Download or read book Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being written by George Lakoff and published by . This book was released on 2000-11-02 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of the cognitive science of mathematical ideas.
Download or read book Reclaiming Cognition written by Rafael E. Núñez and published by Imprint Academic. This book was released on 1999 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditional cognitive science is Cartesian in the sense that it takes as fundamental the distinction between the mental and the physical, the mind and the world. This leads to the claim that cognition is representational and best explained using models derived from AI and computational theory. The authors depart radically from this model.
Download or read book Embodied Artificial Intelligence written by Fumiya Iida and published by Springer Science & Business Media. This book was released on 2004-07-08 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating from a Dagstuhl seminar, the collection of papers presented in this book constitutes on the one hand a representative state-of-the-art survey of embodied artificial intelligence, and on the other hand the papers identify the important research trends and directions in the field. Following an introductory overview, the 23 papers are organized into topical sections on - philosophical and conceptual issues - information, dynamics, and morphology - principles of embodiment for real-world applications - developmental approaches - artificial evolution and self-reconfiguration
Download or read book 18 Unconventional Essays on the Nature of Mathematics written by Reuben Hersh and published by Springer Science & Business Media. This book was released on 2006-01-16 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines
Download or read book Elbow Room new edition written by Daniel C. Dennett and published by MIT Press. This book was released on 2015-08-07 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: A landmark book in the debate over free will that makes the case for compatibilism. In this landmark 1984 work on free will, Daniel Dennett makes a case for compatibilism. His aim, as he writes in the preface to this new edition, was a cleanup job, “saving everything that mattered about the everyday concept of free will, while jettisoning the impediments.” In Elbow Room, Dennett argues that the varieties of free will worth wanting—those that underwrite moral and artistic responsibility—are not threatened by advances in science but distinguished, explained, and justified in detail. Dennett tackles the question of free will in a highly original and witty manner, drawing on the theories and concepts of fields that range from physics and evolutionary biology to engineering, automata theory, and artificial intelligence. He shows how the classical formulations of the problem in philosophy depend on misuses of imagination, and he disentangles the philosophical problems of real interest from the “family of anxieties” in which they are often enmeshed—imaginary agents and bogeymen, including the Peremptory Puppeteer, the Nefarious Neurosurgeon, and the Cosmic Child Whose Dolls We Are. Putting sociobiology in its rightful place, he concludes that we can have free will and science too. He explores reason, control and self-control, the meaning of “can” and “could have done otherwise,” responsibility and punishment, and why we would want free will in the first place. A fresh reading of Dennett's book shows how much it can still contribute to current discussions of free will. This edition includes as its afterword Dennett's 2012 Erasmus Prize essay.
Download or read book Thinking In Numbers written by Daniel Tammet and published by Little, Brown Spark. This book was released on 2013-07-30 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The irresistibly engaging book that "enlarges one's wonder at Tammet's mind and his all-embracing vision of the world as grounded in numbers" (Oliver Sacks, MD). Thinking in Numbers is the book that Daniel Tammet, mathematical savant and bestselling author, was born to write. In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives. Inspired variously by the complexity of snowflakes, Anne Boleyn's eleven fingers, and his many siblings, Tammet explores questions such as why time seems to speed up as we age, whether there is such a thing as an average person, and how we can make sense of those we love. His provocative and inspiring new book will change the way you think about math and fire your imagination to view the world with fresh eyes.
Download or read book How Mathematicians Think written by William Byers and published by Princeton University Press. This book was released on 2010-05-02 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.
Download or read book How Humans Learn to Think Mathematically written by David Tall and published by Cambridge University Press. This book was released on 2013-09-02 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.
Download or read book Math on the Move written by Malke Rosenfeld and published by Heinemann Educational Books. This book was released on 2016-10-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Kids love to move. But how do we harness all that kinetic energy effectively for math learning? In Math on the Move, Malke Rosenfeld shows how pairing math concepts and whole body movement creates opportunities for students to make sense of math in entirely new ways. Malke shares her experience creating dynamic learning environments by: exploring the use of the body as a thinking tool, highlighting mathematical ideas that are usefully explored with a moving body, providing a range of entry points for learning to facilitate a moving math classroom. ..."--Publisher description.
Download or read book The Principles of Mathematics written by Bertrand Russell and published by W. W. Norton & Company. This book was released on 1996 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical--that what is commonly called mathematics is simply later deductions from logical premises.
Download or read book Mind Tools written by Rudy Rucker and published by Courier Corporation. This book was released on 2013-11-21 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: Boston: Houghton Mifflin, 1987.
