Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being PDF Download
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Author: George Lakoff
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 520
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Book Description
A study of the cognitive science of mathematical ideas.
Author: George Lakoff
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 520
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Book Description
A study of the cognitive science of mathematical ideas.
Author: Rafael E. Núñez
Publisher: Imprint Academic
ISBN: 9780907845065
Category : Philosophy
Languages : en
Pages : 310
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Book Description
Traditional cognitive science ('cognitivism') is Cartesian in the sense that it takes as fundamental the distinction between the mind and the world. This leads to the claim that cognition is representational and best explained by classical AI and computational theory. The authors in this volume develop a critique of cognitivism and introduce an alternative approach -- which owes more to evolutionary biology, embodied robotics, phenomenology and dynamical systems.
Author: Fumiya Iida
Publisher: Springer
ISBN: 3540278338
Category : Computers
Languages : en
Pages : 339
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Book Description
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
ISBN: 0387298312
Category : Mathematics
Languages : en
Pages : 346
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Book Description
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: David Tall
Publisher: Cambridge University Press
ISBN: 1107035708
Category : Education
Languages : en
Pages : 483
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Book Description
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: Bertrand Russell
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 565
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Book Description
Author: Rudy Rucker
Publisher: Courier Corporation
ISBN: 0486492281
Category : Computers
Languages : en
Pages : 337
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Book Description
Originally published: Boston: Houghton Mifflin, 1987.
Author: Elizabeth de Freitas
Publisher: Cambridge University Press
ISBN: 1107134633
Category : Education
Languages : en
Pages : 301
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Book Description
Leading thinkers in mathematics, philosophy and education offer new insights into the fundamental question: what is a mathematical concept?
Author: George Lakoff
Publisher: Basic Books
ISBN: 9780465056743
Category : Philosophy
Languages : en
Pages : 644
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Book Description
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: Jan Gullberg
Publisher: W. W. Norton & Company
ISBN: 9780393040029
Category : Mathematics
Languages : en
Pages : 1148
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Book Description
An illustrated exploration of mathematics and its history, beginning with a study of numbers and their symbols, and continuing with a broad survey that includes consideration of algebra, geometry, hyperbolic functions, fractals, and many other mathematical functions.
