Friedrich Waismann (1896-1959) was one of the most gifted students and collaborators of Moritz Schlick. Accepted as a discussion partner by Wittgenstein from 1927 on, he functioned as spokesman for the latter's ideas in the Schlick Circle, until Wittgenstein's contact with this most faithful interpreter was broken off in 1935 and not renewed when exile took Waismann to Cambridge. Nonetheless, at Oxford, where he went in 1939, and eventually became Reader in Philosophy of Mathematics (changing later to Philosophy of Science), Waismann made important and independent contributions to analytic philosophy and philosophy of science (for example in relation to probability, causality and linguistic analysis). The full extent of these only became evident later when the larger (unpublished) part of his writings could be studied. His first posthumous work The Principles of Linguistic Philosophy (1965, 2nd edn.1997; German 1976) and his earlier Einfuhrung in das mathematische Denken (1936) have recently proved of fresh interest to the scientific community. This late flowering and new understanding of Waismann's position is connected with the fact that he somewhat unfairly fell under the shadow of Wittgenstein, his mentor and predecessor. Central to this book about a life and work familiar to few is unpublished and unknown works on causality and probability. These are commented on in this volume, which will also include a publication of new or previously scattered material and an overview of Waismann's life.

The idea for this issue arose during a gathering of scholars to com memorate the hundredth anniversary of Moritz Schlick (1882-1936), the philosopher from Germany whose influence gave Austria its most characteristic philosophical voice between the two world wars. He was cut off, tragically, in his prime and while he escaped the exile that awaited most of those who thought like him, he was unable (sadly for philosophy) to continue to steer their thoughts in his own direction and he even lost some of the credit for work already done. Thus it seemed to some of his former pupils and to others more remote from him in the tra dition that a small collection of papers throwing light on his especial con tribution and on the extent to which it is still active or still needed today was a requirement of justice no less than of piety. Tscha Hung, a mem ber of the Vienna Circle and since director of the Institute for Western Philosophy at Peking University, was the chief mover here. Also among the contributors, Ludovico Geymonat (Professor at Milan) was a visitor to the Circle and a friend of Schlick. Henrich Melzer and Joseph Schlichter were Viennese pupils of Schlick's. The former died in the war of 1939-45, the latter is still prominent in the cultural and educational life of Israel."

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.

a priori, and what is more, to a rejection based ultimately on a posteriori findings; in other words, the "pure" science of nature in Kant's sense of the term had proved to be, not only not pure, but even false. As for logic and mathematics, the decisive works of Frege, Russell, and White head suggested two conclusions: first, that it was possible to construct mathematics on the basis of logic (logicism), and secondly, that logical propositions had an irrevocably analytic status. But within the frame work of logicism, the status of logical propositions is passed on to mathematical ones, and mathematical propositions are therefore also conceived of as analytic. All this creates a situation where the existential presupposition contained in the Kantian question about the possibility of judgements that are both synthetic and a priori must, it seems, be rejected as false. But to drop this presupposition is, at the same time, to strike at the very core of Kant's programme of putting the natural sciences on a philosophical foundation. The failure of the modern attempt to do so suggests at the same time a reversal of the relationship between philosophy and the individual sciences: it is not the task of philosophy to meddle with the foundations of the individual sciences; being the less successful discipline, its task is rather to seek guidance from the principles of rationality operative in the individual sciences."

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.

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."

The role Hans Hahn played in the Vienna Circle has not always been sufficiently appreciated. It was important in several ways. In the ftrst place, Hahn belonged to the trio of the original planners of the Circle. As students at the University of Vienna and throughout the fIrst decade of this century, he and his friends, Philipp Frank and Otto Neurath, met more or less regularly to discuss philosophical questions. When Hahn accepted his fIrSt professorial position, at the University of Czernowitz in the north east of the Austrian empire, and the paths of the three friends parted, they decided to continue such informal discussions at some future time - perhaps in a somewhat larger group and with the cooperation of a philosopher from the university. Various events delayed the execution of the project. Drafted into the Austrian army during the first world war" Hahn was wounded on the Italian front. Toward the end of the war he accepted an offer from the University of Bonn extended in recognition of his remarkable 1 mathematical achievements. He remained in Bonn until the spring of 1921 when he returm: d to Vienna and a chair of mathe matics at his alma mater. There, in 1922, the Mach-Boltzmann professorship for the philosophy of the inductive sciences became vacant by the death of Adolf Stohr; and Hahn saw a chance to realize his and his friends' old plan."

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."

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."

