensive digression, let us return to my main line of discussion, namely, Quine’s critique of Carnap’s notion of analyticity. It is important to bear in mind that Quine’s critique depends on the acceptance of some questionable premises, especially his thesis of the inscrutability of meaning,59 which needs not be admitted as an evident truth. Indeed, one could try to deﬁne meaning as well as different candidates (Fregean and Husserlian) for the notion of referent as equivalence classes by means of transformation groups.60 For example, let us consider a language L with enough linguistic resources as to allow an axiom system powerful enough to derive the whole of current mathematics. Consider now arbitrary transformations between statements (that is, well-formed formulas without free variables). The structure built by the set of transformations that preserve truth-value is a group. It clearly contains a unit element, namely, the identity transformation, which applied to any given statement, has the same statement as output, the concatenation of transformations is associative and for each transformation, there exists an inverse transformation. Such a group of transformations gives rise to two equivalence classes, namely: the true and the false. One can then consider the set of transformations of statements into other statements that are interderivable with them on the basis of the axiom system. The structure of the set of those transformations is also a group. The equivalence classes obtained by abstraction can be identiﬁed with what Husserl called ‘situations of affairs’. This group of transformations is clearly a proper subgroup of the ﬁrst group of transformations considered, since clearly neither all true statements nor all false statements are interderivable. One can, however, restrict the group of transformations to those transformations between interderivable statements that are obtained from each other by the replacement of a constituent 59 Since Quine distinguishes between the theory of reference and the theory of meaning, in the following discussion I will identify Quine’s ‘meaning’ with Frege’s and Husserl’s ‘sense’. 60 On such transformation groups, see my paper ‘Remarks on Sense and Reference in Frege and Husserl’ (Kant-Studien 73, 4, 1982), reprinted as Chapter 2 in Claire O. Hill and Guillermo E. Rosado Haddock, Husserl or Frege?: Meaning, Objectivity and Mathematics, pp. 23–40.

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part by another, for example, the equation ‘5+3=9-1’ is assigned to the statement ‘5+3=4+4’, which results from the ﬁrst by replacing the constituent ‘9-1’ by ‘4+4’. Similarly, the inequality ‘9-1>5+2’ is obtained from the inequality ‘9-1>4+3’ by a replacement of a constituent part by another. It is clear that the structure of the set of these last sort of transformations is also a group and, moreover, a proper subgroup of the second group of transformations, since, for example, the Axiom of Choice and Tychonoff’s theorem belong to the same equivalence class determined by the second group of transformations but to different equivalence classes determined by the third, as also occurs with the inequalities ‘9-1>5+2’ and ‘5+2<9-1’, which belong to the same equivalence class determined by the second group of transformations, but to different equivalence classes determined by the third. Following once more Husserl, let us call the equivalence classes obtained by abstraction from this third group of transformations ‘states of affairs’. Let us observe now that the trivial set of transformations consisting only of the identity transformation forms a group of transformations and, moreover, is a subgroup – the smallest subgroup – of each of the three groups of transformations considered. Finally, let us consider the smallest non-trivial proper subgroup of the three non-trivial groups of transformations already considered. If it exists, let us deﬁne the sense (or meaning) of a statement as the equivalence class of all statements that can be transformed into that statement by means of transformations of this fourth non-trivial group of transformations. If such a group of transformations does not exist, let us identify sense (or meaning) with the equivalence classes of the trivial group – each of which contains only one member. We can now deﬁne the notion of synonymy as follows. Two statements are synonymous if they belong to the same sense (meaning). If senses (meanings) are unit classes, as happens with every sense (meaning) if it is an abstraction class of the trivial subgroup, there are no synonyms in the language. Moreover, one can offer a similar deﬁnition of synonymy for constituent parts of statements and, in particular, words, as follows. Two expressions are synonymous if they can be replaced by each other in such a way that the new statement still belongs to the same sense (or meaning) as the ﬁrst one. The sense of an expression can then be obtained as an equivalence class of synonymous expressions. At ﬁrst sight, the procedure for deﬁning meaning sketched above would seem to be a sort of vindication of Frege’s Context Principle of Die Grundlagen der Arithmetik, since the notion of sense is ﬁrst obtained for statements, then synonymy for statements and synonymy for constituent parts of statements are deﬁned by means of the notion of sense for statements, and, ﬁnally, the notion of sense for constituent parts is introduced with the help of the notion of synonymy for constituent parts. However, one should be careful about such presumed vindication. First of all, one should distinguish the epistemological order from the logical order in a speciﬁc system of deﬁnitions. Epistemologically – as well as semantically – it seems that the sense of statements is founded on that of its constituent parts, not the other way around. Moreover, it is not excluded that in another system of deﬁnitions one could give a similar deﬁnition of the sense (or meaning) of constituent parts of statements directly, that is, without deﬁning the notion ﬁrst for statements. Continuing with the present issue, it should be observed that a similar procedure could in principle lead to a deﬁnition of sense (or meaning) of statements for natural

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language. One ﬁrst obtains the group of transformations of statements into statements with the same truth-value. Secondly – in order to simplify a little – let us consider the group of transformations of the sort of that which transforms ‘The morning star is a planet’ into ‘The evening star is a planet’ and ‘The ﬁrst prime number is referred to by the Roman numeral ii’ and ‘The smallest even number is referred to by the Roman numeral ii’. Let us also consider the trivial group formed only by the identity transformation. It is clearly a subgroup of the ﬁrst two groups of transformations. Finally, let us consider the smallest non-trivial group of transformations that is a proper subgroup of the ﬁrst two groups of transformations under discussion. If it exists, one identiﬁes sense (or meaning) with the equivalence classes abstracted from the transformations of this smallest non-trivial subgroup. If there is no such group, one identiﬁes sense (or meaning) with the unit classes abstracted from the transformations in the trivial subgroup. The notions of synonymy for statements, synonymy for constituent parts and sense of constituent parts can be obtained in a similar way as indicated above. Thus, the notion of synonymy would be deﬁned by means of the notion of sense (or meaning), whereas the notion of Carnapian (linguistic) analyticity does not need to be introduced. As shown above, one can offer a more adequate deﬁnition of analyticity that does not have anything to do with meaning or synonymy. Moreover, only if one were to accept the questionable truth of the thesis of the inscrutability of meaning is the reduction of Carnapian analyticity to the notion of meaning a dead end. Carnap’s deﬁnition of analyticity is inadequate not on the grounds given by Quine, but on the grounds of considering statements like ‘All unmarried men are bachelors’ as analytic, though their truth is based on the historical and, thus, empirical evolution of languages, and, more generally, on its material content. 5 On Quine’s Holism On the other hand, Quine’s ‘solution’ of propounding a holism is not only completely unfounded but also preposterous. The thesis that all our statements, from the most uninteresting everyday life statements to the logical and mathematical ones are connected in a sort of web of belief is simply metaphysical nonsense of the worst kind, on the same level as Marxist and astrological assertions, and it is no wonder that it has opened the door to all sorts of quackery, culminating in present day postmodernism. In order to talk with some rigour of statements that are dependent on each other for their truth, one has to make clear what one is talking about. Logic and mathematics offer the examples and tools to deal with at least the most important and unequivocal of such dependences. Precisely, the semantic notion of logical implication makes it obvious that the truth of the conclusion is dependent on the truth of the premises, and the premises cannot all be true without the conclusion being also true. Thus, logical implication is a clear-cut case of semantic dependence between statements. The truth of logically incompatible statements is also connected, since it is not the case that two logically incompatible statements – be they in immediate contradiction, or deriving together a contradiction in a ﬁnite number of steps – can be both true. Hence, logical inconsistency (or incompatibility) is also an obvious case of dependence

