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Grounding Concepts

Author: C. S. Jenkins
Publisher: Oxford University Press on Demand
ISBN: 0199231575
Size: 20.30 MB
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Grounding Concepts is a book about arithmetical knowledge, which puts forward a new and inventive theory. The book aims to do justice to three intuitions which have hitherto been considered impossible to accommodate simultaneously. The first is that arithmetic is knowable without the need to conduct tests or otherwise gather empirical evidence for it. The second is that arithmetic is a body of mind-independent fact; it is not created by us. The thirdis that our senses supply the basis for all knowledge of the mind-independent world. To resolve this apparent tension, the author contends that there is a way in which experience can influence our concepts. We can then learn about arithmetic in the armchair, just by examining these concepts, withoutneeding to conduct tests or gather evidence. The book brings to bear a wide range of classic and contemporary philosophical issues and influences, and will be accessible to anyone with undergraduate training in philosophy.

Platonism Naturalism And Mathematical Knowledge

Author: James Robert Brown
Publisher: Routledge
ISBN: 1136580387
Size: 68.91 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.

The Bloomsbury Companion To Epistemology

Author: Andrew Cullison
Publisher: Bloomsbury Publishing
ISBN: 1472585798
Size: 52.23 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.

Acquisition Of Complex Arithmetic Skills And Higher Order Mathematics Concepts

Author: David C. Geary
Publisher: Academic Press
ISBN: 0128133686
Size: 70.42 MB
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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: 21.76 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: 49.96 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.

What Love Is

Author: Carrie Jenkins
Publisher: Basic Books
ISBN: 046509886X
Size: 38.22 MB
Format: PDF
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What is love? Aside from being the title of many a popular love song, this is one of life’s perennial questions. In What Love Is, philosopher Carrie Jenkins offers a bold new theory on the nature of romantic love that reconciles its humanistic and scientific components. Love can be a social construct (the idea of a perfect fairy tale romance) and a physical manifestation (those anxiety- inducing heart palpitations); we must recognize its complexities and decide for ourselves how to love. Motivated by her own polyamorous relationships, she examines the ways in which our parameters of love have recently changed—to be more accepting of homosexual, interracial, and non-monogamous relationships—and how they will continue to evolve in the future. Full of anecdotal, cultural, and scientific reflections on love, What Love Is is essential reading for anyone seeking to understand what it means to say “I love you.” Whether young or old, gay or straight, male or female, polyamorous or monogamous, this book will help each of us decide for ourselves how we choose to love.

Kant S Philosophy Of Mathematics

Author: C.J. Posy
Publisher: Springer Science & Business Media
ISBN: 9401580464
Size: 43.32 MB
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Kant's views about mathematics were controversial in his own time, and they have inspired or infuriated thinkers ever since. Though specific Kantian doctrines fell into disrepute earlier in this century, the past twenty-five years have seen a surge of interest in and respect for Kant's philosophy of mathematics among both Kant scholars and philosophers of mathematics. The present volume includes the classic papers from the 1960s and 1970s which spared this renaissance of interest, together with updated postscripts by their authors. It also includes the most important recent work on Kant's philosophy of mathematics. The essays bring to bear a wealth of detailed Kantian scholarship, together with powerful new interpretative tools drawn from modern mathematics, logic and philosophy. The cumulative effect of this collection upon the reader will be a deeper understanding of the centrality of mathematics in all aspects of Kant's thought and a renewed respect for the power of Kant's thinking about mathematics. The essays contained in this volume will set the agenda for further work on Kant's philosophy of mathematics for some time to come.