Vienna Circle Collection – serie

INTRODUCTION The present volume unites contributions by the leading figure of the Vienna Circle and by two of his closest assoCiates, contributions that deal with an area of thought represented, indeed, in this Collection but certainly not the central one in the common picture ofthe Circle's activities. It is no accident that an interest in ethics and the philosophy of action was particularly marked in what Neurath was apt to call the right wing of the Circle. For them, as for Wittgenstein (the respected mentorofSchlickandWaismanninparticular),theadvancetobehoped for in philosophy consisted not solely in freeing natural science from a confused sense of dependence on speculative metaphysics but also in seeingthatotherareasoflanguageandaction hadto bethoughtaboutin theirownterms, whichwereneitherthoseofnaturalsciencenorthoseof philosophy as traditionally conceived. The scepticismofSchlick about theprogrammeofUnifiedSciencewaswellknown: EinheizwissenschaJt he called it, as it might be 'boozified science'.And in sober truth the programme sometimes masked a left-wing set of values taken (surely illogically) for granted, though the membersofthe Circle entertained a wide range ofpolitical views. Schlick's own contribution to the present volume is a section from thenotesforoneofhisfinal lectureseries,forsightofwhich wewarmly thanktheonlysurvivingcontributortoourvolume,DrJosephSchachter: Schlick'sgrandsonDra. M. H. vandeVeldehaskindlyconsentedtotheir publication. This section poses the problem we have outlined: there are questionsandaneedforclarificationinethics,butthesenomoredemand a metaphysical solution than does a similar situation in epistemology. Here, as in his earlier Problems of Ethics,l Schlick sets his face against thewholeprocess,mostobviousin Kant,ofmakingtheconceptofvalue absolute. One might say that for Schlick there is no unhypothetical imperative.

Karl Menger (1902-1985), a pure mathematician, also took an active interest in both philosophy and economics. In this memoir, which he was composing at the time of his death, he relates how all these subjects developed and flourished against the Viennese background (described in depth), and did so despite the political developments of the 20s and 30s, which depressed but did not silence him. He continued his work in the United States. The memoir describes his membership of the Vienna Circle (the scientifically minded philosophers that gathered around Moritz Schlick) for whom he was an intermediary, bringing them into contact with Brouwer's intuitionism, with the work of the Polish logicians, especially that of Tarski, but more generally with rigorous mathematical thinking. Indeed, the other Viennese group described here is the Mathematical Colloquium, which he founded, whose Proceedings show it to have been a powerhouse of ideas. There are also chapters on philosophy and mathematics in the Poland of the 20s and 30s and the United States of the 30s and 40s.The memoir devotes particular attention to Wittgenstein (with whose family Menger was acquainted) and to Goedel, whom he was instrumental in bringing to America. The genesis of Menger's own writings on philosophy is also described and the work features many mathematical examples applied to that subject. This volume gives an impression of the interdisciplinarity of the tradition to which he partly belonged and partly created. A brief account of his life is given in an introduction by the editors (all of whom knew him personally), and his contribution to the social sciences - only touched on in the text - is elucidated by Professor Lionello Punzo.

Karl Menger was born in Vienna on January 13, 1902, the only child of two gifted parents. His mother Hermione, nee Andermann (1870-1922), in addition to her musical abilities, wrote and published short stories and novelettes, while his father Carl (1840-1921) was the noted Austrian economist, one of the founders of marginal utility theory. A highly cultured man, and a liberal rationalist in the nine­ teenth century sense, the elder Menger had witnessed the defeat and humiliation of the old Austrian empire by Bismarck's Prussia, and the subsequent establishment under Prussian leadership of a militaristic, mystically nationalistic, state-capitalist German empire - in effect, the first modern "military-industrial complex. " These events helped frame in him a set of attitudes that he later transmitted to his son, and which included an appreciation of cultural attainments and tolerance and respect for cultural differences, com­ bined with a deep suspicion of rabid nationalism, particularly the German variety. Also a fascination with structure, whether artistic, scientific, philosophical, or theological, but a rejection of any aura of mysticism or mumbo-jumbo accompanying such structure. Thus the son remarked at least once that the archangels' chant that begins the Prolog im Himmel in Goethe's Faust was perhaps the most viii INTRODUCTION beautiful thing in the German language "but of course it doesn't mean anything.

