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Grounding Concepts

Author: C. S. Jenkins
Publisher: OUP Oxford
ISBN: 0191552402
Size: 50.13 MB
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Grounding Concepts tackles the issue of arithmetical knowledge, developing a new position which respects three intuitions which have appeared impossible to satisfy simultaneously: a priorism, mind-independence realism, and empiricism. Drawing on a wide range of philosophical influences, but avoiding unnecessary technicality, a view is developed whereby arithmetic can be known through the examination of empirically grounded concepts. These are concepts which, owing to their relationship to sensory input, are non-accidentally accurate representations of the mind-independent world. Examination of such concepts is an armchair activity, but enables us to recover information which has been encoded in the way our concepts represent. Emphasis on the key role of the senses in securing this coding relationship means that the view respects empiricism, but without undermining the mind-independence of arithmetic or the fact that it is knowable by means of a special armchair method called conceptual examination. A wealth of related issues are covered during the course of the book, including definitions of realism, conditions on knowledge, the problems with extant empiricist approaches to the a priori, mathematical explanation, mathematical indispensability, pragmatism, conventionalism, empiricist criteria for meaningfulness, epistemic externalism and foundationalism. The discussion encompasses themes from the work of Locke, Kant, Ayer, Wittgenstein, Quine, McDowell, Field, Peacocke, Boghossian, and many others.

The Bloomsbury Companion To Epistemology

Author: Andrew Cullison
Publisher: Bloomsbury Publishing
ISBN: 1472585798
Size: 48.68 MB
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For anyone looking to better understand the topics at the centre of contemporary epistemology, The Bloomsbury Companion to Epistemology presents a valuable guide. This up-to-date Companion covers all the fundamental questions asked by epidemiologists today - areas that have continued to attract interest historically as well as topics that have emerged more recently as active areas of research. Fifteen specially-commissioned essays from a respected team of experts reveal where important work continues to be done in the area and the new directions the field is taking, such as: • Foundationalism by Daniel Howard-Snyder • Coherentism by Jonathan Kvanvig • Proper Functionalism by Kenneth Boyce and Alvin Plantinga • Evidentialism by Richard Feldman and Andrew Cullison • Experimental Epistemology by James R. Beebe Clearly written and featuring a detailed list of resources, glossary and a fully annotated bibliography, The Bloomsbury Companion to Epistemology introduces some of the most exciting topics in contemporary analytic philosophy.

Philosophical Methodology The Armchair Or The Laboratory

Author: Matthew C. Haug
Publisher: Routledge
ISBN: 1135107033
Size: 34.46 MB
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What methodology should philosophers follow? Should they rely on methods that can be conducted from the armchair? Or should they leave the armchair and turn to the methods of the natural sciences, such as experiments in the laboratory? Or is this opposition itself a false one? Arguments about philosophical methodology are raging in the wake of a number of often conflicting currents, such as the growth of experimental philosophy, the resurgence of interest in metaphysical questions, and the use of formal methods. This outstanding collection of specially-commissioned chapters by leading international philosophers discusses these questions and many more. It provides a comprehensive survey of philosophical methodology in the most important philosophical subjects: metaphysics, epistemology, philosophy of language, philosophy of mind, phenomenology, philosophy of science, ethics, and aesthetics. A key feature of the collection is that philosophers discuss and evaluate contrasting approaches in each subject, offering a superb overview of the variety of methodological approaches - both naturalistic and non-naturalistic - in each of these areas. They examine important topics at the heart of methodological argument, including the role of intuitions and conceptual analysis, thought experiments, introspection, and the place that results from the natural sciences should have in philosophical theorizing. The collection begins with a fascinating exchange about philosophical naturalism between Timothy Williamson and Alexander Rosenberg, and also includes contributions from the following philosophers: Lynne Rudder Baker, Matt Bedke, Greg Currie, Michael Devitt, Matthew C. Haug, Jenann Ismael, Hilary Kornblith, Neil Levy, E.J. Lowe, Kirk Ludwig, Marie McGinn, David Papineau, Matthew Ratcliffe, Georges Rey, Jeffrey W. Roland, Barry C. Smith, Amie L. Thomasson, Valerie Tiberius, Jessica Wilson, and David W. Smith.