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between statements. In logic and mathematics, there are many statements that are in some sense equivalent, that is, one is true exactly when the other is true. The most interesting case is that already discussed of seemingly unrelated statements, like the Axiom of Choice and its many equivalents in different areas of mathematics. Thus, clearly, the truth of the Axiom of Choice and that of Tychonoff’s Theorem, according to which the product of compact topological spaces is a compact topological space, are connected, being one of those statements true exactly when the other is also true. Moreover, since Tarski’s Ultraﬁlter Theorem – namely: ‘Any ﬁlter can be extended to a maximal ﬁlter’ – is equivalent to Tychonoff’s Theorem applied to Hausdorff spaces, which are obtained from general topological spaces by means of additional properties, the truth of the Ultraﬁlter Theorem is not independent from that of Tychonoff’s Theorem in its more general version, applying to topological spaces in general. Another simpler example of dependence, in this case, interdependence of truth, is given by dual mathematical theorems. Thus, for example, the Ultraﬁlter Theorem has its dual in the Maximal Ideal Theorem, namely: ‘Any ideal can be extended to a maximal ideal.’ Clearly, if one of those theorems is true, its dual is also true. Finally, a member of any such pair of mathematically equivalent statements is logically incompatible with the negation of the other member and with the logical consequences of such negations. Evidently, all those different cases can serve as examples of dependence between statements.61 Another possible source of dependence of the truth of statements would concern Husserl’s presumed examples of synthetic a priori statements, though it is unnecessary here to give too much weight to such a delicate issue.62 Nonetheless, a few words should seem pertinent. Husserl’s examples are of the following sort: ‘A colour cannot exist without an extension covered by it’, ‘Two different colours cannot completely cover the same extension at the same time’ and ‘Of any two musical tones, one is higher than the other’. Analytic philosophers have tried to dismiss such Husserlian presumed examples of synthetic a priori truths. However, such statements are neither derivable from logic (that is, they are not analytic in Frege’s sense), nor are they formalizable salva veritate (and, thus, not analytic in Husserl’s sense), nor are they true in all structures isomorphic to the intended model and, hence, not analytic in the sense I have been discussing. Nonetheless, both on the basis of Husserl’s deﬁnition of synthetic a priori and on that offered by the present author, they seem to be necessarily – not empirically – true.63 Speciﬁcally, such 61 The existence of such dependence of the truth of a statement from the truth of a second seemingly unrelated statement shows that Gupta’s requirement of local determination is too strong. See his epoch-making paper ‘Truth and Paradox’ (Journal of Philosophical Logic 11, 1982), pp. 1–60, reprinted in Robert L. Martin (ed.), Recent Essays on Truth and the Liar Paradox (Oxford: Oxford University Press 1984), pp. 175–235, pp. 196–8. 62 Husserl’s deﬁnition of synthetic a priori was quoted above. For a more detailed acquaintance with those views, see Logische Untersuchungen II, U. III, §§ 10–12 , and especially §11, in which Husserl offers some examples. 63 Husserl has offered some presumed examples of synthetic a priori inferences that I consider less compelling, namely, ‘From a is higher (as a tone) than b, it follows that b is profounder than a’, and ‘If a is higher (as a tone) than b, and b is higher than c, then a is higher than c’. See Alte und Neue Logik: Vorlesungen 1908/09 (Dordrecht, 2003), p. 30. However, I

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statements seem to be true not only in our physical world, but in all possible physical worlds, in which the corresponding expressions have a referent. In any case, whether such statements are examples of synthetic a priori statements and can be in analytic or synthetic a priori dependence with other similar statements – for example, the statement ‘An extension cannot be at the same time red and green’ is clearly a consequence of the second Husserlian example of synthetic a priori statement given above – what is important for the present discussion is that all those cases of analytic dependence, as well as those of a presumed synthetic a priori dependence, that I have considered are examples of precise dependences between statements, whereas what Quine propounds is a general metaphysical thesis about a sort of mysterious interconnection between our whole web of statements, for example, between the statement that I am presently hungry and the Ultraﬁlter Theorem. Moreover, Quine argues that the difference between the truth of a statement about the presumed present state of hunger of a person in the Smith family, let us say, in Boston, and the statement that 2+2=4 is a matter of degree. However, there are no possible circumstances in which the state of affairs referred to by the equation 2+2=4 is not the case, where there are trillions of circumstances in which the statement ‘A member of the Smith family in Boston is hungry’ is false. Quine’s denial of such a fundamental difference and its rendering as a matter of degree borders already on obscurantism. In order to avoid a possible unfounded objection related to the history of mathematics, a brief digression is here pertinent. Of course, mathematics and logic have their history, but that does not mean that mathematical or logical statements are true in this moment and false in the next century. Of course, there could be the case – and has been the case – that mathematicians have taken as true a mathematical statement that a few generations later is discovered to be no truth at all. Such a statement was never true, though mathematicians for decades or centuries had believed it to be true. Another possible confusion is related to the realm in which a statement is true. A statement can be true in a more limited realm but false in a more extensive or general realm. For example, in real analysis Cauchy Convergence of sequences is equivalent to convergence, but such a statement is not valid in the more general realm of metric spaces, where only some special metric spaces, namely, complete ones have per deﬁnitionem the property of Cauchy Convergence.64 It has occurred many times in the history of mathematics that a theorem was believed to be true in a more general realm but later research showed that it is true only in a more limited realm. Once more, the theorem was from the very beginning true only in the limited realm, though mathematicians falsely believed that it was valid in a more

consider such presumed examples perfectly formalizable and, thus, in Husserl’s terminology, analytic-logical, since the ﬁrst simply says that when an ordered pair (a,b) is in a relation, the ordered pair (b,a) is in the inverse relation, whereas the second says that a given relation is transitive. 64 On this point, the reader can look at any good book on real analysis. See, for example, Stephen Abbott’s especially lucid Understanding Analysis (New York et al., Springer 2001), especially p. 59 for Cauchy Convergence in the reals, and p. 223 for Cauchy Convergence in the more general metric spaces.