This was a major work of the physicist turned philosopher, Philipp Frank. Already known for his papers on mathematical physics, and for his collaboration with the philosophers and scientists in the Vienna Circle, Frank developed his early essays of 1907-08 on causal law and human experience into this expository and critical treatise of 1931. How useful the logical empiricist requirement to formulate a "scientific philosophy" was, is demonstrated by Frank's clarifications of the strengths as well as limitations of the several concepts linked to causal explanation, and indeed by his analysis of misuse, what he called metaphysical, obscure misinterpretations. Among the historically significant topics in this classical treatise on science and its humanist import are Laplace's determinist hypothesis, loss of causal simplicity in field concept, causality and miracles, lawfulness in biology, cause and chance, conservation laws and causal laws, irreversibility of natural processes, and "true" world. The work is a classical treatise and should therefore be of interest to university collections in philosophy, physics and history of science.It should appeal to philosophers of science, modern empiricists, historians of science and those interested in the history of the Vienna Circle.

This book makes available for the first time in English a substantial part of Otto Neurath's economic writings. The essays and small monographs translated here extend from his student years to his last ever finished piece. They chart not only Neurath's varied interests in the economic history of antiquity, in war economics and schemes for the socialisation of peacetime economies, in the theory of welfare measures and social indicators and in issues of the theory of collective choice, but also show his philosophical interests emerging in his contributions to seminal debates of the German Social Policy Association. This volume shows that Neurath's important contributions to the socialist calculation debate are but one aspect of a many-sided and original oeuvre. The translations are preceded by an introductory essay by one of the editors which contextualises the selections by locating them in the various debates of the time that provided their original setting. This book is of interest to economists, philosophers of social science and of economics as well as to historians of philosophy of science and of analytic philosophy.

l. The work of Ludwig Boltzmann (1844-1906) consists of two kinds of writings: in the first part of his active life he devoted himself entirely to problems of physics, while in the second part he tried to find a philosoph­ 1 ical background for his activities in and around the natural sciences. Most scientists are much more aware of his creative work in physics than of his digressions on the meaning and structure of science. I think in the present case the reason is not so much that most scientists are usually almost entirely occupied with their trade, because Boltzmann's philosophical work is also concerned with the (natural) sciences. I rather believe that the quality and consistency of Boltzmann's purely scientific work is of a more appealing nature than his less structured considerations on human activity in science and in life in general. 2. I think that it may be appropriate for the readers of this anthology to say a few words on the main findings of Boltzmann in physics, since in the end their 'philosophical' inlpact has been larger than the effect of his later writings. Moreover some knowledge of his scientific achievements can be helpful for the understanding and appreciation of the essays printed in this book, which almost all stem from Boltzmann's philosophical period. Boltzmann was one of the main protagonists - at least in continental Europe - of atomistics for explaining the phenomena of physics.

l. The work of Ludwig Boltzmann (1844-1906) consists of two kinds of writings: in the first part of his active life he devoted himself entirely to problems of physics, while in the second part he tried to find a philosoph­ 1 ical background for his activities in and around the natural sciences. Most scientists are much more aware of his creative work in physics than of his digressions on the meaning and structure of science. I think in the present case the reason is not so much that most scientists are usually almost entirely occupied with their trade, because Boltzmann's philosophical work is also concerned with the (natural) sciences. I rather believe that the quality and consistency of Boltzmann's purely scientific work is of a more appealing nature than his less structured considerations on human activity in science and in life in general. 2. I think that it may be appropriate for the readers of this anthology to say a few words on the main findings of Boltzmann in physics, since in the end their 'philosophical' inlpact has been larger than the effect of his later writings. Moreover some knowledge of his scientific achievements can be helpful for the understanding and appreciation of the essays printed in this book, which almost all stem from Boltzmann's philosophical period. Boltzmann was one of the main protagonists - at least in continental Europe - of atomistics for explaining the phenomena of physics.

On the last day of his life, Otto Neurath had given help to a Chinese philosopher who was writing about Schlick. Only an hour before his death he said to me: "Nobody will do such a thing for me." My answer then was: "Never mind, you have Bilston, isn't that better?" There were con­ sultations in new housing schemes, an exhibition, and hopes for a fruitful relationship of longer duration. I did not dream at that time that I would one day work on a book like this. The idea came from Horace M. Kallen, of the New School for Social Research, New York, years later; to encourage me he sent me his selection from William James' writings. Later I met Robert S. Cohen. Carnap had sent him to me with the message: "If you want to find out what my political views were in the twenties and thirties, read Otto Neurath's books and articles of that time; his views were also mine." In this way Robert Cohen became ac­ quainted with Otto Neurath. Even more: he became interested; and when I asked him, would he help me as an editor of an Otto N eurath volume, he agreed at once. In previous years I had already asked a number of Otto Neurath's friends to write down for me what they especially remembered about him.