Platonism Naturalism And Mathematical Knowledge

Author: James Robert Brown
Publisher: Routledge
ISBN: 1136580387
Size: 43.85 MB
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This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy.

Acquisition Of Complex Arithmetic Skills And Higher Order Mathematics Concepts

Author: David C. Geary
Publisher: Academic Press
ISBN: 0128133686
Size: 62.56 MB
Format: PDF
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Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts focuses on typical and atypical learning of complex arithmetic skills and higher-order math concepts. As part of the series Mathematical Cognition and Learning, this volume covers recent advances in the understanding of children’s developing competencies with whole-number arithmetic, fractions, and rational numbers. Each chapter covers these topics from multiple perspectives, including genetic disorders, cognition, instruction, and neural networks. Covers innovative measures and recent methodological advances in mathematical thinking and learning Contains contributions that improve instruction and education in these domains Informs policy aimed at increasing the level of mathematical proficiency in the general public

What Place For The A Priori

Author: Michael J. Shaffer
Publisher: Open Court
ISBN: 0812697413
Size: 41.26 MB
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This book deals with questions about the nature of a priori knowledge and its relation to empirical knowledge. Until the twentieth century, it was more or less taken for granted that there was such a thing as a priori knowledge, that is, knowledge whose source is in reason and reflection rather than sensory experience. With a few notable exceptions, philosophers believed that mathematics, logic and philosophy were all a priori. Although the seeds of doubt were planted earlier on, by the early twentieth century, philosophers were widely skeptical of the idea that there was any nontrivial existence of a priori knowledge. By the mid to late twentieth century, it became fashionable to doubt the existence of any kind of a priori knowledge at all. Since many think that philosophy is an a priori discipline if it is any kind of discipline at all, the questions about a priori knowledge are fundamental to our understanding of philosophy itself.

Where Mathematics Comes From

Author: George Lakoff
Publisher: Basic Books (AZ)
ISBN:
Size: 78.66 MB
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Provides an in-depth analysis of the cognitive science of mathematical ideas that argues that conceptual metaphor plays a definitive role in mathematical ideas, exploring such concepts as arithmetic, algebra, sets, logic, and infinity. 20,000 first printing.

Grounding Cognition

Author: Diane Pecher
Publisher: Cambridge University Press
ISBN: 9781139442473
Size: 17.82 MB
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One of the key questions in cognitive psychology is how people represent knowledge about concepts such as football or love. Some researchers have proposed that concepts are represented in human memory by the sensorimotor systems that underlie interaction with the outside world. These theories represent developments in cognitive science to view cognition no longer in terms of abstract information processing, but in terms of perception and action. In other words, cognition is grounded in embodied experiences. Studies show that sensory perception and motor actions support understanding of words and object concepts. Moreover, even understanding of abstract and emotion concepts can be shown to rely on more concrete, embodied experiences. Finally, language itself can be shown to be grounded in sensorimotor processes. This book brings together theoretical arguments and empirical evidence from several key researchers in this field to support this framework.

How People Learn

Author: National Research Council
Publisher: National Academies Press
ISBN: 0309131979
Size: 32.15 MB
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First released in the Spring of 1999, How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior. This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning. Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methods--to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb. How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn. The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system. Topics include: How learning actually changes the physical structure of the brain. How existing knowledge affects what people notice and how they learn. What the thought processes of experts tell us about how to teach. The amazing learning potential of infants. The relationship of classroom learning and everyday settings of community and workplace. Learning needs and opportunities for teachers. A realistic look at the role of technology in education.