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general realm. The history of mathematics also progresses the other way around. Very frequently, a statement is believed to be valid only in a limited realm but future generations of mathematicians show that it is valid in a much wider realm. Indeed, it was valid from the very beginning in the wider realm, though mathematicians were not acquainted with that mathematical fact. Finally, some mathematical theories lose interest because all the fruitful results about that theory have already been obtained, or because a more general encompassing theory is discovered. Nonetheless, the statements about the older and more particular theory remain true, notwithstanding the development of the more general theory. Therefore, one can very well acknowledge the importance of the history of mathematics and of the fact that the beliefs of mathematicians are perfectly revisable, without falling into the trap of taking mathematical truths to be revisable. What are revisable are the beliefs of mathematicians, and though those revisions are spatial-temporally localizable, the grounds for the revision are purely mathematical, not spatial-temporally dependent. Moreover, on these issues, it is especially important to bear in mind the realm(s) with which the theory is concerned. The statements of Boolean algebra are true in some mathematical structures called Boolean algebras, whereas the axioms of some sort of non-distributive lattice are true in other mathematical structures. Whether one or the other is better applicable to a particular physical theory is not a mathematical question and does not affect the truth of its axioms in the mathematical structures with which such axioms are concerned. Mathematical truths are analytic and, thus, non-factual, but their application or non-application to physical reality is an empirical issue. Finally, it should be pointed out that the distinction made above between my notion of analyticity and Husserl’s notion of analyticity (or Chateaubriand’s notion of logical truth) is especially apt to deal with the present issue. The mathematical axioms and theorems concerned with a particular sort of mathematical structure, for example, metric spaces or Boolean algebras, topological groups or vector spaces, are analytic in my sense but would probably not be considered logical truths (or analytic in Husserl’s sense) by most logicians or philosophers of mathematics, no matter how one resolves the difﬁculties mentioned in Section 3 concerning the arbitrariness of any deﬁnition of logical truth. Returning once more to Quine, it should be pointed out that Quine’s holistic thesis runs counter to the most fundamental scientiﬁc enterprises. An extremely important feature of progress in the physical sciences – and of the lack of it in the social sciences – is due to the fact that the physical scientist has been able to isolate from the rest of the world the properties and objects that he wants to examine. Thus, for example, in classical mechanics the objects of study were isolated, the physicists built models – in the sense of the natural sciences – to study forces and other mechanical phenomena, and considered other features of the physical universe either as irrelevant or as having negligible effects on the objects of study. Thus, not only the effects of the gravitational force of distant stars was considered negligible in the study of the mechanics of our solar system, but chemical and biological properties of objects, for example, in free fall, were considered perfectly irrelevant for the study of mechanics, not to say, of course, statements like that asserting that Galileo had a toothache while calculating his law of free fall. In present day physics, the success of the two most important theories, namely, quantum mechanics and general

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relativity, is partly due to the fact that they opted to ignore each other. The present struggle in the foundations of physics with a uniﬁed physical theory that would embrace (or supersede) quantum mechanics and general relativity is ironically the best example of the importance and fruitfulness of isolating theories in the natural sciences, even from theories in the same discipline but concerned with other features of physical reality. If general relativity and quantum mechanics had taken into account each other from the very beginning, the development of both theories would have been decisively stymied by their lack of adequacy to each other. Hence, when Quine proclaims his holism, he runs counter to the usual and also very successful procedure in the most advanced empirical sciences of isolating features of physical reality and the statements that talk about such features, even from other features and corresponding statements of the same discipline but concerned with other aspects of physical reality, not to say from statements about other disciplines or statements about our daily lives. There are other two fundamental related Quinean theses that deserve being considered in this context. The ﬁrst one is Quine’s naturalism and, more speciﬁcally, his naturalized epistemology.65 As a consequence of his misguided rejection of any fundamental difference between the logical-mathematical sciences and the empirical sciences, the restricted realm that logical empiricism had assigned to philosophy as a discipline separate from the empirical sciences completely disappeared. The principal task of the Quinean philosopher is to hear what the empirical sciences have to say and learn from them. In particular, according to Quine, there is no place for epistemological concerns that do not result from the teachings of the empirical sciences. However, as already mentioned, this awe of the layman in front of the empirical sciences that is distinctive of Quine’s views, completely ignores the most basic procedures of the most successful empirical disciplines, especially of physics. Quine’s – and his followers’ natural epistemologists’ – reverence for science is that of the layman partially informed of the results of the empirical sciences, but ignorant of its methodology, and – as we will presently see – unable to discern between well established physical theories and questionable empirical theories in psychology or other soft ‘sciences’. It is the other side of the coin of post-modernists, who are completely ignorant of empirical – as well as of logical-mathematical sciences – but instead of revering science, are irreverent and proclaim a sort of total relativism that is, interestingly enough, more consistent with Quine’s holism and blurring of any fundamental distinction between the truths of logical-mathematical disciplines, and those of empirical sciences and even of everyday life, than Quine’s reverence of empirical sciences, whose truths, according to his own lights, do not essentially differ from the truth that I am presently writing on my computer. The last point that I would like to discuss in relation to Quine is his incredible presupposition of the notion of sense data as what is given in experience.66 Such unfounded presupposition is at the basis of analyses such as those of the indetermination of translation and the subdetermination of theories in empirical 65 See, for example, his ‘Epistemology Naturalized’ in his Ontological Relativity and Other Essays (New York, 1969), pp. 69–90. 66 See on this issue Chapter 2 of his Word and Object (Cambridge, MA, 1960).

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science.67 However, the thesis that in experience we relate ourselves directly to some sort of raw sensory data is simply extreme empiricist mythology. As Husserl stressed and the young Carnap of Aufbau repeated, sensory data are in some sense the result of abstractions, since what is really basic are the experiences of consciousness [Erlebnisse]. Moreover, when we have external perceptions, though we only sensibly perceive slices or sides of objects, we not only see the complete object by means of an apperception, but also see the objects spatially related to one another. We see states of affairs, for example, that the apple is on the table at the side of the napkins. Our experience of external objects is already a structured one. We see Peter and John at the door, not Peter, John and the door as isolated objects, though, as Husserl stressed in the Sixth Logical Investigation,68 there is no sensible counterpart – correlate, in Husserl’s terminology – of the word ‘and’, as there are no sensible counterparts of the expressions ‘on’ and ‘at the side of’. Hence, there are already present, as Husserl has argued,69 categorial components in sensible experience. In other words, our sensible experience is already structured by categorial components. Those components are clearly manifest when one considers the truth-conditions of the statements ‘Peter and John are at the door’ and ‘Peter or John is at the door’. If when I go to the door, only John is there, I would take the ﬁrst statement to be false and the second to be true, though there are no sensible counterparts of ‘and’ or of ‘or’. Those two particles correspond to categorial elements in sense perception that serve to structure our experience. In Husserl’s opus magnum of his opus magnum, namely, the Sixth Logical Investigation, the acknowledgement of the presence of categorial components in sense experience is the point of departure of his epistemology of mathematics. But such an interesting issue would take us too far away from the main concerns of this book.70 6 Wither Analytic Philosophy I have been using the expression ‘analytic’ philosophy in a very wide sense, thus, as concerning all such philosophy that considers itself heir of the tradition of logical analysis exempliﬁed in the writings of Frege, Russell, Wittgenstein and Carnap. Therefore, my use of the expression ‘analytic philosophy’ is by no means similar to that restricted usage, according to which analytic philosophy is identiﬁed with the ordinary language philosophy inspired by the later philosophy of Wittgenstein. Quite on the contrary, I mostly exclude from my considerations that speciﬁc trend in 67 Such a reasonable thesis like the subdetermination of theories in empirical science does not need to presuppose that we are acquainted with sense data. It is enough, for example, to bring to the fore Husserl’s notion of hypotheses cum fundamento in re, or Duhem’s analysis of the role of experiments in science. 68 Logische Untersuchungen II, U. VI, Second Part. 69 Ibid. 70 On this point, see my paper ‘Husserl’s Epistemology of Mathematics and the Foundation of Platonism in Mathematics’ 1987, reprinted as Chapter 12 in Claire O. Hill and Guillermo E. Rosado Haddock, Husserl or Frege?: Meaning, Objectivity and Mathematis, pp. 221–39.

