Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

    According to the author, these trends sought to create a unified conceptual apparatus as a common basis for the whole of human knowledge.Because these new developments in logical thought tended to perfect and sharpen the deductive method, an indispensable tool in many fields for deriving conclusions from accepted assumptions, the author decided to widen the scope of the work. In subsequent editions he revised the book to make it also a text on which to base an elementary college course in logic and the methodology of deductive sciences. It is this revised edition that is reprinted here.Part One deals with elements of logic and the deductive method, including the use of variables, sentential calculus, theory of identity, theory of classes, theory of relations and the deductive method. The Second Part covers applications of logic and methodology in constructing mathematical theories, including laws of order for numbers, laws of addition and subtraction, methodological considerations on the constructed theory, foundations of arithmetic of real numbers, and more. The author has provided numerous exercises to help students assimilate the material, which not only provides a stimulating and thought-provoking introduction to the fundamentals of logical thought, but is the perfect adjunct to courses in logic and the foundation of mathematics.

    This book includes criticisms and comments on Russells writings; a brief list of suggested reading; and chronologies that place Russell within his own age and in the broader scheme of philosophy.

    Regularly priced at $4.99. Read on your PC, Mac, smart phone, tablet or Kindle device. Vipassana is not a belief system, religion, or a philosophy. Though Buddhist in origin, it isn’t dependent on Buddhism, and you certainly don’t have to be a Buddhist to practice Vipassana. Vipassana is a form of meditation, or a mental exercise, if you will, that has the capacity to do absolute wonders in your life. It’s a fantastic way to relieve stress, anxiety, depression, reduce blood pressure, end drug dependency, and help with pain management – greatly minimizing the need for medication. It’s also effective in dealing with anger management issues, post traumatic stress, and hormonal changes. The list doesn’t end there. It’s proven to increase productivity in the workplace, heighten memory, concentration, and focus, and helps those with cognitive difficulties. And best of all? It requires absolutely no investment or special equipment. It’s free! This book will delve into Vipassana, explaining everything you need to know to practice Vipassana regularly (and successfully) in your life so that you can reap all its benefits, most especially ridding yourself of stress and anxiety, instead living with happiness, peace, and joy. Here Is A Preview Of What You'll Learn... What is Vipassana? Preliminary Preparations Sitting Vipassana (the First Exercise) Labelling Observing Motion Observing Sensation If You ABSOLUTELY Have to Move A Few Warnings Active Vipassana Much, much more! Download your copy today! Tags: vipassana, mindfulness, meditation, vipassana meditation, dhamma, dharma, mindfulness exercises, mindfulness training, vipassana yoga, vipassana meditation technique, Buddhism, vipassana buddhism, vipassana goenka, vipassana mindfulness, meditation, buddhist

    The work of Yagyῡ Munenori from 1632 concerns martial arts and military science. It is translated by Thomas Cleary and can be found tucked behind Miyamoto Musashi‘s “the Book of five rings” from 1643. Both these texts analyse conflict between two men armed with swords and scale this up bigger battles. These important treaties on swordsmanship, and have been taken as giving lessons on life in general.

    The Preface to Hegel's first major work, the Phenomenology of Spirit, lays the groundwork for all his other writing by explaining what is most innovative about Hegel's philosophy.This new translation combines readability with maximum precision, breaking Hegel's long sentences and simplifying their often complex structure. At the same time, it is more faithful to the original than any previous translation.The heart of the book is the detailed commentary, supported by an introductory essay. Together they offer a lucid and elegant explanation of the text and elucidate difficult issues in Hegel, making his claims and intentions intelligible to the beginner while offering interesting and original insights to the scholar and advanced student. The commentary often goes beyond the particular phrase in the text to provide systematic context and explain related topics in Hegel and his predecessors (including Kant, Spinoza, and Aristotle, as well as Fichte, Schelling, Holderlin, and others).The commentator refrains from playing down (as many interpreters do today) those aspects of Hegel's thought that are less acceptable in our time, and abstains from mixing his own philosophical preferences with his reading of Hegel's text. His approach is faithful to the historical Hegel while reconstructing Hegel's ideas within their own context."

    The lectures provided a backdrop for the degrees by giving lessons in comparative religion, history, and philosophy."

