Mathematical Epistemology And Psychology
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| Author | : E.W. Beth |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 391 |
| Release | : 2013-03-09 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9401721939 |
One of the controversial philosophical issues of recent years has been the question of the nature of logical and mathematical entities. Platonist or linguistic modes of explanation have become fashionable, whilst abstrac tionist and constructionist theories have ceased to be so. Beth and Piaget approach this problem in their book from two somewhat different points of view. Beth's approach is largely historico-critical, although he discusses the nature of heuristic thinking in mathematics, whilst that of Piaget is psycho-genetic. The major purpose of this introduction is to summarise some of the main points of their respective arguments. In the first part of this book Beth makes a detailed study of the history of philosophical thinking about mathematics, and draws our attention to the important role played by the Aristotelian methodology of the demon strative sciences. This, he tells us, is characterised by three postulates: (a) deductivity, (b) self-evidence, and (c) reality. The last postulate asserts that the primitive notions of a demonstrative science must have reference to a domain of real entities in order to have significance. On the Aristote lian view discursive reasoning plays a major role in mathematics, whilst pure intuition plays a somewhat subordinate one.
| Author | : Sorin Bangu |
| Publisher | : Routledge |
| Total Pages | : 319 |
| Release | : 2018-02-01 |
| Genre | : Mathematics |
| ISBN | : 1351998447 |
This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. Naturalizing Logico-Mathematical Knowledge contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers’ willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.
| Author | : Paul Ernest |
| Publisher | : Routledge |
| Total Pages | : 295 |
| Release | : 2012-10-12 |
| Genre | : Education |
| ISBN | : 1136364722 |
First published in 1994. This book and its companion volume, Mathematics, Education and Philosophy: An International Perspective are edited collections. Instead of the sharply focused concerns of the research monograph, the books offer a panorama of complementary and forward-looking perspectives. They illustrate the breadth of theoretical and philosophical perspectives that can fruitfully be brough to bear on the mathematics and education. The empathise of this book is on epistemological issues, encompassing multiple perspectives on the learning of mathematics, as well as broader philosophical reflections on the genesis of knowledge. It explores constructivist and social theories of learning and discusses the rile of the computer in light of these theories.
| Author | : Barbara K. Hofer |
| Publisher | : Routledge |
| Total Pages | : 429 |
| Release | : 2012-08-21 |
| Genre | : Education |
| ISBN | : 113660863X |
This is the first book to provide a comprehensive overview of the theoretical and methodological approaches to the study of personal epistemology from a psychological and educational perspective. Both theory building and empirical research have grown dramatically in the past decade but, until now, this work has not been pulled together in a single volume. That is the mission of this volume whose state-of-the-art theory and research are likely to define the field for the next 20 years. Key features of this important new book include: *Pioneering Contributors--The book provides current perspectives of each of the major theoreticians and researchers who pioneered this growing field, as well as contributions from new researchers. *Diverse Perspectives--The contributors represent a variety of perspectives, including education, educational psychology, developmental psychology, higher education, and science and mathematics education. *Editorial Integration--Opening and closing chapters by the editors set out key issues confronting the field.
| Author | : Jacques Hadamard |
| Publisher | : Read Books Ltd |
| Total Pages | : 130 |
| Release | : 2011-10-25 |
| Genre | : Mathematics |
| ISBN | : 1447493273 |
Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.
| Author | : Jerome R. Busemeyer |
| Publisher | : |
| Total Pages | : 425 |
| Release | : 2015 |
| Genre | : Psychology |
| ISBN | : 0199957991 |
This Oxford Handbook offers a comprehensive and authoritative review of important developments in computational and mathematical psychology. With chapters written by leading scientists across a variety of subdisciplines, it examines the field's influence on related research areas such as cognitive psychology, developmental psychology, clinical psychology, and neuroscience. The Handbook emphasizes examples and applications of the latest research, and will appeal to readers possessing various levels of modeling experience. The Oxford Handbook of Computational and mathematical Psychology covers the key developments in elementary cognitive mechanisms (signal detection, information processing, reinforcement learning), basic cognitive skills (perceptual judgment, categorization, episodic memory), higher-level cognition (Bayesian cognition, decision making, semantic memory, shape perception), modeling tools (Bayesian estimation and other new model comparison methods), and emerging new directions in computation and mathematical psychology (neurocognitive modeling, applications to clinical psychology, quantum cognition). The Handbook would make an ideal graduate-level textbook for courses in computational and mathematical psychology. Readers ranging from advanced undergraduates to experienced faculty members and researchers in virtually any area of psychology--including cognitive science and related social and behavioral sciences such as consumer behavior and communication--will find the text useful.
| Author | : Imre Lakatos |
| Publisher | : Cambridge University Press |
| Total Pages | : 302 |
| Release | : 1980-10-16 |
| Genre | : Mathematics |
| ISBN | : 9780521280303 |
Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics together with some critical essays on contemporary philosophers of science.
| Author | : Paolo Mancosu |
| Publisher | : Oxford University Press on Demand |
| Total Pages | : 460 |
| Release | : 2008-06-19 |
| Genre | : Philosophy |
| ISBN | : 0199296456 |
There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.
| Author | : Mary Leng |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 199 |
| Release | : 2007-11-15 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 0199228248 |
What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions. Written by some of the world's leading philosophers of mathematics, psychologists, and mathematicians, Mathematical Knowledge gives a lively sense of the current state of debate in this fascinating field.
| Author | : Pearla Nesher |
| Publisher | : CUP Archive |
| Total Pages | : 234 |
| Release | : 1990-02-23 |
| Genre | : Education |
| ISBN | : 9780521367875 |
This 1990 book is aimed at teachers, mathematics educators and general readers who are interested in mathematics education from a psychological point of view.