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analytic philosophy, agreeing in principle with Katz and Fodor’s71 assertion that the study of natural (ordinary) language is the task of a body of especially trained scholars, namely, linguists, not of philosophers trying to extract philosophical juice from peculiar features of a particular natural language, usually English. Hence, although I do not exclude ordinary language philosophy from the realm of analytic philosophy, the analytic philosophy with which I am especially concerned is that which values the rigour of scientiﬁc endeavours, both in the logical-mathematical as well as in the physical sciences, and avails itself of the logical-mathematical tools and results in doing philosophy. In some sense, I could very well avoid completely the expression ‘analytic philosophy’ and replace it by a wider one like ‘rigorous philosophy’, in order to include also at least Kant’s, Husserl’s, Popper’s and others’ undertakings, since though they availed themselves of different tools, they felt the same critical healthy respect for rigorous science that Frege, Russell and Carnap felt, a respect that allows for a place for philosophy at the side of science, not a blind uncritical reverence to science, which makes philosophy an appendix of science, or an even more ignorant irreverence of science, which converges to individual relativism. The usage of logical-mathematical tools in philosophy is probably the most important, decisive and enduring contribution of Frege, Russell and Carnap to philosophy. Even if their particular conceptions have turned out to be mistaken, they have showed the way to follow in order to attack many philosophical problems. Without having the intention of excluding possibly very valuable contributions using Kant’s method of transcendental argumentation to the conditions of possibility, or Husserl’s methods of categorial intuition and intuition of essences – which should not be confused – it would be very difﬁcult to overestimate the fruitfulness of the application of logical-mathematical tools to philosophical problems. However, the commitment to the application of those tools to philosophy by no means conveys a commitment to an empiricist or pragmatist philosophy. There are clear historical reasons that can explain why analytic philosophy, as I conceive it, developed into a tool of twentieth-century empiricism. First of all, there is the inﬂuence of Russell and, more generally, of the English classic empiricist tradition. Secondly, there is the demise of classical science and its Kantian philosophical foundations, which so deeply impacted the ﬁrst writings of Schlick and Reichenbach, and in the case of the former probably also the inﬂuence of Mach, whose chair he occupied at the University of Vienna. Finally and most importantly, the emigration of most logical empiricists to the United States of America, at a time in which there was a very strong tradition not only of pragmatism, but also of behaviourism, played a decisive role in determining the philosophical applications of the new logical-mathematical tools. This last tradition stemming from psychology also played a hindering role in linguistics, which was only superseded by Chomsky, Harris and their followers in the 1950s,72 opening the door to an unexpected development of linguistics in the 71 See their joint paper ‘What is Wrong with the Philosophy of Language?’, Inquiry 1962, reprint in an abridged form – with omission of parts III and IV – in Thomas M. Olshewsky (ed.), Problems in the Philosophy of Language (New York, 1969), pp. 71–88. 72 See Chomsky’s already classic Syntactic Structures (1957, sixth printing, Den Haag et al., 1966) and Aspects of the Theory of Syntax (1965, fourth printing, Cambridge, MA, 1967).

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hands of Chomsky, Katz, Fodor, Postal and others, who began to serve themselves of logical results in the study of language, and which in some sense also opened the door of linguistic research to the school of Montague and other similar schools that have made even more extensive use of logical-mathematical tools and results in the study of language. However, there was no Anglo-American Chomsky in philosophy, and Quine and his followers remained imprisoned in the straitjacket of behaviourism. The inﬂuence of Quine’s views has been both very strong and paralysing for analytic philosophy. The ultimate consequences of his views have inadvertently and indirectly helped anti-rationalist post-modernism to ﬂourish. It is time for rigorous philosophy to return from the dead end to which Quine’s philosophy has taken it. Rigorous philosophy and the application of logical-mathematical tools and results in philosophy are not the private property of empiricism or pragmatism. On the contrary, they can probably be used against the radical sorts of empiricism in a similar fashion as some metamathematical results can be used to show the falsity of conventionalism, ﬁctionalism, formalism and constructivism in mathematics. Indeed, the demise of the most liberal brand of empiricism – namely, Carnap’s late attempt to rescue empiricism by establishing a dichotomy in the language of science between an observation language and a theoretical language, linked by some rules of correspondence73 – which was not capable of dealing with the essentially theoretical nature of most terms in the advanced natural sciences, shows a fortiori the inadequacy of more radical brands of empiricism, like Quine’s, to deal with those paradigmatic empirical sciences. In fact, Quine’s views on science, inspired by behaviourism, are not even capable of assessing Newtonian mechanics, being simply pre-Newtonian and counter to actual science. And that is already more than enough.

73 See, for example, Carnap’s ‘The Methodological Character of Theoretical Concepts’, in Herbert Feigl and Michael Scriven (eds), Minnesota Studies in the Philosophy of Science I (Minneapolis, Minnesota 1956), pp. 38–76; his ‘Observation Language and Theoretical Language’, published posthumously in Jaakko Hintikka (ed.), Rudolf Carnap: Logical Empiricist (Dordrecht, 1975), pp. 75–85, and his book Philosophical Foundations of Physics (New York et al., 1966). There is a revised edition under the title Introduction to the Philosophy of Science (New York, 1995).

