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Numerical Cognition and the Epistemology of Arithmetic

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Release : 2024-03-31
Genre : Science
Kind : eBook
Book Rating : 88X/5 ( reviews)

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Book Synopsis Numerical Cognition and the Epistemology of Arithmetic by : Markus Pantsar

Download or read book Numerical Cognition and the Epistemology of Arithmetic written by Markus Pantsar. This book was released on 2024-03-31. Available in PDF, EPUB and Kindle. Book excerpt: The first book-length philosophical account of arithmetical knowledge that is based on the state-of-the-art empirical studies of numerical cognition.

Dual-Process Theories of Numerical Cognition

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Release : 2018-08-12
Genre : Science
Kind : eBook
Book Rating : 975/5 ( reviews)

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Book Synopsis Dual-Process Theories of Numerical Cognition by : Mario Graziano

Download or read book Dual-Process Theories of Numerical Cognition written by Mario Graziano. This book was released on 2018-08-12. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a philosophical interpretation to numerical cognition based on dual process theories and heuristics. It shows how investigations in cognitive science can shed light on issues traditionally raised by philosophers of mathematics. The analysis will also help readers to better understand the relationship between current neuroscientific research and the philosophical reflection on mathematics. The author seeks to explain the acquisition of mathematical concepts. To accomplish this, he needs to answer two questions. How can the concepts of approximate numerosity become an object of thought that is so accessible to our consciousness? How are these concepts refined and specified in such a way as to become numbers? Unfortunately, there is currently no model that can truly demonstrate the role of language in the development of numerical skills starting from approximate pre-verbal skills. However, the author details a solution to this problem: dual process theories. It is an approach widely used by theorists focusing on reasoning, decision making, social cognition, and consciousness. Here, he applies this approach to the studies on mathematical knowledge. He details the results brought about by psychological and neuroscientific studies conducted on numerical cognition by key neuroscientists. In the process, he develops the foundations of a new, potential philosophical explanation on mathematical knowledge.

Naturalizing Logico-Mathematical Knowledge

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Release : 2018-02-01
Genre : Mathematics
Kind : eBook
Book Rating : 447/5 ( reviews)

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Book Synopsis Naturalizing Logico-Mathematical Knowledge by : Sorin Bangu

Download or read book Naturalizing Logico-Mathematical Knowledge written by Sorin Bangu. This book was released on 2018-02-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Visual Thinking in Mathematics

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Release : 2007-07-05
Genre : Philosophy
Kind : eBook
Book Rating : 942/5 ( reviews)

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Book Synopsis Visual Thinking in Mathematics by : Marcus Giaquinto

Download or read book Visual Thinking in Mathematics written by Marcus Giaquinto. This book was released on 2007-07-05. Available in PDF, EPUB and Kindle. Book excerpt: Visual thinking - visual imagination or perception of diagrams and symbol arrays, and mental operations on them - is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquintoargues that visual thinking in mathematics is rarely just a superfluous aid; it usually has epistemological value, often as a means of discovery. Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition,Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis. He shows how we can discern abstract general truths by means of specific images, how synthetic a priori knowledge is possible, and how visual means can help us grasp abstract structures.Visual Thinking in Mathematics reopens the investigation of earlier thinkers from Plato to Kant into the nature and epistemology of an individual's basic mathematical beliefs and abilities, in the new light shed by the maturing cognitive sciences. Clear and concise throughout, it will appeal to scholars and students of philosophy, mathematics, and psychology, as well as anyone with an interest in mathematical thinking.

The Oxford Handbook of Numerical Cognition

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Release : 2015
Genre : Medical
Kind : eBook
Book Rating : 346/5 ( reviews)

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Book Synopsis The Oxford Handbook of Numerical Cognition by : Roi Cohen Kadosh

Download or read book The Oxford Handbook of Numerical Cognition written by Roi Cohen Kadosh. This book was released on 2015. Available in PDF, EPUB and Kindle. Book excerpt: How do we understand numbers? Do animals and babies have numerical abilities? Why do some people fail to grasp numbers, and how we can improve numerical understanding? Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards. Numerical cognition is a vibrant area that brings together scientists from different and diverse research areas (e.g., neuropsychology, cognitive psychology, developmental psychology, comparative psychology, anthropology, education, and neuroscience) using different methodological approaches (e.g., behavioral studies of healthy children and adults and of patients; electrophysiology and brain imaging studies in humans; single-cell neurophysiology in non-human primates, habituation studies in human infants and animals, and computer modeling). While the study of numerical cognition had been relatively neglected for a long time, during the last decade there has been an explosion of studies and new findings. This has resulted in an enormous advance in our understanding of the neural and cognitive mechanisms of numerical cognition. In addition, there has recently been increasing interest and concern about pupils' mathematical achievement in many countries, resulting in attempts to use research to guide mathematics instruction in schools, and to develop interventions for children with mathematical difficulties. This handbook brings together the different research areas that make up the field of numerical cognition in one comprehensive and authoritative volume. The chapters provide a broad and extensive review that is written in an accessible form for scholars and students, as well as educationalists, clinicians, and policy makers. The book covers the most important aspects of research on numerical cognition from the areas of development psychology, cognitive psychology, neuropsychology and rehabilitation, learning disabilities, human and animal cognition and neuroscience, computational modeling, education and individual differences, and philosophy. Containing more than 60 chapters by leading specialists in their fields, the Oxford Handbook of Numerical Cognition is a state-of-the-art review of the current literature.

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