To understand the universe in the far future, we must first describe its present state and structure on the grand scale, and how its present properties arose. Dr Islam explains these topics in an accessible way in the first part of the book. From this background he speculates about the future evolution of the universe and predicts the major changes that will occur. The author has largely avoided mathematical formalism and therefore the book is well suited to general readers with a modest background knowledge of physics and astronomy.

    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.

    This 8-hour free course introduced the study of philosophy and the methods employed by The Open University in teaching philosophy.

    Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.

    Suitable for a two semester course in complex analysis, or as a supplementary text for an advanced course in function theory, this book aims to give students a good foundation of complex analysis and provides a basis for solving problems in mathematics, physics, engineering and many other sciences.

    Have you ever stopped to think about what it is that will make your life worth living? Is it the large amount of money that you have in the bank? The prestigious education that you have? The family and friends that surround you? Or your spiritual belief that there is someone greater than you in the world? Most people will spend their entire lifetimes trying to figure it out, but only a few will have the privilege of really understanding and experiencing themselves what it means to live a fulfilled life. Over the past years, we’ve seen many life philosophies take center stage, all claiming to hold to secret to happiness and fulfillment. While all of them may have very convincing premises, only one truly stands out. Ikigai, or the Japanese concept of finding your purpose, is the key to living a meaningful life. If there’s one people group who have mastered the art of living - and living well, it’s definitely the Okinawans of Japan. Famous for being the world’s longest-living people, they attribute their joy and contentment to finding their ikigai. It’s the reason why they live longer, happier, and better lives than the rest of us. So how does knowing your ikigai change your life? And what should you do to help you uncover your ikigai? Well, you’ll discover all that and more after you’ve listened to this audiobook. This audiobook is packed with helpful insights that will change not just the way you think, but also the way you live. You’ll learn how to slow down and let go of the things that stop you from finding your ultimate purpose. This audiobook will also give you the blueprint to living the life that you always wanted so you won’t have to feel your life is meaningless ever again. I hope that through this audiobook, you will see joy, meaning, and purpose in every single day of your life.©2018 Zen Mastery (P)2018 Zen Mastery

    In this book, the American pragmatist Richard Rorty and the French analytic philosopher Pascal Engel present their radically different perspectives on truth and its correspondence to reality.Rorty doubts that the notion of truth can be of any practical use and points to the preconceptions that lie behind truth in both the intellectual and social spheres. Engel prefers a realist conception, defending the relevance and value of truth as a norm of belief and inquiry in both science and the public domain. Rorty finds more danger in using the notion of truth than in getting rid of it. Engel thinks it is important to hold on to the idea that truth is an accurate representation of reality.In Rorty's view, epistemology is an artificial construct meant to restore a function to philosophy usurped by the success of empirical science. Epistemology and ontology are false problems, and with their demise goes the Cartesian dualism of subject and object and the ancient problematic of appearance and reality. Conventional "philosophical problems," Rorty asserts, are just symptoms of the professionalism that has disfigured the discipline since the time of Kant. Engel, however, is by no means as complacent as Rorty in heralding the "end of truth," and he wages a fierce campaign against the "veriphobes" who deny its value.What's the Use of Truth? is a rare opportunity to experience each side of this impassioned debate clearly and concisely. It is a subject that has profound implications not only for philosophical inquiry but also for the future study of all aspects of our culture.

    Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, intuitive visual representations of real-world examples are used to show how Bayes' rule is actually a form of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to gain an intuitive understanding of Bayesian analysis. As an aid to understanding, online computer code (in MatLab, Python and R) reproduces key numerical results and diagrams.Stone's book is renowned for its visually engaging style of presentation, which stems from teaching Bayes' rule to psychology students for over 10 years as a university lecturer.

    The arguement is developed by means of the notion of possible worlds and ranges over key problems including the nature of essence, trans-world identity, negative existential propositions, and the existence of unactual objects in other possible worlds. In the final chapters Professor Plantinga applies his logical theories to the elucidation of two problems in the philosophy of religion: the Problem of Evil and the Ontological Arguement. The first of these, the problem of reconciling the moral perfection and omnipotence of God with the existence of evil, can, he concludes, be resolved, and the second given a sound formulation. The book ends with an appendix on Quine's objection to quantified modal logic.

    

    Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.

    

    

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    A timeless introduction to the field and a landmark in symbolic logic, showing that classical logic can be treated algebraically.