Bibliography I. Writings of Rudolf Carnap Der Raum (1922, Vaduz: Topos Verlag, 1991). Der logische Aufbau der Welt 1928 (third edition, Hamburg: Felix Meiner, 1961). ‘Überwindung der Metaphysik durch logische Analyse der Sprache’, 1932, reprinted in Thomas Mormann (ed.), Scheinprobleme in der Philosophie und andere metaphysikkritische Aufsätze (Hamburg, 2004). Die logische Syntax der Sprache 1934 (English revised edition, London: Routledge, 1937). ‘Testability and Meaning’, Philosophy of Science 3 (4) (1936): 419–71 and 4 (1) (1937): 1–40. Foundations of Logic and Mathematics (Chicago: University of Chicago Press, 1939). Introduction to Semantics (Cambridge, MA: Harvard University Press, 1942). Formalization of Logic (Cambridge, MA: Harvard University Press, 1943). Meaning and Necessity (Chicago: University of Chicago Press, 1947). Logical Foundations of Probability (Chicago: University of Chicago Press, 1950). ‘The Methodological Character of Theoretical Concepts’, in Herbert Feigl and Michael Scriven (eds), Minnesota Studies in the Philosophy of Science I (Minneapolis: University of Minnesota Press, 1956), pp. 38–76. Philosophical Foundations of Physics (New York: Basic Books, 1966), revised edition with new title Introduction to the Philosophy of Science (New York: Dover, 1995). Scheinprobleme in der Philosophie und andere metaphysikkritische Schriften, Thomas Mormann (ed.), (Hamburg: Felix Meiner, 2004). II. Writings of Edmund Husserl Referred to in the Book Philosophie der Arithmetik (Den Haag: M. Nijhoff, 1970). Logische Untersuchungen (2 vols, 1900–1901 Den Haag: M. Nijhoff, (I) 1975, (II) 1984, English translation, London: Routledge, 1970, paperback edition with a Preface by Michael Dummett and an Introduction by Dermot Moran, 2001). Ideen zu einer reinen Phänomenologie und einer phänomenologiaschen Philosophie I, (1913, Den Haag: M. Nijhoff, 1950). Ideen zu einer reinen Phänomenologie und einer phänomenologischen Philosophie II, (Den Haag: M. Nijhoff, 1952). Cartesianische Meditationen (1928, Den Haag: M. Nijhoff, 1963). Vorlesungen zur Phänomenologie des inneren Zeitbewußtseins (1928, Den Haag: M. Nijhoff, 1966). Formale und transzendentale Logik (1929, Den Haag: M. Nijhoff, 1974).

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Zur Phänomenologie der Intersubjektivität : Erster Teil 1905–1920 (Den Haag: M. Nijhoff, 1973). Zur Phänomenologie der Intersubjektivität: Zweiter Teil 1921–1928 (Den Haag: M. Nijhoff, 1973). Zur Phänomenologie der Intersubjektivität: Dritter Teil 1929–1935 (Den Haag: M. Nijhoff, 1973). Aufsätze und Rezensionen 1890–1910 (Den Haag: M. Nijhoff, 1979). Studien zur Arithmetik und Geometrie (Den Haag: M. Nijhoff, 1983). Einführung in die Logik und Erkenntnistheorie (Den Haag: M. Nijhoff, 1984). Erfahrung und Urteil (1939, sixth edition , with a Preface by Lothar Eley, Hamburg: Felix Meiner, 1985). Introduction to the Logical Investigations (Den Haag: M. Nijhoff, 1975). Briefwechsel (10 vols, K. Schuhmann and E. Schuhmann (eds), Dordrecht: Kluwer 1994). Alte und Neue Logik (Dordrecht: Kluwer, 2003). III. Books of other Logical Empiricists and Related Authors Hempel, Carl G., Aspects of Scientiﬁc Explanation (New York: The Free Press, 1965). Reichenbach, Hans, Relativitätstheorie und Erkenntnis Apriori (1920, English translation, Berkeley: University of California Press, 1965). ——, Axiomatik der relativistischen Raum-Zeit-Lehre (1924, English translation, Berkeley: University of California Press, 1969). ——, Philosophie der Raum-Zeit-Lehre (1928, English translation, New York: Dover, 1958). Schlick, Moritz, Allgemeine Erkenntnislehre (1916, revised edition 1925, English translation, General Theory of Knowledge, La Salle: Open Court, 1985). ——, Raum und Zeit in der gegenwärtigen Physik (1918, third edition 1920, English translation, New York: Dover, 1963). ——, Gesammelte Aufsätze, (Hildesheim: Georg Olms, 1969). Wittgenstein, Ludwig, Logisch-philosophische Abhandlung (1921, English translation, Tractatus Logico-philosophicus 1922, bilingual reprint, London: Routledge, 1961). IV. Books on Carnap and Logical Empiricism I: Traditional Achinstein, Peter and Barker, Stephen F. (eds), The Legacy of Logical Positivism (Baltimore: John Hopkins University Press, 1969). Ayer, Alfred J., Language, Truth and Logic 1936, (reprint, Dover: New York, 1946). —— (ed.), Logical Positivism (The Free Press: New York, 1959). Bergmann, Gustav, The Metaphysics of Logical Positivism, (Madison: The University of Wisconsin Press, 1967). Butrick, Richard, Carnap on Meaning and Analyticity (Den Haag: Mouton, 1970).

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Fano, Giorgio, Neopositivismo, Analisi del Linguaggio e Cibernetica (Turin: Einaudi, 1968). Hanﬂing, Oswald, Logical Positivism (Oxford: Blackwell, 1981). Hintikka, Jaakko (ed.), Rudolf Carnap, Logical Empiricist (Dordrecht: Reidel, 1975). Joergensen, Joergen, The Development of Logical Positivism (International Encyclopedia of Uniﬁed Science, Chicago: University of Chicago Press, 1951). Kazemier, B.H. and Vuysje, D. (eds), Logic and Language (Dordrecht: Reidel, 1962). Kraft, Viktor, Der Wiener Kreis (second edition, Vienna: Springer, 1968). Krauth, Lothar, Die Philosophie Carnaps (Vienna: Springer, 1970). Norton, Brian G., Linguistic Frameworks: A Re-Examination of Carnap’s Metaphilosophy (Den Haag: Mouton, 1977). Pasquinelli, Alberto, Introduzione a Carnap (Bari: Editori Laterza, 1972). Schilpp, Paul A. (ed.), The Philosophy of Rudolf Carnap (La Salle: Open Court, 1963). Suppe, Frederick (ed.), The Structure of Science (Urbana: University of Illinois Press, second edition, 1977). V. Writings on Carnap and Logical Empiricism II: Recent Awodey, Steve and Klein, Carsten (eds), Carnap Brought Home (Chicago and La Salle: Open Court, 2004). Beaney, Michael, ‘Carnap’s Conception of Explication: From Frege to Husserl?’, in Steve Awodey and Carsten Klein (eds), Carnap Brought Home, pp. 117–50. Bell, David and Vossenkuhl, Wilhelm (eds), Wissenschaft und Subjektivität (Berlin: Akademie Verlag, 1992). Bonk, Thomas (ed.), Language, Truth and Logic: Contributions to the Philosophy of Rudolf Carnap (Dordrecht: Kluwer, 2003). Cirera, Ramón, Carnap and the Vienna Circle (Amsterdam: Rodopi, 1994). ——, Ibarra, Andoni and Mormann, Thomas (eds), El Programa de Carnap (Barcelona: C.E.L.C., 1996). Coffa, J. Alberto, The Semantic Tradition from Kant to Carnap (Cambridge: Cambridge University Press, 1991). Dahms, Hans Joachim (ed), Philosophie, Wissenschaft, Aufklärung: Beiträge zur Geschichte und Wirkung des Wiener Kreises (Berlin: de Gruyter, 1985). Friedman, Michael, Reconsidering Logical Positivism (Cambridge: Cambridge University Press, 1999 ). ——, Parting of the Ways (Chicago and La Salle: Open Court, 2000). ——, The Dynamics of Reason, (Chicago: University of Chicago Press, 2001). Giere, Ronald and Richardson, Alan W. (eds), Origins of Logical Empiricism (Minneapolis: University of Minnesota Press, 1996). Haller, Rudolf and Stadler, Friedrich (eds), Der Aufstieg der wissenschaftlichen Philosophie (Vienna: Hölder-Tempsky, 1993).