On the last day of his life, Otto Neurath had given help to a Chinese philosopher who was writing about Schlick. Only an hour before his death he said to me: "Nobody will do such a thing for me." My answer then was: "Never mind, you have Bilston, isn't that better?" There were con­ sultations in new housing schemes, an exhibition, and hopes for a fruitful relationship of longer duration. I did not dream at that time that I would one day work on a book like this. The idea came from Horace M. Kallen, of the New School for Social Research, New York, years later; to encourage me he sent me his selection from William James' writings. Later I met Robert S. Cohen. Carnap had sent him to me with the message: "If you want to find out what my political views were in the twenties and thirties, read Otto Neurath's books and articles of that time; his views were also mine." In this way Robert Cohen became ac­ quainted with Otto Neurath. Even more: he became interested; and when I asked him, would he help me as an editor of an Otto N eurath volume, he agreed at once. In previous years I had already asked a number of Otto Neurath's friends to write down for me what they especially remembered about him.

Erkenntnis und Irrtum. Skizzen zur Psychologie der Forschung. Von E. MACH Emer. Professor an der Unlversltlt Wlen. LEIPZIG Verlag von Johann Ambrosius Barth 1905. INTRODUCTION XIII On a number of occasions Mach expressed the sentiment, especially in his correspondence, that America was the land of intellectual freedom and opportunity, the coming frontier for a new radical empiricism that would help to wash metaphysics out of philosophy. In 1901 he sponsored the German edition of Concepts and Theories of Modern Physics (1881) 2 by J. B. Stallo, Cincinnati lawyer and philosopher. Mach warmly endorsed Stallo's book because his scientific aims so closely approximated his own, and because Stallo rejected the latent metaphysical elements and concealed ontological assumptions of the mechanical-atomistic inter- pretation of the world. The second edition of Wiirmelehre was dedicated to Stallo in 1900. The fourth edition of Populiir-wissenschaftliche Vorlesungen (1910), containing seven new essays, was dedicated to Harvard Professor of physiology, philosophY, and psychology, William James.Mach had a strong intellectual affinity for James' pragmatism because, like himself, he recognized that James had come to radically empirical views from science. Both men took pure pre-conceptualized experience, from which the mental and physical predicates of experience are composed, to be neutral rather than real, unreal, objective or subjective.

Erkenntnis und Irrtum. Skizzen zur Psychologie der Forschung. Von E. MACH Emer. Professor an der Unlversltlt Wlen. LEIPZIG Verlag von Johann Ambrosius Barth 1905. INTRODUCTION XIII On a number of occasions Mach expressed the sentiment, especially in his correspondence, that America was the land of intellectual freedom and opportunity, the coming frontier for a new radical empiricism that would help to wash metaphysics out of philosophy. In 1901 he sponsored the German edition of Concepts and Theories of Modern Physics (1881) 2 by J. B. Stallo, Cincinnati lawyer and philosopher. Mach warmly endorsed Stallo's book because his scientific aims so closely approximated his own, and because Stallo rejected the latent metaphysical elements and concealed ontological assumptions of the mechanical-atomistic inter- pretation of the world. The second edition of Wiirmelehre was dedicated to Stallo in 1900. The fourth edition of Populiir-wissenschaftliche Vorlesungen (1910), containing seven new essays, was dedicated to Harvard Professor of physiology, philosophY, and psychology, William James.Mach had a strong intellectual affinity for James' pragmatism because, like himself, he recognized that James had come to radically empirical views from science. Both men took pure pre-conceptualized experience, from which the mental and physical predicates of experience are composed, to be neutral rather than real, unreal, objective or subjective.

