Download or read book Platonism Naturalism and Mathematical Knowledge written by James Robert Brown and published by Routledge. This book was released on 2013-06-17 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Naturalism in Mathematics written by Penelope Maddy and published by Clarendon Press. This book was released on 1997-11-13 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Platonism and Anti Platonism in Mathematics written by Mark Balaguer and published by Oxford University Press, USA. This book was released on 2001 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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)
Download or read book Mathematical Knowledge written by Mary Leng and published by Oxford University Press, USA. This book was released on 2007-11-15 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Autonomy Platonism and the Indispensability Argument written by Russell Marcus and published by Lexington Books. This book was released on 2015-06-11 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Plato s Heaven A User s Guide written by Howard Burton and published by Open Agenda Publishing. This book was released on 1901-01-01 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on an in-depth filmed conversation between Howard Burton and James Robert Brown, Emeritus Professor of Philosophy at the University of Toronto. This wide-ranging conversation addresses a central theme in current philosophy: Platonism vs. Naturalism and provides accounts of both approaches to mathematics. The Platonist-Naturalist debate over mathematics is explored in a comprehensive fashion and also sheds light on non-mathematical aspects of a dispute that is central to contemporary philosophy. Thought experiments stand as a fascinating challenge to the necessity of data in the empirical sciences. Are these experiments, conducted uniquely in our imagination, simply rhetorical devices or communication tools or are they an essential part of scientific practice? This book also surveys the current state of this debate and explores new avenues of research into the epistemology of thought experiments. This carefully-edited book includes an introduction, Mathematical Metaphysics, and questions for discussion at the end of each chapter: I. Introducing Platonism - An explanation for what mathematics really is II. Attacks and Defenses - Platonism under fire III. Seeing With the Mind’s Eye - Two revealing examples IV. Platonism Bounces Back - From quantum physics to the mind-body problem V. The Philosophical Life - On sociological divides and being a team player About Ideas Roadshow Conversations: This book is part of an expanding series of 100+ Ideas Roadshow conversations, each one presenting a wealth of candid insights from a leading expert through a focused yet informal setting to give non-specialists a uniquely accessible window into frontline research and scholarship that wouldn't otherwise be encountered through standard lectures and textbooks.
Download or read book Knowledge Cause and Abstract Objects written by C. Cheyne and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to platonists, entities such as numbers, sets, propositions and properties are abstract objects. But abstract objects lack causal powers and a location in space and time, so how could we ever come to know of the existence of such impotent and remote objects? In Knowledge, Cause, and Abstract Objects, Colin Cheyne presents the first systematic and detailed account of this epistemological objection to the platonist doctrine that abstract objects exist and can be known. Since mathematics has such a central role in the acquisition of scientific knowledge, he concentrates on mathematical platonism. He also concentrates on our knowledge of what exists, and argues for a causal constraint on such existential knowledge. Finally, he exposes the weaknesses of recent attempts by platonists to account for our supposed platonic knowledge. This book will be of particular interest to researchers and advanced students of epistemology and of the philosophy of mathematics and science. It will also be of interest to all philosophers with a general interest in metaphysics and ontology.
Download or read book Plato s Problem written by M. Panza and published by Springer. This book was released on 2013-01-21 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is mathematics about? And how can we have access to the reality it is supposed to describe? The book tells the story of this problem, first raised by Plato, through the views of Aristotle, Proclus, Kant, Frege, Gödel, Benacerraf, up to the most recent debate on mathematical platonism.
Download or read book From Plato to Platonism written by Lloyd P. Gerson and published by Cornell University Press. This book was released on 2013-11-27 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Was Plato a Platonist? While ancient disciples of Plato would have answered this question in the affirmative, modern scholars have generally denied that Plato’s own philosophy was in substantial agreement with that of the Platonists of succeeding centuries. In From Plato to Platonism, Lloyd P. Gerson argues that the ancients are correct in their assessment. He arrives at this conclusion in an especially ingenious manner, challenging fundamental assumptions about how Plato’s teachings have come to be understood. Through deft readings of the philosophical principles found in Plato's dialogues and in the Platonic tradition beginning with Aristotle, he shows that Platonism, broadly conceived, is the polar opposite of naturalism and that the history of philosophy from Plato until the seventeenth century was the history of various efforts to find the most consistent and complete version of "anti-naturalism." Gerson contends that the philosophical position of Plato—Plato’s own Platonism, so to speak—was produced out of a matrix he calls "Ur-Platonism." According to Gerson, Ur-Platonism is the conjunction of five "antis" that in total arrive at anti-naturalism: anti-nominalism, anti-mechanism, anti-materialism, anti-relativism, and anti-skepticism. Plato’s Platonism is an attempt to construct the most consistent and defensible positive system uniting the five "antis." It is also the system that all later Platonists throughout Antiquity attributed to Plato when countering attacks from critics including Peripatetics, Stoics, and Sceptics. In conclusion, Gerson shows that Late Antique philosophers such as Proclus were right in regarding Plotinus as "the great exegete of the Platonic revelation."
