Download Full eBooks in PDF
Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being book. This book definitely worth reading, it is an incredibly well-written.
Author : George Lakoff,Rafael E. Nunez
Publisher : Unknown
Page : 520 pages
File Size : 41,9 Mb
Release : 2000-11-02
Category : Mathematics
ISBN : UOM:39015049551552
A study of the cognitive science of mathematical ideas.
Author : Rafael E. Núñez,Rafael Núñez,Walter J. Freeman
Publisher : Imprint Academic
Page : 310 pages
File Size : 48,7 Mb
Release : 1999
Category : Brain
ISBN : 0907845061
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.
Author : Fumiya Iida,Rolf Pfeifer,Luc Steels,Yasuo Kuniyoshi
Publisher : Springer
Page : 334 pages
File Size : 43,6 Mb
Release : 2004-07-02
Category : Computers
ISBN : 9783540278337
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
Author : Reuben Hersh
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 49,5 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9780387298313
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
Author : William Byers
Publisher : Princeton University Press
Page : 424 pages
File Size : 53,5 Mb
Release : 2010-05-02
Category : Mathematics
ISBN : 9780691145990
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.
Author : David Tall
Publisher : Cambridge University Press
Page : 483 pages
File Size : 44,9 Mb
Release : 2013-09-02
Category : Education
ISBN : 9781107035706
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.
Author : Bonnie Gold,Sandra Keith,William A. Marion
Publisher : MAA Press
Page : 308 pages
File Size : 53,7 Mb
Release : 1999
Category : Education
ISBN : STANFORD:36105111521345
The collection of 72 articles offers the mathematics teacher suggestions for assessing testing and grading, teaching efficacy, how departments place students into courses, the effectiveness of the major, and the quantitative literacy of the graduating students. Lacks an index. Annotation c. Book New
Author : Paul Lockhart
Publisher : Bellevue Literary Press
Page : 144 pages
File Size : 43,7 Mb
Release : 2009-04-01
Category : Mathematics
ISBN : 9781934137338
“One of the best critiques of current mathematics education I have ever seen.”—Keith Devlin, math columnist on NPR’s Morning Edition A brilliant research mathematician who has devoted his career to teaching kids reveals math to be creative and beautiful and rejects standard anxiety-producing teaching methods. Witty and accessible, Paul Lockhart’s controversial approach will provoke spirited debate among educators and parents alike and it will alter the way we think about math forever. Paul Lockhart, has taught mathematics at Brown University and UC Santa Cruz. Since 2000, he has dedicated himself to K-12 level students at St. Ann’s School in Brooklyn, New York.
Author : Mark Johnson
Publisher : University of Chicago Press
Page : 265 pages
File Size : 54,5 Mb
Release : 2017-11-20
Category : Philosophy
ISBN : 9780226500393
Mark Johnson is one of the great thinkers of our time on how the body shapes the mind. This book brings together a selection of essays from the past two decades that build a powerful argument that any scientifically and philosophically satisfactory view of mind and thought must ultimately explain how bodily perception and action give rise to cognition, meaning, language, action, and values. A brief account of Johnson’s own intellectual journey, through which we track some of the most important discoveries in the field over the past forty years, sets the stage. Subsequent chapters set out Johnson’s important role in embodied cognition theory, including his cofounding (with George Lakoff) of conceptual metaphor theory and, later, their theory of bodily structures and processes that underlie all meaning, conceptualization, and reasoning. A detailed account of how meaning arises from our physical engagement with our environments provides the basis for a nondualistic, nonreductive view of mind that he sees as most congruous with the latest cognitive science. A concluding section explores the implications of our embodiment for our understanding of knowledge, reason, and truth. The resulting book will be essential for all philosophers dealing with mind, thought, and language.
Author : George Lakoff
Publisher : Basic Books
Page : 644 pages
File Size : 46,6 Mb
Release : 1999-10-08
Category : Philosophy
ISBN : 0465056741
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.
Author : Jamie I.D. Campbell
Publisher : Psychology Press
Page : 528 pages
File Size : 55,5 Mb
Release : 2005-08-15
Category : Psychology
ISBN : 9781135423650
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. The Handbook of Mathematical Cognition is a collection of 27 essays by leading researchers that provides a comprehensive review of this important research field.
Author : Wolfgang Tschacher,Claudia Bergomi
Publisher : Andrews UK Limited
Page : 268 pages
File Size : 55,7 Mb
Release : 2015-10-27
Category : Psychology
ISBN : 9781845405519
This edited volume is scientifically based, but readable for a larger audience, covering the concept of "embodied cognition" and its implications from a transdisciplinary angle. The contributions are from the fields of psychology, computer science, biology, philosophy, and psychiatry. First, the roots of embodiment are described with historical, computer-science, and phenomenological viewpoints. It is argued that embodied cognition is relevant for the discussion of intentionality, with a particular focus on underlying neural processes as well as the context of synergetics and self-organization theory. As cognition is socially embedded, a large section of this book concentrates on "embodied communication": How does embodiment influence the way to approach others, what role do body movements play in social interaction, what is the function of nonverbal synchrony in interpersonal relationships and psychotherapy? Embodied cognitive agents are further embedded in particular cultural and environmental contexts. This book thus addresses the active role that cultural and environmental aspects play in driving cognition. Some applications of embodiment, e.g. to psychotherapy and aesthetics are also presented.
Author : Reuben Hersh
Publisher : Oxford University Press
Page : 368 pages
File Size : 49,5 Mb
Release : 1997-08-21
Category : Mathematics
ISBN : 9780198027362
Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.
Author : Bertrand Russell
Publisher : Courier Corporation
Page : 230 pages
File Size : 52,8 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 0486277240
In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy. In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.
Author : Avishai Henik,Wim Fias
Publisher : Academic Press
Page : 480 pages
File Size : 53,8 Mb
Release : 2018-05-17
Category : Science
ISBN : 9780128115305
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