Karl Menger (1902--1985), a pure mathematician of distinction, 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 (itself described in depth and with affection), 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 invaluable 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 (still read) show it to have been a powerhouse of ideas. There are also valuable chapters on philosophy and mathematics in the Poland of the '20s and '30s and the U.S. of the '30s and '40s. The memoir devotes particular attention to Wittgenstein (with whose family Menger was acquainted) and to GAdel, whom he was instrumental in bringing to America. The genesis of Menger's own writings on philosophy is also described and the work abounds in mathematical examples lucidly applied to that subject. This volume (which can now be placed beside the two by Menger already published in the Vienna Circle Collection) gives an unequalled impression of the fruitful interdisciplinarity of the tradition to which he partly belonged and partly created. It testifiesboth to Menger's power to inspire and to the critical eye he always turned on even the philosophers he most approved of. A brief account of his life is given in an Introduction by the Editors (all of whom knew him personally), and his important contribution to the social sciences -- only touched on in the text -- is elucidated by Professor Lionello Punzo.

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.

xi should hope for "first and foremost" from any historical investigation, including his own, was that "it may not be too tedious. " II That hope is generally realized in Mach's historical writings, most of which are as lively and interesting now as they were when they appeared. Mach did not follow any existing model of historical or philosophical or scientific exposition, but went at things his own way combining the various approaches as needed to reach the goals he set for himself. When he is at his best we get a sense of the Mach whom William James met on a visit to Prague, the Mach whose four hours of "unforgettable conversation" gave the forty year old, well traveled James the strongest "impression of pure intellectual genius" he had yet received, and whose "absolute simplicity of manner and winningness of smile" captivated him completely. 12 Consider, for example, the first few chapters of this book, Principles of the Theory of Heat, which Mach devotes to the notion of temperature, that most fundamental of all thermal concepts. He begins by trying to trace the path that leads from our sensations of hot and cold to a numerical temperature scale.

The present collection of papers derives from a philosophy conference organised in the Sicilian town of M ussomeli in September 1991. The con ference aimed at providing an analysis of certain aspects of the thought of Michael Dummett, whose contributions have been very influential in several aspects of the philosophical debate continuing within the analyt ical tradition. Logic, the philosophy of mathematics, the interpretation of Frege's philosophy, and metaphysics are only some of the areas within which Dummett's ideas have been fruitful over the years. The papers contained in this book, and Dummett's replies, will, it is hoped, not merely offer a partial reconstruction of a philosopher's life work, but provide an exciting and challenging vantage point from which to look at some of the main problems of contemporary philosophy. The First International Philosophy Conference of M ussomeli - this is what the conference was called - was an extraordinary event in many ways. The quality of the papers presented, the international reputa tion of many of the participants, the venue itself, together with the unavoidable, and sometimes quite funny, organisational hiccups, made that meeting memorable. Perhaps principally memorable was the warmth and sympathy of the people of Mussomeli who strongly supported and encouraged this initia tive. A special mention is also due to the City Council Administrators, who spared no effort to make the Conference a success."

Friedrich Waismann (1896-1959) was one of the most gifted students and collaborators of Moritz Schlick. Accepted as a discussion partner by Wittgenstein from 1927 on, he functioned as spokesman for the latter's ideas in the Schlick Circle, until Wittgenstein's contact with this most faithful interpreter was broken off in 1935 and not renewed when exile took Waismann to Cambridge. Nonetheless, at Oxford, where he went in 1939, and eventually became Reader in Philosophy of Mathematics (changing later to Philosophy of Science), Waismann made important and independent contributions to analytic philosophy and philosophy of science (for example in relation to probability, causality and linguistic analysis). The full extent of these only became evident later when the larger (unpublished) part of his writings could be studied. His first posthumous work The Principles of Linguistic Philosophy (1965, 2nd edn.1997; German 1976) and his earlier Einfuhrung in das mathematische Denken (1936) have recently proved of fresh interest to the scientific community. This late flowering and new understanding of Waismann's position is connected with the fact that he somewhat unfairly fell under the shadow of Wittgenstein, his mentor and predecessor. Central to this book about a life and work familiar to few is unpublished and unknown works on causality and probability. These are commented on in this volume, which will also include a publication of new or previously scattered material and an overview of Waismann's life.

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.

a priori, and what is more, to a rejection based ultimately on a posteriori findings; in other words, the "pure" science of nature in Kant's sense of the term had proved to be, not only not pure, but even false. As for logic and mathematics, the decisive works of Frege, Russell, and White head suggested two conclusions: first, that it was possible to construct mathematics on the basis of logic (logicism), and secondly, that logical propositions had an irrevocably analytic status. But within the frame work of logicism, the status of logical propositions is passed on to mathematical ones, and mathematical propositions are therefore also conceived of as analytic. All this creates a situation where the existential presupposition contained in the Kantian question about the possibility of judgements that are both synthetic and a priori must, it seems, be rejected as false. But to drop this presupposition is, at the same time, to strike at the very core of Kant's programme of putting the natural sciences on a philosophical foundation. The failure of the modern attempt to do so suggests at the same time a reversal of the relationship between philosophy and the individual sciences: it is not the task of philosophy to meddle with the foundations of the individual sciences; being the less successful discipline, its task is rather to seek guidance from the principles of rationality operative in the individual sciences."