These two volumes form a full portrait of Hans Reichenbach, from the school boy and university student to the maturing and creative scholar, who was as well an immensely devoted teacher and a gifted popular writer and speaker on science and philosophy. We selected the articles for several reasons. Many of them have not pre­ viously been available in English; many are out of print, either in English or in German; some, especially the early ones, have been little known, and deal with subject-matters other than philosophy of science. The genesis and evolu­ tion of Reichenbach's ideas appeared to be of deep interest, and so we in­ cluded papers from four decades, despite occasional redundancy. We were, for example, pleased to include his extensive review article from the encyclo­ pedic Handbuch der Physik of 1929 on 'The Aims and Methods of Physical Knowledge', written at a time of creative collaboration between Reichenbach's Berlin group and the Vienna Circle of Schlick and Carnap. Reichenbach was a pioneer, opening new pathways to the solution of age-old problems in many fields: space, time, causality, induction and probability - philosophical analysis and interpretation of classical physics, relativity and quantum physics - logic, language, ethics, scientific explanation and methodology, critical appreciation and reconstruction of past metaphysical thinkers and scientists from Plato to Leibniz and Kant. Indeed, his own philosophical journey was initiated by his passage from Kant to anti-Kant.

These two volumes form a full portrait of Hans Reichenbach, from the school boy and university student to the maturing and creative scholar, who was as well an immensely devoted teacher and a gifted popular writer and speaker on science and philosophy. We selected the articles for several reasons. Many of them have not pre­ viously been available in English; many are out of print, either in English or in German; some, especially the early ones, have been little known, and deal with subject-matters other than philosophy of science. The genesis and evolu­ tion of Reichenbach's ideas appeared to be of deep interest, and so we in­ cluded papers from four decades, despite occasional redundancy. We were, for example, pleased to include his extensive review article from the encyclo­ pedic Handbuch der Physik of 1929 on 'The Aims and Methods of Physical Knowledge', written at a time of creative collaboration between Reichenbach's Berlin group and the Vienna Circle of Schlick and Carnap. Reichenbach was a pioneer, opening new pathways to the solution of age-old problems in many fields: space, time, causality, induction and probability - philosophical analysis and interpretation of classical physics, relativity and quantum physics - logic, language, ethics, scientific explanation and methodology, critical appreciation and reconstruction of past metaphysical thinkers and scientists from Plato to Leibniz and Kant. Indeed, his own philosophical journey was initiated by his passage from Kant to anti-Kant.

This book is the first English version of Prolegomena zu einer kritischen Grammatik, published by Julius Springer, Vienna, 1935, as Volume 10 of the Vienna Circle's series Schriften zur wissenschaftlichen Weltauffassung. The prefatory remarks of both editor and author acknowledge the influence ofWittgenstein in a general way. However, in aim and approach, the work differs from Wittgenstein's Philosophische Grammatik (l969). This is indeed based on material going back to 1932, some of which Schachter must have known. On the other hand, the present Prolegomena not only explains the general, philosophical principles to be followed, but in the light of these proceeds to cover the entire range of conventional grammar, showing where that is uncritical. Whether Wittgenstein in his turn knew of Schachter's work has never been explored. Schachter's object is universal grammar. As is natural, the examples in the original are largely drawn from German grammar, with occasional minor excursions into other languages. For English readers, what matters are the general problems of grammar: there is no point in tying these to the linguistic peculiarities of German, let alone a local variety of it. One who can grasp German at that level might as well read the original. The translation is therefore twofold: the text as a whole has been rendered into English, and the entire apparatus of examples has been replaced, as far as this can be done, by illustrations from English grammar, chosen so as to bring out the same kinds of problem as in the original.

This book is the first English version of Prolegomena zu einer kritischen Grammatik, published by Julius Springer, Vienna, 1935, as Volume 10 of the Vienna Circle's series Schriften zur wissenschaftlichen Weltauffassung. The prefatory remarks of both editor and author acknowledge the influence ofWittgenstein in a general way. However, in aim and approach, the work differs from Wittgenstein's Philosophische Grammatik (l969). This is indeed based on material going back to 1932, some of which Schachter must have known. On the other hand, the present Prolegomena not only explains the general, philosophical principles to be followed, but in the light of these proceeds to cover the entire range of conventional grammar, showing where that is uncritical. Whether Wittgenstein in his turn knew of Schachter's work has never been explored. Schachter's object is universal grammar. As is natural, the examples in the original are largely drawn from German grammar, with occasional minor excursions into other languages. For English readers, what matters are the general problems of grammar: there is no point in tying these to the linguistic peculiarities of German, let alone a local variety of it. One who can grasp German at that level might as well read the original. The translation is therefore twofold: the text as a whole has been rendered into English, and the entire apparatus of examples has been replaced, as far as this can be done, by illustrations from English grammar, chosen so as to bring out the same kinds of problem as in the original.

