Lectures On Inductive Logic

Logic is a field studied mainly by researchers and students of philosophy, mathematics and computing. Inductive logic seeks to determine the extent to which the premisses of an argument entail its conclusion, aiming to provide a theory of how one should reason in the face of uncertainty. It has applications to decision making and artificial intelligence, as well as how scientists should reason when not in possession of the full facts. In this book, Jon Williamson embarks on a quest to find a general, reasonable, applicable inductive logic (GRAIL), all the while examining why pioneers such as Ludwig Wittgenstein and Rudolf Carnap did not entirely succeed in this task. Along the way he presents a general framework for the field, and reaches a new inductive logic, which builds upon recent developments in Bayesian epistemology (a theory about how strongly one should believe the various propositions that one can express). The book explores this logic in detail, discusses some key criticisms, and considers how it might be justified. Is this truly the GRAIL? Although the book presents new research, this material is well suited to being delivered as a series of lectures to students of philosophy, mathematics, or computing and doubles as an introduction to the field of inductive logic

Logic is a field studied mainly by researchers and students of philosophy, mathematics and computing. Inductive logic seeks to determine the extent to which the premisses of an argument entail its conclusion, aiming to provide a theory of how one should reason in the face of uncertainty. It has applications to decision making and artificial intelligence, as well as how scientists should reason when not in possession of the full facts. In this book, Jon Williamson embarks on a quest to find a general, reasonable, applicable inductive logic (GRAIL), all the while examining why pioneers such as Ludwig Wittgenstein and Rudolf Carnap did not entirely succeed in this task. Along the way he presents a general framework for the field, and reaches a new inductive logic, which builds upon recent developments in Bayesian epistemology (a theory about how strongly one should believe the various propositions that one can express). The book explores this logic in detail, discusses some key criticisms, and considers how it might be justified. Is this truly the GRAIL? Although the book presents new research, this material is well suited to being delivered as a series of lectures to students of philosophy, mathematics, or computing and doubles as an introduction to the field of inductive logic

Excerpt from The Elements of Inductive Logic: Designed Mainly for the Use of Students in the Universities The precise object of the following pages is (without pre-supposing any technical acquaintance with logical terminology) to enable a student of average intelligence to acquire for himself an elementary knowledge of the main problems, principles, and rules of Deductive logic. They are not designed to save him the trouble of afterwards consulting more advanced text-books, either in his own or other languages. The English student who wishes to gain an exact and detailed knowledge of the relations of Deduction to Induction, and consequently of the true place and value of the former process in any special science, must still have recourse to the works of Mr. Mill; or, if he wish to trace the history of logical terms and doctrines (one of the most important chapters in the history of both ancient and modern literature), he must still consult Sir W. Hamilton's lectures, and the Appendices and Notes of Dr. Mansel to Aldrich's Logic. To these works, as well as to Archbishop Whately's luminous Chapter on Fallacies, and to the original and suggestive work of Mr. James Mill on the Analysis of the Phenomena of the Human Mini, the Author must, once for all, express his obligations. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

"The following Lectures on Metaphysics constitute the first portion of the Biennial Course which the author was in the habit of delivering during the period of his occupation of the Chair of Logic and Metaphysics in the University of Edinburgh. The Author himself, adopting the Kantian division of the mental faculties into those of Knowledge, Feeling, and Conation, considers the Philosophy of Mind as comprehending, in relation to each of these, the three great subdivisions of Psychology, or the Science of the Phenomena of Mind; Nomology, or the Science of its Laws; and Ontology, or the Science of Results and Inferences. The term Metaphysics, in its strictest sense, is synonymous with the last of these subdivisions; while, in its widest sense, it may be regarded as including the first also, --the second being, in practice at least, if not in scientific accuracy, usually distributed among other departments of Philosophy. The following Lectures cannot be considered as embracing the whole province of Metaphysics in either of the above senses"--Preface. (PsycINFO Database Record (c) 2008 APA, all rights reserved).

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing.