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Boston Studies in the Philosophy of Science are devoted to symposia, con gresses, colloquia, monographs and collected papers on the philosophical foundations of the sciences. It is now our pleasure to include A. A. Zi nov'ev's treatise on complex logic among these volumes. Zinov'ev is one of the most creative of modern Soviet logicians, and at the same time an innovative worker on the methodological foundations of science. More over, Zinov'ev, although still a developing scholar, has exerted a sub stantial and stimulating influence upon his colleagues and students in Moscow and within other philosophical and logical circles of the Soviet Union. Hence it may be helpful, in bringing this present work to an English-reading audience, to review briefly some contemporary Soviet investigations into scientific methodology. During the 1950's, a vigorous new research program in logic was under taken, and the initial published work -characteristic of most Soviet pub lications in the logic and methodology of the sciences - was a collection of essays, Logical Investigations (Moscow, 1959). Among the authors, in addition to Zinov'ev himself, were the philosophers A. Kol'man and P. V. Tavanec, and the mathematicians and linguists, S. A. Janovskaja, A. S. Esenin-Vol'pin, S. K. Saumjan, G. N. Povarov.
"This long awaited book ... fills essential gaps in monographic literature on proof theory and prepares readers for volume 2 (to be published soon) containing an exposition of the author's new approach to proof theory for higher order logic. Even in traditional topics, like Gödel's completeness and incompleteness theorems, and cut elemination, accents are different compared to books by Kleene, Schütte, or Takeuti, which are strongly influenced by Hilbert's aim: to make mathematical theories (number theory, analysis etc.) more reliable by transformations of formalized proofs. The author is much closer to the approach of G. Kreisel (to whom this book is dedicated): Hilbert's program needs drastic rethinking and one of the main tasks is in finding mathematical applications of the results obtained in proof theory. Possibly, it is not a pure chance that the system of second order functionals developed by the author in his normalization proof for second order logic (was rediscovered and) became a tool in computer science. The book under review presents not only this material, but also other results by the author which became a part of modern proof theory including analysis of cut-free provability in terms of 3-valued logic. The material which was not previously covered (at least in such detail) in proof-theoretic monographs includes strong normalizability proofs (after Tait and Gandy), applications of reflection principles, recursive ordinals, operations on local correct (but not necessarily well-founded) omega-derivations, no-counterexample interpretation, using proof theory to extract combinatory estimates with a detailed treatment of van der Waerden's theorem. This is a difficult, but rewarding postgraduate-level textbook. The author does not avoid philosophical questions, and such discussion supported by theorems is certainly fruitful, although the reviewer would not agree with all author's conclusions"-- description of volume 1.
Despite the resurgence of interest in the philosophy of John Dewey, his work on logical theory has received relatively little attention. Ironically, Dewey's logic was his "first and last love." The essays in this collection pay tribute to that love by addressing Dewey's philosophy of logic, from his work at the beginning of the twentieth century to the culmination of his logical thought in the 1938 volume, Logic: The Theory of Inquiry. All the essays are original to this volume and are written by leading Dewey scholars. Ranging from discussions of propositional theory to logic's social and ethical implications, these essays clarify often misunderstood or misrepresented aspects of Dewey's work, while emphasizing the seminal role of logic to Dewey's philosophical endeavors. This collection breaks new ground in its relevance to contemporary philosophy of logic and epistemology and pays special attention to applications in ethics and moral philosophy.
The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality.
This book brings together essays by one of the pre-eminent scholars of informal logic.
This book reclaims logic as a branch of philosophy, offering a self-contained and complete introduction to the three traditional systems of classical logic (term, sentence, and predicate logic) and the philosophical issues that surround those systems. The exposition is lucid, clear, and engaging. Practical methods are favored over the traditional, and creative approaches over the merely mechanical. The author’s guiding principle is to introduce classical logic in an intellectually honest way, and not to shy away from difficulties and controversies where they arise. Relevant philosophical issues, such as the relation between the meaning and the referent of a proper name, logical versus metaphysical possibility, and the conceptual content of an expression, are discussed throughout. In this way, the book is not only an introduction to the three main systems of classical logic, but also an introduction to the philosophy of classical logic.
For centuries, educational policymakers have believed that studying mathematics is important, in part because it develops general thinking skills that are useful throughout life. This 'Theory of Formal Discipline' (TFD) has been used as a justification for mathematics education globally. Despite this, few empirical studies have directly investigated the issue, and those which have showed mixed results.Does Mathematical Study Develop Logical Thinking? describes a rigorous investigation of the TFD. It reviews the theory's history and prior research on the topic, followed by reports on a series of recent empirical studies. It argues that, contrary to the position held by sceptics, advanced mathematical study does develop certain general thinking skills, however these are much more restricted than those typically claimed by TFD proponents.Perfect for students, researchers and policymakers in education, further education and mathematics, this book provides much needed insight into the theory and practice of the foundations of modern educational policy.
Claire Ortiz Hill The publication of all but a small, unfound, part of the complete text of the lecture course on logic and theory of knowledge that Edmund Husserl gave at Göttingen during the winter semester of 1906/07 became a reality in 1984 with the publication of Einleitung in die Logik und Erkenntnistheorie, Vorlesungen 1906/07 edited by 1 Ullrich Melle. Published in that volume were also 27 appendices containing material selected to complement the content of the main text in significant ways. They provide valuable insight into the evolution of Husserl’s thought between the Logical Investigations and Ideas I and, therefore, into the origins of phenomenology. That text and all those appendices but one are translated and published in the present volume. Omitted are only the “Personal Notes” dated September 25, 1906, November 4, 1907, and March 6, 1908, which were translated by Dallas Willard and published in his translation of Husserl’s Early 2 Writings in the Philosophy of Logic and Mathematics. Introduction to Logic and Theory of Knowledge, Lectures 1906/07 provides valuable insight into the development of the ideas fun- mental to phenomenology. Besides shedding considerable light on the genesis of phenomenology, it sheds needed light on many other dimensions of Husserl’s thought that have puzzled and challenged scholars.
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.