Platonism, Naturalism, and Mathematical Knowledge - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Platonism, Naturalism, and Mathematical Knowledge write by James Robert Brown. This book was released on 2013-06-17. Platonism, Naturalism, and Mathematical Knowledge available in PDF, EPUB and Kindle. 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.
Naturalism in Mathematics
Naturalism in Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Naturalism in Mathematics write by Penelope Maddy. This book was released on 1997-11-13. Naturalism in Mathematics available in PDF, EPUB and Kindle. Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress in work on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view—realism—is assessed and finally rejected in favour of another—naturalism—which attends less to metaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomatic status in set theory. Maddy's clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.
Platonism and Anti-Platonism in Mathematics
Platonism and Anti-Platonism in Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Platonism and Anti-Platonism in Mathematics write by Mark Balaguer. This book was released on 2001. Platonism and Anti-Platonism in Mathematics available in PDF, EPUB and Kindle. In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible. (Philosophy)
Autonomy Platonism and the Indispensability Argument
Autonomy Platonism and the Indispensability Argument - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Autonomy Platonism and the Indispensability Argument write by Russell Marcus. This book was released on 2015-06-11. Autonomy Platonism and the Indispensability Argument available in PDF, EPUB and Kindle. Mathematical platonism is the view that mathematical statements are true of real mathematical objects like numbers, shapes, and sets. One central problem with platonism is that numbers, shapes, sets, and the like are not perceivable by our senses. In contemporary philosophy, the most common defense of platonism uses what is known as the indispensability argument. According to the indispensabilist, we can know about mathematics because mathematics is essential to science. Platonism is among the most persistent philosophical views. Our mathematical beliefs are among our most entrenched. They have survived the demise of millennia of failed scientific theories. Once established, mathematical theories are rarely rejected, and never for reasons of their inapplicability to empirical science. Autonomy Platonism and the Indispensability Argument is a defense of an alternative to indispensability platonism. The autonomy platonist believes that mathematics is independent of empirical science: there is purely mathematical evidence for purely mathematical theories which are even more compelling to believe than empirical science. Russell Marcus begins by contrasting autonomy platonism and indispensability platonism. He then argues against a variety of indispensability arguments in the first half of the book. In the latter half, he defends a new approach to a traditional platonistic view, one which includes appeals to a priori but fallible methods of belief acquisition, including mathematical intuition, and a natural adoption of ordinary mathematical methods. In the end, Marcus defends his intuition-based autonomy platonism against charges that the autonomy of mathematics is viciously circular. This book will be useful to researchers, graduate students, and advanced undergraduates with interests in the philosophy of mathematics or in the connection between science and mathematics.
Mathematical Knowledge
Mathematical Knowledge - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematical Knowledge write by Mary Leng. This book was released on 2007-11-15. Mathematical Knowledge available in PDF, EPUB and Kindle. 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.
