Henk L. Mulder - Böcker

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.

In English-speaking countries Victor Kraft is known principally for his account of the Vienna Circle. ! That group of thinkers has exercised in recent decades a significant influence not only on the philosophy of the western world, but also, at least indirectly, on that of the East, where there is now taking place a slow but clearly irresistible erosion of dogmatic Marxism by ways of think­ ing derived from a modem scientific conception of the world. Kraft's work as historian of the Vienna Circle has led to his being classed, without further qua1ification, as a neo-positivist philosopher. It is, however, only partially correct to count him as such. To be sure, he belonged to the group named, he took part in its meetings, and he drew from it suggestions central to his own work; but he did not belong to the hard core of the Circle and was a con­ scious opponent of certain radical tendencies espoused, at least from time to time, by some of its members. Evidence of this is provided by the theory of value now presented in English translation, since no less a thinker than Rudolf Carnap had, originally at any rate, obeyed a very narrowly conceived criterion of sense and declared value judgements to be senseless.

In English-speaking countries Victor Kraft is known principally for his account of the Vienna Circle. ! That group of thinkers has exercised in recent decades a significant influence not only on the philosophy of the western world, but also, at least indirectly, on that of the East, where there is now taking place a slow but clearly irresistible erosion of dogmatic Marxism by ways of think­ ing derived from a modem scientific conception of the world. Kraft's work as historian of the Vienna Circle has led to his being classed, without further qua1ification, as a neo-positivist philosopher. It is, however, only partially correct to count him as such. To be sure, he belonged to the group named, he took part in its meetings, and he drew from it suggestions central to his own work; but he did not belong to the hard core of the Circle and was a con­ scious opponent of certain radical tendencies espoused, at least from time to time, by some of its members. Evidence of this is provided by the theory of value now presented in English translation, since no less a thinker than Rudolf Carnap had, originally at any rate, obeyed a very narrowly conceived criterion of sense and declared value judgements to be senseless.