    The book has been designed to offer maximal accessibility to the widest range of students (not only those majoring in philosophy) and assumes no formal training in elementary symbolic logic. It offers a comprehensive course covering all basic definitions of induction and probability, and considers such topics as decision theory, Bayesianism, frequency ideas, and the philosophical problem of induction. The key features of the book are: * A lively and vigorous prose style* Lucid and systematic organization and presentation of the ideas* Many practical applications* A rich supply of exercises drawing on examples from such fields as psychology, ecology, economics, bioethics, engineering, and political science* Numerous brief historical accounts of how fundamental ideas of probability and induction developed.* A full bibliography of further reading Although designed primarily for courses in philosophy, the book could certainly be read and enjoyed by those in the social sciences (particularly psychology, economics, political science and sociology) or medical sciences such as epidemiology seeking a reader-friendly account of the basic ideas of probability and induction. Ian Hacking is University Professor, University of Toronto. He is Fellow of the Royal Society of Canada, Fellow of the British Academy, and Fellow of the American Academy of Arts and Sciences. he is author of many books including five previous books with Cambridge (The Logic of Statistical Inference, Why Does Language Matter to Philosophy?, The Emergence of Probability, Representing and Intervening, and The Taming of Chance).

    In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Godel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

    Notions like denumerability, modal scope distinction, Bayesian conditionalization, and logical completeness are usually only elucidated deep within difficultspecialist texts. By offering simple explanations that by-pass much irrelevant and boring detail, Philosophical Devices is able to cover a wealth of material that is normally only available to specialists.The book contains four sections, each of three chapters. The first section is about sets and numbers, starting with the membership relation and ending with the generalized continuum hypothesis. The second is about analyticity, a prioricity, and necessity. The third is about probability, outliningthe difference between objective and subjective probability and exploring aspects of conditionalization and correlation. The fourth deals with metalogic, focusing on the contrast between syntax and semantics, and finishing with a sketch of Godel's theorem.Philosophical Devices will be useful for university students who have got past the foothills of philosophy and are starting to read more widely, but it does not assume any prior expertise. All the issues discussed are intrinsically interesting, and often downright fascinating. It can be read withpleasure and profit by anybody who is curious about the technical infrastructure of contemporary philosophy.

    The Road Since Structure, assembled with Kuhn's input before his death in 1996, follows the development of his thought through the later years of his life: collected here are several essays extending and rethinking the perspectives of Structure as well as an extensive, fascinating autobiographical interview in which Kuhn discusses the course of his life and philosophy.

    In this book Saul Kripke brings his powerful philosophic intelligence to bear on Wittgenstein's analysis of the notion of following a rule.

    One likely reason why the first edition was ignored is that it contained many untranslated quotations from French and German authors. For this new edition these passages have all been translated into English. Perhaps the main reason why it was denounced is that Cartesian Linguistics contains, implicitly if not explicitly, trenchant criticisms of empiricist theories about linguistics and the mind. Due largely to Chomsky's efforts, these are not so dominant now as they were when the first edition appeared in 1966, although they still command the attention of researchers and the public imagination. In his introduction Professor McGilvray focuses on the contrast between rationalist and empiricist approaches to language and the mind. He discusses at length the two most distinctive features of what he calls Chomsky's "rationalist-romantic" approach: its emphasis on linguistic creativity and its insistence that this creativity can be explained only by assuming that humans are endowed with innate concepts and mental faculties. In the course of the discussion he connects Chomsky's early treatment of these themes with his later development of them, and with Chomsky's well-known views on politics and education.

    This is the initial volume of a four-book set in which Kenny will unfold a magisterial new history of Western philosophy, the first major single-author history of philosophy to appear in decades.Ancient Philosophy spans over a thousand years and brings to life the great minds of the past, from Thales, Pythagoras, and Parmenides, to Socrates, Epictetus, Marcus Aurelius, and Augustine. The book's great virtue is that it is written by one of the world's leading authorities on the subject. Instead of an uncritical, straightforward recitation of known facts—Plato and his cave of shadows, Aristotle's ethics, Augustine's City of God—we see the major philosophers through the eyes of a man who has spent a lifetime contemplating their work. Thus we do not simply get an overview of Aristotle, for example, but a penetrating and insightful critique of his thought. Kenny offers an illuminating account of the various schools of thought, from the Pre-Socratics to the Epicureans. He examines the development of logic and reason, ancient ideas about physics ("how things happen"), metaphysics and ethics, and the earliest thinking about the soul and god.Vividly written, but serious and deep enough to offer a genuine understanding of the great philosophers, Kenny's lucid and stimulating history will become the definitive work for anyone interested in the people and ideas that shaped the course of Western thought.Sir Anthony Kenny is one of Britain's most distinguished academic figures. He has been Pro-Vice-Chancellor of the University of Oxford, Master of Balliol College, Chairman of the Board of the British Library, and President of the British Academy. He has published more than forty books on philosophy and history.

    W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.