Download or read book Women Fire and Dangerous Things written by George Lakoff and published by University of Chicago Press. This book was released on 2008-08-08 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Its publication should be a major event for cognitive linguistics and should pose a major challenge for cognitive science. In addition, it should have repercussions in a variety of disciplines, ranging from anthropology and psychology to epistemology and the philosophy of science. . . . Lakoff asks: What do categories of language and thought reveal about the human mind? Offering both general theory and minute details, Lakoff shows that categories reveal a great deal."—David E. Leary, American Scientist
Download or read book Mysticism and Logic written by Bertrand Russell and published by . This book was released on 1918 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Philosophy In The Flesh written by George Lakoff and published by Basic Books. This book was released on 1999-10-08 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: What are human beings like? How is knowledge possible? What is truth? Where do moral values come from? Questions like these have stood at the center of Western philosophy for centuries. In addressing them, philosophers have made certain fundamental assumptions-that we can know our own minds by introspection, that most of our thinking about the world is literal, and that reason is disembodied and universal-that are now called into question by well-established results of cognitive science. It has been shown empirically that:Most thought is unconscious. We have no direct conscious access to the mechanisms of thought and language. Our ideas go by too quickly and at too deep a level for us to observe them in any simple way.Abstract concepts are mostly metaphorical. Much of the subject matter of philosopy, such as the nature of time, morality, causation, the mind, and the self, relies heavily on basic metaphors derived from bodily experience. What is literal in our reasoning about such concepts is minimal and conceptually impoverished. All the richness comes from metaphor. For instance, we have two mutually incompatible metaphors for time, both of which represent it as movement through space: in one it is a flow past us and in the other a spatial dimension we move along.Mind is embodied. Thought requires a body-not in the trivial sense that you need a physical brain to think with, but in the profound sense that the very structure of our thoughts comes from the nature of the body. Nearly all of our unconscious metaphors are based on common bodily experiences.Most of the central themes of the Western philosophical tradition are called into question by these findings. The Cartesian person, with a mind wholly separate from the body, does not exist. The Kantian person, capable of moral action according to the dictates of a universal reason, does not exist. The phenomenological person, capable of knowing his or her mind entirely through introspection alone, does not exist. The utilitarian person, the Chomskian person, the poststructuralist person, the computational person, and the person defined by analytic philosopy all do not exist.Then what does?Lakoff and Johnson show that a philosopy responsible to the science of mind offers radically new and detailed understandings of what a person is. After first describing the philosophical stance that must follow from taking cognitive science seriously, they re-examine the basic concepts of the mind, time, causation, morality, and the self: then they rethink a host of philosophical traditions, from the classical Greeks through Kantian morality through modern analytic philosopy. They reveal the metaphorical structure underlying each mode of thought and show how the metaphysics of each theory flows from its metaphors. Finally, they take on two major issues of twentieth-century philosopy: how we conceive rationality, and how we conceive language.
Download or read book The Handbook of Mathematical Cognition written by Jamie I.D. Campbell and published by Psychology Press. This book was released on 2005-08-15 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: How does the brain represent number and make mathematical calculations? What underlies the development of numerical and mathematical abilities? What factors affect the learning of numerical concepts and skills? What are the biological bases of number knowledge? Do humans and other animals share similar numerical representations and processes? What underlies numerical and mathematical disabilities and disorders, and what is the prognosis for rehabilitation? These questions are the domain of mathematical cognition, the field of research concerned with the cognitive and neurological processes that underlie numerical and mathematical abilities. TheHandbook of Mathematical Cognition is a collection of 27 essays by leading researchers that provides a comprehensive review of this important research field.
Download or read book Heterogeneity of Function in Numerical Cognition written by Avishai Henik and published by Academic Press. This book was released on 2018-05-17 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heterogeneity of Function in Numerical Cognition presents the latest updates on ongoing research and discussions regarding numerical cognition. With great individual differences in the development or function of numerical cognition at neuroanatomical, neuropsychological, behavioral, and interactional levels, these issues are important for the achievement of a comprehensive understanding of numerical cognition, hence its brain basis, development, breakdown in brain-injured individuals, and failures to master mathematical skills. These functions are essential for the proper development of numerical cognition. Provides an innovative reference on the emerging field of numerical cognition and the branches that converge on this diverse cognitive domain Includes an overview of the multiple disciplines that comprise numerical cognition Focuses on factors that influence numerical cognition, such as language, executive attention, memory and spatial processing Features an innovative organization with each section providing a general overview, developmental research, and evidence from neurocognitive studies
Download or read book Introduction to Mathematical Philosophy written by Bertrand Russell and published by . This book was released on 1920 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