The idea for this issue arose during a gathering of scholars to com memorate the hundredth anniversary of Moritz Schlick (1882-1936), the philosopher from Germany whose influence gave Austria its most characteristic philosophical voice between the two world wars. He was cut off, tragically, in his prime and while he escaped the exile that awaited most of those who thought like him, he was unable (sadly for philosophy) to continue to steer their thoughts in his own direction and he even lost some of the credit for work already done. Thus it seemed to some of his former pupils and to others more remote from him in the tra dition that a small collection of papers throwing light on his especial con tribution and on the extent to which it is still active or still needed today was a requirement of justice no less than of piety. Tscha Hung, a mem ber of the Vienna Circle and since director of the Institute for Western Philosophy at Peking University, was the chief mover here. Also among the contributors, Ludovico Geymonat (Professor at Milan) was a visitor to the Circle and a friend of Schlick. Henrich Melzer and Joseph Schlichter were Viennese pupils of Schlick's. The former died in the war of 1939-45, the latter is still prominent in the cultural and educational life of Israel."

xi should hope for "first and foremost" from any historical investigation, including his own, was that "it may not be too tedious. " II That hope is generally realized in Mach's historical writings, most of which are as lively and interesting now as they were when they appeared. Mach did not follow any existing model of historical or philosophical or scientific exposition, but went at things his own way combining the various approaches as needed to reach the goals he set for himself. When he is at his best we get a sense of the Mach whom William James met on a visit to Prague, the Mach whose four hours of "unforgettable conversation" gave the forty year old, well traveled James the strongest "impression of pure intellectual genius" he had yet received, and whose "absolute simplicity of manner and winningness of smile" captivated him completely. 12 Consider, for example, the first few chapters of this book, Principles of the Theory of Heat, which Mach devotes to the notion of temperature, that most fundamental of all thermal concepts. He begins by trying to trace the path that leads from our sensations of hot and cold to a numerical temperature scale.

The present collection of papers derives from a philosophy conference organised in the Sicilian town of M ussomeli in September 1991. The con ference aimed at providing an analysis of certain aspects of the thought of Michael Dummett, whose contributions have been very influential in several aspects of the philosophical debate continuing within the analyt ical tradition. Logic, the philosophy of mathematics, the interpretation of Frege's philosophy, and metaphysics are only some of the areas within which Dummett's ideas have been fruitful over the years. The papers contained in this book, and Dummett's replies, will, it is hoped, not merely offer a partial reconstruction of a philosopher's life work, but provide an exciting and challenging vantage point from which to look at some of the main problems of contemporary philosophy. The First International Philosophy Conference of M ussomeli - this is what the conference was called - was an extraordinary event in many ways. The quality of the papers presented, the international reputa tion of many of the participants, the venue itself, together with the unavoidable, and sometimes quite funny, organisational hiccups, made that meeting memorable. Perhaps principally memorable was the warmth and sympathy of the people of Mussomeli who strongly supported and encouraged this initia tive. A special mention is also due to the City Council Administrators, who spared no effort to make the Conference a success."

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."

The role Hans Hahn played in the Vienna Circle has not always been sufficiently appreciated. It was important in several ways. In the ftrst place, Hahn belonged to the trio of the original planners of the Circle. As students at the University of Vienna and throughout the fIrst decade of this century, he and his friends, Philipp Frank and Otto Neurath, met more or less regularly to discuss philosophical questions. When Hahn accepted his fIrSt professorial position, at the University of Czernowitz in the north east of the Austrian empire, and the paths of the three friends parted, they decided to continue such informal discussions at some future time - perhaps in a somewhat larger group and with the cooperation of a philosopher from the university. Various events delayed the execution of the project. Drafted into the Austrian army during the first world war" Hahn was wounded on the Italian front. Toward the end of the war he accepted an offer from the University of Bonn extended in recognition of his remarkable 1 mathematical achievements. He remained in Bonn until the spring of 1921 when he returm: d to Vienna and a chair of mathe matics at his alma mater. There, in 1922, the Mach-Boltzmann professorship for the philosophy of the inductive sciences became vacant by the death of Adolf Stohr; and Hahn saw a chance to realize his and his friends' old plan."

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."

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.

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."