This volume brings together those papers of mine which may be of interest not only to various specialists but also to philosophers. Many of my writings in mathematics were motivated by epistemological considerations; some papers originated in the critique of certain views that at one time dominated the discussions of the Vienna Cirele; others grew out of problems in teaching fundamental ideas of mathematics; sti II others were occasioned by personal relations with economists. Hence a wide range of subjects will be discussed: epistemology, logic, basic concepts of pure and applied mathematics, philosophical ideas resulting from geometric studies, mathematical didactics and, finally, economics. The papers also span a period of more than fifty years. What unifies the various parts of the book is the spirit of searching for the elarification of basic concepts and methods and of articulating hidden ideas and tacit procedures. Part 1 ineludes papers published about 1930 which expound an idea that Carnap, after a short period of opposition in the Cirele, fully adopted ; and, under the name "Princip/e of To/erance", he eloquently formulated it in great generality in his book, Logica/ Syntax of Language (1934), through which it was widely disseminated. "The New Logic" in Chapter 1 furthermore ineludes the first report (I932) to a larger public of Godel's epochal discovery presented among the great logic results of ali time. Chapter 2 is a translation of an often quoted 1930 paper presenting a detailed exposition and critique of intuitionism.

This volume brings together those papers of mine which may be of interest not only to various specialists but also to philosophers. Many of my writings in mathematics were motivated by epistemological considerations; some papers originated in the critique of certain views that at one time dominated the discussions of the Vienna Cirele; others grew out of problems in teaching fundamental ideas of mathematics; sti II others were occasioned by personal relations with economists. Hence a wide range of subjects will be discussed: epistemology, logic, basic concepts of pure and applied mathematics, philosophical ideas resulting from geometric studies, mathematical didactics and, finally, economics. The papers also span a period of more than fifty years. What unifies the various parts of the book is the spirit of searching for the elarification of basic concepts and methods and of articulating hidden ideas and tacit procedures. Part 1 ineludes papers published about 1930 which expound an idea that Carnap, after a short period of opposition in the Cirele, fully adopted ; and, under the name "Princip/e of To/erance", he eloquently formulated it in great generality in his book, Logica/ Syntax of Language (1934), through which it was widely disseminated. "The New Logic" in Chapter 1 furthermore ineludes the first report (I932) to a larger public of Godel's epochal discovery presented among the great logic results of ali time. Chapter 2 is a translation of an often quoted 1930 paper presenting a detailed exposition and critique of intuitionism.

It was as a result of having known Juhos personally over many years that I became familiar with his thought. I met him and Viktor Kraft in Vienna soon after the War and through their acquaintance I first came into contact with the tradition of the Vienna Circle. To their conversation .too lowe much as regards the clarification of my own views, even if in the end these took quite a different turn in many essentials. At this point my gratitude goes first of all to Mrs. Lia J uhos for the gen­ erous help she has given me and the editors of the Vienna Circle collection in selecting the contents of this volume. Next, we owe a special debt to Dr. Paul Foulkes for his splendid translation of the text. Finally, I wish to thank Dr. Veit Pittioni for his constant assistance. As Juhos' last student, he was thoro).lghly familiar with his supervisor's mode of thought and has significantly furthered the assembly and execution of this book.

It was as a result of having known Juhos personally over many years that I became familiar with his thought. I met him and Viktor Kraft in Vienna soon after the War and through their acquaintance I first came into contact with the tradition of the Vienna Circle. To their conversation .too lowe much as regards the clarification of my own views, even if in the end these took quite a different turn in many essentials. At this point my gratitude goes first of all to Mrs. Lia J uhos for the gen­ erous help she has given me and the editors of the Vienna Circle collection in selecting the contents of this volume. Next, we owe a special debt to Dr. Paul Foulkes for his splendid translation of the text. Finally, I wish to thank Dr. Veit Pittioni for his constant assistance. As Juhos' last student, he was thoro).lghly familiar with his supervisor's mode of thought and has significantly furthered the assembly and execution of this book.

