Gathered together here are the fundamental texts of the great classical period in modern logic. A complete translation of Gottlob Frege's Begriffsschrift--which opened a great epoch in the history of logic by fully presenting propositional calculus and quantification theory--begins the volume, which concludes with papers by Herbrand and by Gödel.

I first became interested in Husserl and Heidegger as long ago as 1980, when as an undergraduate at the Freie Universitat Berlin I studied the books by Professor Ernst Tugendhat. Tugendhat's at tempt to bring together analytical and continental philosophy has never ceased to fascinate me, and even though in more recent years other influences have perhaps been stronger, I should like to look upon the present study as still being indebted to Tugendhat's initial incentive. It was my good fortune (...) that for personal reasons I had to con tinue my academic training from 1981 onwards in Finland. Even though Finland is a stronghold of analytical philosophy, it also has a tradition of combining continental and Anglosaxon philosophical thought. Since I had already admired this line of work in Tugendhat, it is hardly surprising that once in Finland I soon became impressed by Professor Jaakko Hintikka's studies on Husserl and intentionality, and by Professor Georg Henrik von Wright's analytical hermeneu tics. While the latter influence has-at least in part-led to a book on the history of hermeneutics, the former influence has led to the present work. My indebtedness to Professor Hintikka is enormous. Not only is the research reported here based on his suggestions, but Hintikka has also commented extensively on different versions of the manuscript, helped me to make important contacts, found a publisher for me, and-last but not least-was a never failing source of encouragement. (shrink)

The great influence of Georg Cantor's theory of sets and transfinite arithmetic has led to a considerable interest in his life. It is well known that he had a remarkable and unusual personality, and that he suffered from attacks of mental illness; but the ‘popular’ account of his life is richer in falsehood and distortion than in factual content. This paper attempts to correct these misrepresentations by drawing on a wide variety of manuscript sources concerning Cantor's life and career, including (...) the texts of some important documents. An appendix describes the most important collection of missing manuscripts, whose location would help further the preparation of a biographical study of Cantor. (shrink)

This paper is concerned with the influence that the set theory of Georg Cantor bore upon the mathematical logic of Bertrand Russell. In some respects the influence is positive, and stems directly from Cantor's writings or through intermediary figures such as Peano; but in various ways negative influence is evident, for Russell adopted alternative views about the form and foundations of set theory. After an opening biographical section, six sections compare and contrast their views on matters of common interest; irrational (...) numbers, infinitesimals, cardinal and ordinal numbers, the axiom of infinity, the paradoxes, and the axioms of choice. Two further sections compare the two men over more general questions: the role of logic and the philosophy of mathematics. In a final section I draw some conclusions. (shrink)

In this paper I consider three mathematicians who allowed some role for menial processes in the foundations of their logical or mathematical theories. Boole regarded his Boolean algebra as a theory of mental acts; Cantor permitted processes of abstraction to play a role in his set theory; Brouwer took perception in time as a cornerstone of his intuitionist mathematics. Three appendices consider related topics.

The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for ...

CHAPTER I THE EMERGENCE AND DEVELOPMENT OF HUSSERL'S 'PHILOSOPHY OF ARITHMETIC'. HISTORICAL BACKGROUND: WEIERSTRASS AND THE ARITHMETIZATION OF ANALYSIS In ...

Einladung zur Mitgliederversammlung der Kant-Gesellschaft.

This book makes available to the English reader nearly all of the shorter philosophical works, published or unpublished, that Husserl produced on the way to the phenomenological breakthrough recorded in his Logical Investigations of 1900-1901. Here one sees Husserl's method emerging step by step, and such crucial substantive conclusions as that concerning the nature of Ideal entities and the status the intentional `relation' and its `objects'. Husserl's literary encounters with many of the leading thinkers of his day illuminates both the (...) context and the content of his thought. Many of the groundbreaking analyses provided in these texts were never again to be given the thorough expositions found in these early writings. Early Writings in the Philosophy of Logic and Mathematics is essential reading for students of Husserl and all those who enquire into the nature of mathematical and logical knowledge. (shrink)