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Mayer, Verena, ‘Die Konstruktion der Erfahrungs welt: Carnap und Husserl’, in Wolfgang Spohn (ed.), Erkenntnis Orientated, 1991, pp. 287–303. ——, ‘Carnap und Husserl’, in David Bell and Wilhelm Vossenkuhl (eds), Wissenschaft und Subjektivität, 1992, pp. 185–201. Mormann, Thomas, Rudolf Carnap (Munich: C.H. Beck, 2000). ——, ‘Geometrical Leitmotifs in Carnap’s Early Philosophy’, unpublished paper. ——, ‘Carnap’s Metrical Conventionalism versus Differential Topology’, unpublished paper. Moulines, C. Ulises, ‘Las Raíces Epistemológicas del Aufbau de Carnap’, Dianoia 1982 (reprint in Ramón Cirera, Andoni Ibarra and Thomas Mormann (eds), El Programa de Carnap), pp. 45–74. Oberdan, Thomas, Protocols, Truth and Convention (Amsterdam: Rodopi, 1993). Parrini, Paolo, Salmon, Wesley C. and Salmon, Merrilee H., Logical Empiricism: Historical and Contemporary Perspectives (Pittsburgh: University of Pittsburgh Press, 2003). Pasquinelli, Alberto, L’Eredità di Carnap (Bologna: CLUEB, 1995). Proust, Joëlle, Questions de Forme: Logique et Proposition Analytique de Kant a Carnap (Paris: Fatard, 1986, English translation, Minneapolis: University of Minnesota Press, 1989). Rescher, Nicholas (ed.), The Heritage of Logical Positivism (Lanham: University Press of America, 1985). Richardson, Alan W., Carnap’s Construction of the World (Cambridge: Cambridge University Press, 1998). Rosado Haddock, Guillermo E., ‘Releyendo al Joven Carnap’, Critical Study of Der Raum, Manuscrito 29, No. 1, Jan.–Jun. 2006, pp. 259–96. ——, ‘La Relevancia de Carnap’, Critical Study of Andoni Ibarra, Ramón Cirera and Thomas Mormann (eds), El Programa de Carnap, Principia 10, n. 2, 2006, pp. 209–35. Roy, Jean Michel, ‘Carnap’s Husserlian Reading of the Aufbau’, in Steve Awodey and Carsten Klein (eds), Carnap Brought Home (Chicago: Open Court, 2004), pp. 41–62. Runggaldier, Edmund, Carnap’s Early Conventionalism (Amsterdam: Rodopi, 1984). Salmon, Wesley C. and Wolters, Gereon (eds), Logic, Language and the Structure of Scientiﬁc Theories (Pittsburgh: University of Pittsburgh Press, 1994). Sarkar, Sahotra (ed.), Science and Philosophy in the Twentieth Century (six vols, New York: Garland, 1996). ——, ‘Husserl’s Role in Carnap’s Der Raum’, in Thomas Bonk (ed.), Language, Truth and Logic: Contributions to the Philosophy of Rudolf Carnap, 2003, pp. 179–90. Schipper, Frederik, Intuitie en Constructie in de Filosoﬁe van Husserl en Carnap (Amsterdam: Rodopi, 1980). Spohn, Wolfgang (ed.), Erkenntnis Orientated: A Centennial Volume for Rudolf Carnap and Hans Reichenbach (Dordrecht: Kluwer, 1991). Stadler, Friedrich, Vom Positivismus zur «Wissentschaftlichen Weltauffassung» (Vienna: Hölder-Tempsky, 1982).

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Name Index

Abbott, Stephen, 119 n.64, 129 Achinstein, Peter, 126 Angelleli, Ignacio, 65 n.85, 130 Avenarius, Richard, 35, 49 Awodey, Steve, ix, 1 n.4, 73 n.104, 101 n.12, 127–8 Ayer, Alfred J., 126 Balzer, Wolfgang, 105–6, 129 Bar-Hillel, Yehoshua, viii, 100, 129 Barker, Stephen F., 126 Bauch, Bruno, ix–x, 1–2, 8, 30, 72 Beaney, Michael, ix, 101–3, 127, 129 Becker, Oskar, 3 n.9, 33 Bell, David, 33 n.152, 72 n.100, 127–8 Benacerraf, Paul, 112–13, 129 Bergmann, Gustav, 126 Bolyai, Janos, 4 Bolzano, Bernard, 4, 103, 107, 129, 132 Bonk, Thomas, 25 n.121, 73 n.101, 127–8 Boole, George, 4 Born, Max, 34 Bourbaki, Nicholas, 103, 105 Brentano, Franz, x, 31 Butrick, Richard, 126 Cantor, Georg, 4, 103 Cassirer, Ernst, 72 Cauchy, Louis Auguste, 4, 119 Cederberg, Judith N., 31 n.148, 129 Centrone, Stefania, 101 n.10, 129 Chateaubriand, Oswaldo, 109, 111, 115, 120, 129 Chomsky, Noam, 123–4, 129 Cirera, Ramón, ix, 27 n.128, 73 n.102, 127–8 Coffa, J. Alberto, 127 Cohen, I. Bernard, 106 n.35, 129 Coleman, Robert, 14 n.59, 32 n.149, 129 Cornelius, Hans, 35 Cunningham, Suzanne, 98 n.51, 129

Dahms, Hans Joachim, 127 Dathe, Uwe, 8 n.33, 129 Dedekind, Richard, 4, 112 De Morgan, Augustus, 4 Descartes, Réné, 76, 129 Diederich, Werner, viii, xi, 26 n.123, 129 Dingler, Hugo, 23, 33, 35–6, 51, 55 Driesch, Hans, 7, 26–7, 35–6, 55 Duhem, Pierre, 106, 122 n.67, 130 Dummet, Michael, 125 Einstein, Albert, x, 11, 22–3, 30–31, 130 Erdmann, Benno, 75 Eucken, Rudolf, 8 n.33 Feigl, Herbert, 124 n.73, 125 Fodor, Jerry, 123–4, 131 Føllesdal, Dagﬁnn, 71, 102, 130 Frege, Gottlob, vii, xi–xii, 1–4, 9, 25, 27, 34–6, 39–40, 47, 59–60, 62–6, 70– 71, 75, 100–104, 107, 109, 112–13, 116, 118, 122–3, 127, 129–131 Friedman, Michael, 36, 38, 41, 77, 127 Gabbay, D.M., 114 n.56, 130 Gabriel, Gottfried, 1, 130 Galileo, 120 Gauß, Carl Friedrich, 4, 10 Geiger, Moritz, 33 Giere, Ronald, 127 Gödel, Kurt, 113, 130 Gomperz, Heinrich, 55 Grünbaum, Adolf, vii Guenthner, F., 114 n.56 Gupta, Anil, 47, 118 n.61, 130 Haaparanta, Leila, 130 Haller, Rudolf, 127 Hanﬂing, Oswald, 127 Harris, Zellig, 123 Heidegger, Martin, 3 n.9, 33, 70, 130 Helmholtz, Hermann, 26, 31

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Hempel, Carl, 105, 126 Henkin, Leon, 112 Herberger, Hans, 47 Hilbert, David, 3, 9, 30, 100, 130 Hill, Claire O., xii, 45 n.30, 104 n.29, 112 n.54, 115 n.60, 122 n.70, 130 Hintikka, Jaakko, 124 n.73, 127 Hirsch, Morris W., 10 n.43, 130 Hodges, Wilfrid, 113–14, 130 Hume, David, 35, 51, 99 Husserl, Edmund, iii, v, vii–xii, 1–3, 7–8, 15, 23–8, 30–37, 41–9, 51–8, 60–73, 75–9, 81, 86–7, 89–96, 98–107, 109–10, 114–16, 118, 120, 122–3, 125, 127–32 Husserl, Malvine, 33 Ibarra, Andoni, ix, 27 n.128, 73 n.102, 127–8 Ingarden, Roman, 33 Jacoby, Günther, 36, 55 Joergensen, Joergen, 127 Kambartel, Friedrich, 109 n.50, 129–30 Kant, Immanuel, vii, ix–x, 8, 17, 25–7, 30–32, 35, 38, 41–2, 71–2, 76–9, 101–2, 104, 107, 110, 123, 127–8, 130–131 Katz, Jerrold J., 123–4, 131 Kaufmann, Felix, xi Kazemier, B.H., 127 Kleene, Stephen C., 101 n.10 Klein, Carsten, ix, 1 n.4, 4, 73 n.104, 101 n.12, 127–8 Klein, Felix, 2 n.6 Kohler, Wolfgang, 129 Korté, Herbert, 14 n.59, 32 n.149, 129 Kraft, Viktor, 127 Krauth, Lothar, 127 Kronecker, Leopold, 2 n.6 Kuhn, Thomas, 105 Landgrebe, Ludwig, vii–viii, x, 2–3, 33, 47–8, 95 Langford, Cooper H., 101 Leibniz, Gottfried Wilhelm, 23, 103–4 Lie, Sophus, 4 Lindström, Per, 112, 115 Linke, Paul F., 104 n.29 Lobatschevsky, Nicolai, 4

Locke, John, 35, 51, 99 Ludwig, Günther, 106, 131 Luft, Sebastian, ix Mach, Ernst, 35–6, 49–51, 71, 123 Mahnke, Dietrich, 33 Martin, Robert L., 118 n.61, 131 Mayer, Verena, viii–ix, 33, 36, 72–3, 128 Mill, John Stuart, 99 Minkowski, Hermann, 18 Montague, Richard, 124 Moore, Gregory H., 114 n.58, 131 Moran, Dermot, 125 Mormann, Thomas, ix–xi, 6 n.22, 14 n.59, 18 n.77, 27 n.128, 32 n.150, 51 n.48, 73 n.102, 99 n.1, 100 n.2, 105, 125, 127–8, 131 Moulines, Carlos Ulises, ix, 27, 35–6, 55, 105–6, 128–9 Natorp, Paul, x, 31, 36 Neurath, Otto, x, 38, 48, 66, 69, 95, 99, 101, 105 Norton, Brian G., 127 Oberdan, Thomas, 128 Olshewsky, Thomas M., 123 n.71, 131 Ostwald, Wilhelm, 23 Parrini, Paolo, 128 Pasquinelli, Alberto, 127–8 Paton, Herbert J., 38 Peano, Giuseppe, 4, 110 Pearce, David, 106, 131 Peirce, Charles S., 4 Poincaré, Henri, 13 n.57, 22–3, 35, 51, 131–2 Popper, Karl, 105, 123 Postal, Paul M., 124 Proust, Joëlle, 128 Putnam, Hilary, 112 n.53, 114, 129, 131 Quine, Willard O., v, vii, ix, xi, 3, 49, 51, 71, 105, 107, 109, 111–13, 115, 117, 119–21, 124, 131 Rantala, Veikko, 106 Reichenbach, Hans, 1, 4, 23, 106–7, 123, 126, 128 Reininger, Robert, 55 Rescher, Nicholas, 128

Name Index Richardson, Alan, 36, 41 n.17, 51 n.48, 77, 127–8 Rickert, Heinrich, 1–2, 72 Riemann, Bernhard, 4–5, 10–11, 30–31, 103, 131–2 Rosado Haddock, Guillermo E., 45 n.30, 112 n.54, 115 n.60, 122 n.70, 128, 130–131 Roy, Jean-Michel, ix, 73, 128 Rubin, Herman, 114 n.58, 131 Rubin, Jean E., 114 n.58, 131 Runes, Dagobert, 101, 131 Runggaldier, Edmund, 128 Russell, Bertrand, 3–5, 6 n.2, 11, 25, 30, 34–6, 40, 49, 51, 70–71, 95, 99–100, 122–3, 131–2 Ryckman, Thomas, ix, 73, 132

135

Sklar, Lawrence, 10 n.47, 14 n.59, 18 n.77, 132 Skolem, Thoralf, 110–111 Sluga, Hans, 36 Sneed, Joseph D., 105–6, 129 Spohn, Wolfgang, 33 n.152, 72 n.100, 128 Stadler, Friedrich, 127–8 Stegmüller, Wolfgang, 105–6, 132 Stelzner, Werner, 8 n.33, 129, 132 Suppe, Frederick, 106 n.35, 127, 129, 132 Szaniawski, Klemens, 129 Tarski, Alfred, vii, 105, 114, 118, 129, 132 Thiel, Christian, 130 Torretti, Roberto, 6 n.21, 132 Toulmin, Stephen, 106 n.35, 132 Uebel, Thomas, 129

Salmon, Merrilee H., 128 Salmon, Wesley C., 128 Sarkar, Sahotra, ix–x, 25 n.121, 73, 128, 130 Sauer, Werner, 36 Scheibe, Erhard, 106, 132 Scheler, Max, 68 Schilpp, Paul A., vii, 1, 2 n.5, 95, 127 Schipper, Frederik, 72 n.100, 128 Schlick, Moritz, x, 1, 4, 34–6, 38, 66, 69, 95, 101, 106, 123, 126 Scholz, Erhard, 14 n.59, 32 n.149, 129, 132 Scholz, Heinrich, 33 Schröder, Ernst, 4, 47 n.37, 102–3 Schuhmann, Karl, vii–ix, xi–xii, 2 n.7, 2 n.8, 126, 132 Scriven, Michael, 124 n.73, 125 Sebestik, Jan, 109 n.50, 132 Sepp, Hans-Rainer, viii–ix, xii, 3 n.9, 132 Shapiro, Stewart, 110 n.52, 132 Sigwart, Christian, 75

