First published in in 1976, Hermann Levin Goldschmidt's Contradiction Set Free, (Freiheit für den Widerspruch), reflects the push to explore new forms of critical thinking that gained momentum in the decade between Theodor Adorno's Negative Dialectics of 1966 and Paul Feyerabend's Against Method in 1975. The book articulates Goldschmidt's reclamation of an epistemologically critical position that acknowledges the deep underlying link between the modes of production of knowledge and the social and political life they produce. In signalling a breakout from the academic rut and its repressive hold, Goldschmidt pointed beyond the ossified methods of a philosophical discourse whose oppressive consequences could no longer be ignored.Contradiction Set Free makes available for the first time in English a pivotal work by one of the great critical thinkers of the 20th century.

Finsler's papers on set theory are presented, here for the first time in English translation, in three parts, and each is preceded by an introduction to the field written by the editors. In the philosophical part of his work Finsler develops his approach to the paradoxes, his attitude toward formalized theories and his defense of Platonism in mathematics. He insisted on the existence of a conceptual realm within mathematics that transcends formal systems. From the foundational point of view, Finsler's set theory contains a strengthened criterion for set identity and a coinductive specification of the universe of sets. The notion of the class of circle free sets introduced by Finsler is potentially a very fertile one although not very widespread today. Combinatorially, Finsler considers sets as generalized numbers to which one may apply arithmetical techniques. The introduction to this third section of the book extends Finsler's theory to non-well-founded sets. The present volume makes Finsler's papers on set theory accessible at long last to a wider group of mathematicians, philosophers and historians of science. A technical background is not necessary to appreciate the satisfying interplay of philosophical and mathematical ideas that characterizes this work.

First published in in 1976, Hermann Levin Goldschmidt's Contradiction Set Free, (Freiheit für den Widerspruch), reflects the push to explore new forms of critical thinking that gained momentum in the decade between Theodor Adorno's Negative Dialectics of 1966 and Paul Feyerabend's Against Method in 1975. The book articulates Goldschmidt's reclamation of an epistemologically critical position that acknowledges the deep underlying link between the modes of production of knowledge and the social and political life they produce. In signalling a breakout from the academic rut and its repressive hold, Goldschmidt pointed beyond the ossified methods of a philosophical discourse whose oppressive consequences could no longer be ignored.Contradiction Set Free makes available for the first time in English a pivotal work by one of the great critical thinkers of the 20th century.

This volume is based on the International Conference Logic at Work, held in Amsterdam, The Netherlands, in December 1992. The 14 papers in this volume are selected from 86 submissions and 8 invited contributions and are all devoted to knowledge representation and reasoning under uncertainty, which are core issues of formal artificial intelligence. Nowadays, logic is not any longer mainly associated to mathematical and philosophical problems. The term applied logic has a far wider meaning, as numerous applications of logical methods, particularly in computer science, artificial intelligence, or formal linguistics, testify. As demonstrated also in this volume, a variety of non-standard logics gained increased importance for knowledge representation and reasoning under uncertainty.

It is commonplace that in our time science and technology cannot be mastered without the tools of mathematics; but the same applies to an ever growing extent to many domains of everyday life, not least owing to the spread of cybernetic methods and arguments. As a consequence, there is a wide demand for a survey of the results of mathematics, for an unconventional approach that would also make it possible to fill gaps in one's knowledge. We do not think that a mere juxtaposition of theorems or a collection of formulae would be suitable for this purpose, because this would over emphasize the symbolic language of signs and letters rather than the mathematical idea, the only thing that really matters. Our task was to describe mathematical interrelations as briefly and precisely as possible. In view of the overwhelming amount of material it goes without saying that we did not just compile details from the numerous text-books for individual branches: what we were aiming at is to smooth out the access to the specialist literature for as many readers as possible. Since well over 700000 copies of the German edition of this book have been sold, we hope to have achieved our difficult goal. Colours are used extensively to help the reader. Important definitions and groups of formulae are on a yellow background, examples on blue, and theorems on red.

The Capitalist-Christian Contradiction exposes the political, economic, and spiritual contradictions in our society and the church. It points out how Americas capitalist system creates and maintains economic inequality, political corruption, economic exploitation , racial oppression, and spiritual poverty to worship the almighty dollar bill. Furthermore, the love of money has transformed many churches into a den of thieves that promulgates a prosperity gospel, enriching its clergy and impoverishing the community. Humanitys only hope is to seek Gods kingdom or the beloved community of peace, justice, equality, and freedom for all people regardless of race, class, creed, level of morality, gender, or religion.

A unique approach to mathematical logic where students implement the underlying concepts and proofs in the Python programming language.