A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.

    Far from the thankless, pointless exercises they are often thought to be, mathematics and logic are indispensable guides to ridding ourselves of dominant opinions and making possible an access to truths, or to a human experience of the utmost value. That is why mathematics may well be the shortest path to the true life, which, when it exists, is characterized by an incomparable happiness.

    ASIN: 0312295170

    

    We're all looking for new ways of thinking that can bring about real solutions to modern problems, from the pursuit of inner serenity to solving world conflicts. In Do You QuantumThink? author Dianne Collins shares her ingenious discovery that reveals a critical missing link to make sense of our changing times. Her discovery provides us with the understanding and methodology to rise above problems of today by laying the foundation for an entirely new way to think.Part science, part philosophy, part spirituality, Do You QuantumThink? draws on a wide spectrum of sources, from cutting edge innovations in the sciences to the insights of the world's greatest spiritual leaders. This book will make you laugh, free you from limiting ideas, and introduce you to the most advanced principles and practical methods for living. Do You QuantumThink? will rock your world in the best of ways as you experience one revelation after another.

     Lessons From Critical Thinkers provides intellectual power to engage with and participate in effective critical thoughts, arguments, debates, reading, and reflection drawn from methods in the history of philosophical cognitive development. •Learn to think slowly and deliberately before making a decision •Get ready to question opinions and even facts •Learn to gather information before jumping to conclusions •Accept and expect the biased and flawed nature of human cognition Lessons From Critical Thinkers gives you a thorough presentation of the ideas and principles of critical thinking practiced by the greatest minds in history. Learn about the most important critical thinking methods to make better decisions in your personal life, career, and friendships. Equip yourself with the essential methods for clear, analytical, logical thinking and critique in a range of ideas and everyday situations. • Discover critical thinking by familiarizing with concepts from other disciplines, like philosophy, cognitive biases and errors, race and gender from sociology and political science, and symbols from rhetoric. • Apply critical thinking and reasoning skills to your day to day problems • Find the most rewarding options in any opportunity. Lessons From Critical Thinkers is a helpful book for readers of any age and background who want to improve their critical thinking skills by learning from the greatest thinkers of all time. Learn to filter out irrelevant information efficiently and prioritize your resources to get the best results. Enhance your communication skills, reasoning, and logic. Improve your critical, logical, observational, and rational thinking skills with the timeless principles presented in this book.

    

    

    An acclaimed author and public speaker, Black shows how this body of knowledge has been declared ‘heretical’ both by the established church and by today’s atheistic intellectual elite.Finally, he outlines in the clearest terms possible the supernatural laws that govern our universe, and describes rules for living that take us beyond consensual thought, rules that may at first seem crazy, even dangerous, but which contain the secrets for achieving success, happiness and a higher state of being.

    

    - help is finally at hand. That help comes in the comfortingly accessible form of Stephen Trombley's Short History of Western Thought, which outlines the 2,500-year history of European ideas from the philosophers of Classical Antiquity to the thinkers of today, No major representative of any significant strand of Western thought escapes Trombley's attention: the Christian Scholastic theologians of the Middle Ages, the great philosophers of the Enlightenment, the German idealists from Kant to Hegel; the utilitarians Bentham and Mill; the transcendentalists Emerson and Thoreau; Kierkegaard and the existentialists; the analytic philosophers Russell, Moore, Whitehead and Wittgenstein; and - last but not least - the four shapers-in-chief of our modern world: the philosopher, historian and political theorist Karl Marx; the naturalist Charles Darwin, proposer of the theory of evolution; Sigmund Freud, the father of psychoanalysis; and the theoretical physicist Albert Einstein, begetter of the special and general theories of relativity and founder of post-Newtonian physics.

    But Tao cannot fully be explained in words; it can only felt and experienced. Tao is something you live, day by day, moment by moment. It s the omnipresent oneness beyond ephemeral phenomena that expresses itself in everything. New York Times bestselling author Ilchi Lee, an enlightened Tao master from South Korea, has laid out a path to living Tao everyday. Along this path, he guides you to an understanding of the meaning of birth, death, and everything in between, building a foundation for living a complete and whole life. The universal principles contained in "Living Tao: Timeless Principles for Everyday Enlightenment" stem from the Korean practice of Sundo, an ancient tradition of mind-body training, as well as Lee s own life experience. With these tangible principles, Ilchi Lee makes this profound topic simple and accessible. "Living Tao" has an unparalleled depth in its simplicity that anyone can absorb and immediately apply. * 2015 INDIEFAB Book of the Year Award Winner, Bronze, Body, Mind & Spirit"

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    The objective here is to explain science in a simple, attractive and fun form that is open to all.The first axiom of this approach was set out as follows: “We believe in the magic of science. We hope to show you that sci-ence is not a secret art, accessible only to a dedicated few. It involves learning about nature and society, and aspects of our existence which affect us all, and which we should all therefore have the chance to understand. We shall interpret science for those who might not speak its language fluently, but want to understand its meaning. We don’t teach, we just tell stories about the beginnings of science, the natural phenomena and the underlying principles through which they occur, and the lives of the people who discovered them.”The aim of the writings collected in this series is to present some key scientific events, ideas and personalities in the form of short stories that are easy and fun to read. Scientific and philo-sophical concepts are explained in a way that anyone may under-stand. Each story may be read separately, but at the same time they all band together to form a wide-ranging introduction to the history of science and areas of contemporary scientific research, as well as some of the recurring problems science has encountered in history and the philosophical dilemmas it raises today.Review“If I were the only survivor on a remote island and all I had with me were this book, a Swiss army knife and a bottle, I would throw the bottle into the sea with the note: ‘Don’t worry, I have everything I need.’”— Ciril Horjak, alias Dr. Horowitz, a comic artist“The writing is understandable, but never simplistic. Instructive, but never patronizing. Straightforward, but never trivial. In-depth, but never too intense.”— Ali Žerdin, editor at Delo, the main Slovenian newspaper“Does science think? Heidegger once answered this question with a decisive No. The writings on modern science skillfully penned by Sašo Dolenc, these small stories about big stories, quickly convince us that the contrary is true. Not only does science think in hundreds of unexpected ways, its intellectual challenges and insights are an inexhaustible source of inspiration and entertainment. The clarity of thought and the lucidity of its style make this book accessible to anyone … in the finest tradition of popularizing science, its achievements, dilemmas and predicaments.”— Mladen Dolar, philosopher and author of A Voice and Nothing More“Sašo Dolenc is undoubtedly one of our most successful authors in the field of popular science, possessing the ability to explain complex scientific achievements to a broader audience in a clear and captivating way while remaining precise and scientific. His collection of articles is of particular importance because it encompasses all areas of modern science in an unassuming, almost light-hearted manner.”— Boštjan Žekš, physicist and former president of the Slovenian Academy of Sciences and Arts

    Hacker leads us into a world of philosophical investigation in which to smell a rat is ever so much easier than to trap it. Wittgenstein defined humans as language-using creatures. The role of philosophy is to ask questions which reveal the limits and nature of language. Taking the expression, description and observation of pain as examples, Hacker explores the ingenuity with which Wittgenstein identified the rules and set the limits of language. (less)