This book includes some of the most original and influential contributions to logic and the philosophy of logic during the past twenty years. It contains thirty-five essays, many of which started new trends in logic. For example, some of the essays in Part One gave birth to what is now known as free logic, and some of the essays in Part Two were among the earliest contributions to what is now known as truth-value semantics. The essays in Part Three are contributions to and improvements of already extant logics, such as intuitionistic logic, natural deduction, and the logic of sequents. Introductions to the parts of the book cover the history of the contributions and their importance. The essays have been thoroughly revised since their publication in learned journals.

Does God exist? This is probably the most debated question in the history of mankind. Scholars, scientists, and philosophers have spent their lifetimes trying to prove or disprove the existence of God, only to have their theories crucified by other scholars, scientists, and philosophers. Where the debate breaks down is in the ambiguities and colloquialisms of language. But, by using a universal, unambiguous language—namely, mathematics—can this question finally be answered definitively? That’s what Dr. Stephen Unwin attempts to do in this riveting, accessible, and witty book, The Probability of God. At its core, this groundbreaking book reveals how a math equation developed more than 200 years ago by noted European philosopher Thomas Bayes can be used to calculate the probability that God exists. The equation itself is much more complicated than a simple coin toss (heads, He’s up there running the show; tails, He’s not). Yet Dr. Unwin writes with a clarity that makes his mathematical proof easy for even the nonmathematician to understand and a verve that makes his book a delight to read. Leading you carefully through each step in his argument, he demonstrates in the end that God does indeed exist. Whether you’re a devout believer and agree with Dr. Unwin’s proof or are unsure about all things divine, you will find this provocative book enlightening and engaging. “One of the most innovative works [in the science and religion movement] is The Probability of God...An entertaining exercise in thinking.”—Michael Shermer, Scientific American “Unwin’s book [is] peppered with wry, self-deprecating humor that makes the scientific discussions more accessible...Spiritually inspiring.”--Chicago Sun Times “A pleasantly breezy account of some complicated matters well worth learning about.”--Philadelphia Inquirer “One of the best things about the book is its humor.”--Cleveland Plain Dealer “In a book that is surprisingly lighthearted and funny, Unwin manages to pack in a lot of facts about science and philosophy.”--Salt Lake Tribune

It is tempting to think that, if a person's beliefs are coherent, they are also likely to be true. Indeed, this truth-conduciveness claim is the cornerstone of the popular coherence theory of knowledge and justification. Hitherto much confusion has been caused by the inability of coherence theorists to define their central concept. Nor have they succeeded in specifying in unambiguous terms what the notion of truth-conduciveness involves. This book is the most extensive and detailedstudy of coherence and probable truth to date.Erik Olsson argues that the value of coherence has been generally overestimated; it is severely problematic to maintain that coherence has a role to play in the process whereby beliefs are acquired or justified. He proposes that the opposite of coherence, i.e. incoherence, can still be the driving force in the process whereby beliefs are retracted, so that the role of coherence in our enquiries is negative rather than positive. Another innovative feature of Olsson's book is its unified,interdisciplinary approach to the issues at hand. The arguments are equally valid for coherence among any items of information, regardless of their sources (beliefs, memories, testimonies, and so on). Writing in accessible, non-technical language, Olsson takes the reader through much of the history of thesubject, from early theorists like A. C. Ewing and C. I. Lewis to contemporary figures like Laurence BonJour and C. A. J. Coady. Against Coherence will make stimulating reading for epistemologists and anyone with a serious interest in truth.

F. P. Ramsey was a remarkably creative and subtle philosopher who made significant contributions to logic, philosophy of mathematics, philosophy of language and decision theory.

Resonance examines some building blocks of epistemology as a prelude to the careful analysis of the foundations of probability. The concept of resonance is introduced to shed light on the philosophical problems of induction, consciousness, intelligence and free will. The same concept is later applied to provide support for a new philosophical theory of probability.Although based on existing ideas and theories, the epistemological concept of resonance is investigated for the first time in this book. The best-known philosophical theories of probability, frequency and subjective, are shown to be unrealistic and dissociated from the two main branches of statistics: frequency statistics and Bayesian statistics.Written in an accessible style, this book can be enjoyed by philosophers, statisticians and mathematicians, and also by anyone looking to expand their understanding of the disciplines of epistemology and probability.

It is a commonplace that scientific inquiry makes extensive use of probabilities, many of which seem to be objective chances, describing features of reality that are independent of our minds. Such chances appear to have a number of paradoxical or puzzling features: they appear to be mind-independent facts, but they are intimately connected with rational psychology; they display a temporal asymmetry, but they are supposed to be grounded in physical laws that are time-symmetric; and chances are used to explain and predict frequencies of events, although they cannot be reduced to those frequencies. This book offers an accessible and non-technical introduction to these and other puzzles. Toby Handfield engages with traditional metaphysics and philosophy of science, drawing upon recent work in the foundations of quantum mechanics and thermodynamics to provide a novel account of objective probability that is empirically informed without requiring specialist scientific knowledge.

An introductory 2001 textbook on probability and induction written by a foremost philosopher of science.

Charles Peirce’s Illustrations of the Logic of Science is an early work in the philosophy of science and the official birthplace of pragmatism. It contains Peirce’s two most influential papers: “The Fixation of Belief” and “How to Make Our Ideas Clear,” as well as discussions on the theory of probability, the ground of induction, the relation between science and religion, and the logic of abduction. Unsatisfied with the result and driven by a constant, almost feverish urge to improve his work, Peirce spent considerable time and effort revising these papers. After the turn of the century these efforts gained significant momentum when Peirce sought to establish his role in the development of pragmatism while distancing himself from the more popular versions that had become current. The present edition brings together the original series as it appeared in Popular Science Monthly and a selection of Peirce’s later revisions, many of which remained hidden in the mass of messy manuscripts that were left behind after his death in 1914.

This volume presents 38 classic texts in formal epistemology, and strengthens the ties between research into this area of philosophy and its neighbouring intellectual disciplines. The editors provide introductions to five subsections: Bayesian Epistemology, Belief Change, Decision Theory, Interactive Epistemology and Epistemic Logic. 'Formal epistemology' is a term coined in the late 1990s for a new constellation of interests in philosophy, the origins of which are found in earlier works of epistemologists, philosophers of science and logicians. It addresses a growing agenda of problems concerning knowledge, belief, certainty, rationality, deliberation, decision, strategy, action and agent interaction – and it does so using methods from logic, probability, computability, decision and game theory. The volume also includes a thorough index and suggestions for further reading, and thus offers a complete teaching and research package for students as well as research scholars of formal epistemology, philosophy, logic, computer science, theoretical economics and cognitive psychology.

A compilation of all previously published writings on philosophy and the foundations of mathematics from the greatest of the generation of Cambridge scholars that included G.E. Moore, Bertrand Russell, Ludwig Wittgenstein and Maynard Keynes.