Volkelt, Johannes, 55 Von Neumann, John, 112 Vossenkuhl, Wilhelm, 33 n.152, 72 n.100, 127–8 Vuysje, D., 127 Weierstraß, Karl, 2 n.6, 4 Weiner, Joan, 36 Weyl, Hermann, 14 n.59, 31–2, 36, 73, 129, 132 Whitehead, Alfred North, 2 n.6, 4, 25, 30, 34–6, 70, 100, 132 Wittgenstein, Ludwig, 98 n.51, 122, 126 Wolenski, Jan, 129 Wolters, Gereon, 128 Zermelo, Ernst, 112, 114 n.58, 131 Ziehen, Theodor, 55

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Subject Index

afﬁne geometry, 6 n.22, 14 n.59 afﬁne space, 9, 14, 14 n.59, 17, 17 n.76 afﬁne structure, 22 afﬁne transformation, 31 analytic, v, vii, xi, 1, 2 n.6, 26, 36, 66–7, 71– 2, 71 n.99, 76, 79 n.12, 99, 102–5, 107–11, 114–15, 117–20, 122–4 analytically, 32, 108 analyticity, 76, 107, 109–11, 113–15, 117, 120, 126 a posteriori, 27 a priori, x, 23, 26–7, 26 n.123, 29–32, 35, 38, 72, 76, 90–91, 99, 107–8, 110–11, 118–19, 118 n.62–3 aprioricity, 30, 32 Aristotelian, 7, 76 autopsychological, v, 48–9, 51, 53, 55, 67, 71, 75–8, 80, 82–5, 87, 93 Axiom of Choice, 114, 116, 118, 131

constitutional system, v, 37–41, 45, 48–52, 54, 58, 66, 69–72, 75, 80, 82–5, 95 constitutional subject, 80, 83–5, 87–92, 95–8 construct(ed), 35, 38, 41–2, 114 construction, 41, 113, 128 constructivism, 114, 124

Brentanian, 103

Gaussian, 10 geometry, x, 4, 6 n.21–2, 9, 11, 13, 22–3, 25, 30–31, 76, 103, 107, 132

Carnapian, v, vii, 1–2, 25, 27, 35, 51, 56–7, 65, 70–71, 73, 101, 117 categorial intuition, 123 categoricity, 111 Compactness theorem, 112 Completeness theorem, 112, 115 consciousness, 49–56, 69, 77, 83, 90 consciousness, experiences of, 37 n.4, 42–3, 45, 49–56, 62, 66–7, 69–70, 77–8, 83–5, 87, 92–3, 95, 122 consciousness, stream of, 42, 45, 53–6, 69, 78, 84–5, 90, 97 constitute(d), 19, 38–46, 50, 53, 64, 67, 69, 77–8, 80, 82–8, 90–91, 93, 96 constitution, v, 37, 38 n.5, 38 n.7, 39–47, 52, 66–7, 69, 72, 75–6, 78–86, 88, 90–93, 95, 99 constitutional basis, 49 constitutional deﬁnition, 39

empiricism, xi, 1, 3, 36, 71, 99, 105–7, 121, 123–4, 126–8 Euclidean, x, 4, 9–11, 13, 13 n.57, 17, 19, 21–2, 30–31, 76, 110 factual content, 17–22, 26–9 formal space, v, 5–6, 9, 24–6, 30, 35 Fregean, 34, 36, 39, 47 n.37, 60, 63–5, 79 n.12, 84, 101–3, 109, 115 function, 18–19, 21–2, 39–40, 61–3, 84, 93, 101 n.10

Hausdorff space, 118 heteropsychological, 36, 48, 72–3, 77, 79–85, 93, 95 homeomorphism, 17, 28, 110 Husserlian, v, 1, 3, 5, 26, 33–4, 36–7, 47 n.37, 52–4, 56–7, 60, 63–4, 66, 69, 73 n.104, 78, 99, 115, 118–19, 128 Husserlianism, 9 Incompleteness theorems, 115 individual relativism, 75, 123 intentionality, 69, 91 intentional object, 64, 69 intersubjectivity, v, viii, x, 36–7, 45, 60, 70, 75–9, 81, 86–7, 89, 95–8 intuition, 8–9, 13, 24, 26–7, 44, 57, 77, 123 intuition of essences, 9, 26–7, 44, 123 intuitionist, 111

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The Young Carnap’s Unknown Master

intuitive space, v, 5, 7, 9–10, 14, 25–30, 72 isomorphic, 110–113, 115, 118 isomorphism, 113 Kantian, ix, 4, 28, 34, 36, 38 n.6, 57, 71–3, 77–8, 123 Lindstöm’s theorem, 112, 115 logical empiricism, xi, 1, 3, 99, 105–7, 121, 126–8 logical positivism, 99, 126–9 logical truth, 107, 109–11, 115, 120 logical validity, 110, 112 logicism, 25, 107, 109 Löwenheim-Skolem theorem, 112, 114–15 Machian, 34–5, 49, 51 Marxist, 102 n.18, 117 Maximal Ideal theorem, 118 metric space, 6–7, 9–11, 13, 17–18, 22, 26 model, 105, 110–112, 114, 118 model-theoretic, 110 model theory, 111, 114 morphism, 113 multiplicity, 18, 55 neo-Kantian, ix, 1, 8, 30–31, 36, 70–72, 78 neo-Kantianism, 38, 72, 77 Newtonian, 4, 38, 76, 124 Non-Euclidean, 4, 11 phenomenalism, 37, 51, 71 phenomenalist, 35, 49, 51 phenomenology, v, 30, 42, 45, 58, 66–7, 70–71, 73, 76, 79 n.12, 87, 95 physical geometry, 22–3 physical space, v, 5–6, 11, 15–20, 22–4, 26–8, 30, 32, 35, 90–91

Platonism, 45 n.30, 103, 113 n.55, 114, 122 n.70, 131 postmodernism, 117 projective geometry, 6 n.22 projective space, 6–7, 11, 14, 18 psychologism, 40, 67, 71, 75, 77, 103 Quinean, 36, 71, 121 relation, v, viii–ix, 2–3, 7, 10, 12, 14, 19, 23–4, 32, 36, 37 n.4, 39–41, 43–4, 46, 51 n.48, 54–6, 59–65, 68–9, 73, 76, 79, 81–2, 84–6, 88–90, 104, 114, 119 n.63, 121 relational, 5, 28, 37 Riemannian, 9–10, 110 Russellian, 34 set, 16, 18, 76, 104, 109, 112–13, 115–16 set-theoretic, 112–13 set-theoreticist, 103 set theory, 109, 113 spacetime, 10 n.47, 11, 14 n.59, 18, 132 structure, vii, 5, 9, 11, 14, 17–18, 20–22, 24–6, 28–9, 31–2, 45, 77–8, 103 n.28, 106, 110–112, 114–16, 120, 122, 127–9, 131–2 synthetic a priori, 26–7, 31, 35, 38, 72, 76, 107–8, 110–111, 118–19 topological space, v, 6–7, 9, 14, 16–18, 22, 25–6, 28–30, 118 three-dimensionality, 17, 29–31, 110 Tychonoff’s theorem, 114, 116, 118 Ultraﬁlter theorem, 118–19 Upward Löwenheim-Skolem theorem, 114

The Young Carnaps Unknown Master

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