Friedrich Waismann was born in Vienna in 1896 and lived there until the time of the Anschluss in 1938. From then until his death in 1959 he lived in England; this, apart from a brief period at Cambridge early on, was almost wholly at Oxford, \,Vhere he held the posts, first, or reader in the philosophy of mathematics and then of reader in the philosophy of science. He was of Jewish descent -his father being Russian, his mother German. He studied mathematics and physics at the University of Vienna and attended the lec- tures of Hahn. Beginning his career as a teacher of mathematics he soon be- came an unofficial assistant to Moritz Schlick. It was Schlick's concern to see that the new philosophical ideas developed by Wittgenstein from the time of his return to philosophy in the later 1920s were made public that de- termined the subsequent shape of Waismann's activities. Until the out- break of the war in 1939 his main task was the preparation of a book in which Wittgenstein's thought was to be systematically expounded. Be- tween 1927 and 1935 this project was carried on in close personal conjunc- tion with Wittgenstein. A first version of the planned book, Logik. Sprache.Philosophie seems to have been completed by 1931. A very differ- ent version came to England with Waismann in 1938. It finally appeared, in an English translation, as Principles of Linguistic Philosophy.

Friedrich Waismann was born in Vienna in 1896 and lived there until the time of the Anschluss in 1938. From then until his death in 1959 he lived in England; this, apart from a brief period at Cambridge early on, was almost wholly at Oxford, \,Vhere he held the posts, first, or reader in the philosophy of mathematics and then of reader in the philosophy of science. He was of Jewish descent -his father being Russian, his mother German. He studied mathematics and physics at the University of Vienna and attended the lec- tures of Hahn. Beginning his career as a teacher of mathematics he soon be- came an unofficial assistant to Moritz Schlick. It was Schlick's concern to see that the new philosophical ideas developed by Wittgenstein from the time of his return to philosophy in the later 1920s were made public that de- termined the subsequent shape of Waismann's activities. Until the out- break of the war in 1939 his main task was the preparation of a book in which Wittgenstein's thought was to be systematically expounded. Be- tween 1927 and 1935 this project was carried on in close personal conjunc- tion with Wittgenstein. A first version of the planned book, Logik. Sprache.Philosophie seems to have been completed by 1931. A very differ- ent version came to England with Waismann in 1938. It finally appeared, in an English translation, as Principles of Linguistic Philosophy.

The main item in the present volume was published in 1930 under the title Das Unendliche in der Mathematik und seine Ausschaltung. It was at that time the fullest systematic account from the standpoint of Husserl's phenomenology of what is known as 'finitism' (also as 'intuitionism' and 'constructivism') in mathematics. Since then, important changes have been required in philosophies of mathematics, in part because of Kurt Godel's epoch-making paper of 1931 which established the essential in­ completeness of arithmetic. In the light of that finding, a number of the claims made in the book (and in the accompanying articles) are demon­ strably mistaken. Nevertheless, as a whole it retains much of its original interest and value. It presents the issues in the foundations of mathematics that were under debate when it was written (and in some cases still are); , and it offers one alternative to the currently dominant set-theoretical definitions of the cardinal numbers and other arithmetical concepts. While still a student at the University of Vienna, Felix Kaufmann was greatly impressed by the early philosophical writings (especially by the Logische Untersuchungen) of Edmund Husser!' He was never an uncritical disciple of Husserl, and he integrated into his mature philosophy ideas from a wide assortment of intellectual sources. But he thought of himself as a phenomenologist, and made frequent use in all his major publications of many of Husserl's logical and epistemological theses.

The main item in the present volume was published in 1930 under the title Das Unendliche in der Mathematik und seine Ausschaltung. It was at that time the fullest systematic account from the standpoint of Husserl's phenomenology of what is known as 'finitism' (also as 'intuitionism' and 'constructivism') in mathematics. Since then, important changes have been required in philosophies of mathematics, in part because of Kurt Godel's epoch-making paper of 1931 which established the essential in­ completeness of arithmetic. In the light of that finding, a number of the claims made in the book (and in the accompanying articles) are demon­ strably mistaken. Nevertheless, as a whole it retains much of its original interest and value. It presents the issues in the foundations of mathematics that were under debate when it was written (and in some cases still are); , and it offers one alternative to the currently dominant set-theoretical definitions of the cardinal numbers and other arithmetical concepts. While still a student at the University of Vienna, Felix Kaufmann was greatly impressed by the early philosophical writings (especially by the Logische Untersuchungen) of Edmund Husser!' He was never an uncritical disciple of Husserl, and he integrated into his mature philosophy ideas from a wide assortment of intellectual sources. But he thought of himself as a phenomenologist, and made frequent use in all his major publications of many of Husserl's logical and epistemological theses.