Best of
Logic

1966

Set Theory and the Continuum Hypothesis


Paul Cohen - 1966
    The independence of the continuum hypothesis is the focus of this study by Paul J. Cohen. It presents not only an accessible technical explanation of the author's landmark proof but also a fine introduction to mathematical logic. An emeritus professor of mathematics at Stanford University, Dr. Cohen won two of the most prestigious awards in mathematics: in 1964, he was awarded the American Mathematical Society's Bôcher Prize for analysis; and in 1966, he received the Fields Medal for Logic. In this volume, the distinguished mathematician offers an exposition of set theory and the continuum hypothesis that employs intuitive explanations as well as detailed proofs. The self-contained treatment includes background material in logic and axiomatic set theory as well as an account of Kurt Gödel's proof of the consistency of the continuum hypothesis. An invaluable reference book for mathematicians and mathematical theorists, this text is suitable for graduate and postgraduate students and is rich with hints and ideas that will lead readers to further work in mathematical logic.

The Ways of Paradox and Other Essays


Willard Van Orman Quine - 1966
    V. Quine's most important and influential, such as "Truth by Convention," "Carnap and Logical Truth," "On Carnap's Views on Ontology," "The Scope and Language of Science," and "Posits and Reality." Many of these essays deal with unresolved issues of central interest to philosophers today. About half of them are addressed to "a wider public than philosophers." The remainder are somewhat more professional and technical. This new edition of The Ways of Paradox contains eight essays that appeared after publication of the first edition, and it retains the seminal essays that must be read by anyone who seeks to master Quine's philosophy.Quine has been characterized, in The New York Review of Books, as "the most distinguished American recruit to logical empiricism, probably the contemporary American philosopher most admired in the profession, and an original philosophical thinker of the first rank." His "philosophical innovations add up to a coherent theory of knowledge which he has for the most part constructed single-handed." In The Ways of Paradox new generations of readers will gain access to this philosophy.

Analyses Concerning Passive and Active Synthesis: Lectures on Transcendental Logic


Edmund Husserl - 1966
    These lectures are the first extensive application of Husserl's newly developed genetic phenomenology to perceptual experience and to the way in which it is connected to judgments and cognition. They include an historical reflection on the crisis of contemporary thought and human spirit, provide an archaeology of experience by questioning back into sedimented layers of meaning, and sketch the genealogy of judgment in `active synthesis'. Drawing upon everyday events and personal experiences, the Analyses are marked by a patient attention to the subtle emergence of sense in our lives. By advancing a phenomenology of association that treats such phenomena as bodily kinaesthesis, temporal genesis, habit, affection, attention, motivation, and the unconscious, Husserl explores the cognitive dimensions of the body in its affectively significant surroundings. An elaboration of these diverse modes of evidence and their modalizations (transcendental aesthetic), allows Husserl to trace the origin of truth up to judicative achievements (transcendental logic). Joined by several of Husserl's essays on static and genetic method, the Analyses afford a richness of description unequalled by the majority of Husserl's works available to English readers. Students of phenomenology and of Husserl's thought will find this an indispensable work.