Download or read book Naturalism in Mathematics Naturalism Wittgensteinian anti philosophy A second G delian theme Quinean naturalism Mathematical naturalism The problem revisited A naturalist s case against written by Penelope Maddy and published by . This book was released on 1997 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set theory has rendered the notion of self-evident truths to be obsolete in mathematics. Penelope Maddy examines this dilemma using the minimum of technical jargon. Set theory is explained in a manner that can be understood by non-mathematicians.
Download or read book Understanding Naturalism written by Jack Ritchie and published by Routledge. This book was released on 2014-12-05 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many contemporary Anglo-American philosophers describe themselves as naturalists. But what do they mean by that term? Popular naturalist slogans like, "there is no first philosophy" or "philosophy is continuous with the natural sciences" are far from illuminating. "Understanding Naturalism" provides a clear and readable survey of the main strands in recent naturalist thought. The origin and development of naturalist ideas in epistemology, metaphysics and semantics is explained through the works of Quine, Goldman, Kuhn, Chalmers, Papineau, Millikan and others. The most common objections to the naturalist project - that it involves a change of subject and fails to engage with "real" philosophical problems, that it is self-refuting, and that naturalism cannot deal with normative notions like truth, justification and meaning - are all discussed. "Understanding Naturalism" distinguishes two strands of naturalist thinking - the constructive and the deflationary - and explains how this distinction can invigorate naturalism and the future of philosophical research.
Download or read book Naturalizing Logico Mathematical Knowledge written by Sorin Bangu and published by Routledge. This book was released on 2018-02-01 with total page 319 pages. 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.
Download or read book Emergence and Empire written by John Bonnett and published by McGill-Queen's Press - MQUP. This book was released on 2013-11-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harold Innis was one of the most profound thinkers that Canada ever produced. Such was his influence on the field of communication that Marshall McLuhan once declared his own work was a mere footnote to Innis. But over the past sixty years scholars have had a hard time explaining his brilliance, in large measure because Innis's dense, elliptical writing style has hindered easy explication and interpretation. But behind the dense verbiage lies a profound philosophy of history. In Emergence and Empire, John Bonnett offers a fresh take on Innis's work by demonstrating that his purpose was to understand the impact of self-organizing, emergent change on economies and societies. Innis's interest in emergent change induced him to craft an original and bold philosophy of history informed by concepts as diverse as information, Kantian idealism, and business cycle theory. Bonnett provides a close reading of Innis's oeuvre that connects works of communication and economic history to present a fuller understanding of Innis's influences and influence. Emergence and Empire presents a portrait of an original and prescient thinker who anticipated the importance of developments such as information visualization and whose understanding of change is remarkably similar to that which is promoted by the science of complexity today.
Download or read book Platonism and Naturalism written by Lloyd P. Gerson and published by Cornell University Press. This book was released on 2020-03-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his third and concluding volume, Lloyd P. Gerson presents an innovative account of Platonism, the central tradition in the history of philosophy, in conjunction with Naturalism, the "anti-Platonism" in antiquity and contemporary philosophy. Gerson contends that Platonism identifies philosophy with a distinct subject matter, namely, the intelligible world and seeks to show that the Naturalist rejection of Platonism entails the elimination of a distinct subject matter for philosophy. Thus, the possibility of philosophy depends on the truth of Platonism. From Aristotle to Plotinus to Proclus, Gerson clearly links the construction of the Platonic system well beyond simply Plato's dialogues, providing strong evidence of the vast impact of Platonism on philosophy throughout history. Platonism and Naturalism concludes that attempts to seek a rapprochement between Platonism and Naturalism are unstable and likely indefensible.
Download or read book Philosophy of Mathematics Oxford Bibliographies Online Research Guide written by Oxford University Press and published by Oxford University Press, USA. This book was released on 2010-06-01 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ebook is a selective guide designed to help scholars and students of social work find reliable sources of information by directing them to the best available scholarly materials in whatever form or format they appear from books, chapters, and journal articles to online archives, electronic data sets, and blogs. Written by a leading international authority on the subject, the ebook provides bibliographic information supported by direct recommendations about which sources to consult and editorial commentary to make it clear how the cited sources are interrelated related. This ebook is a static version of an article from Oxford Bibliographies Online: Philosophy, a dynamic, continuously updated, online resource designed to provide authoritative guidance through scholarship and other materials relevant to the study Philosophy. Oxford Bibliographies Online covers most subject disciplines within the social science and humanities, for more information visit www.oxfordbibligraphies.com.
Download or read book Science with Numbers written by Linnebo Øystein and published by . This book was released on 2002 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Weirdness written by Taner Edis and published by Pitchstone Publishing (US&CA). This book was released on 2021-11-09 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a world where science faces challenges from creationists and climate change deniers, and where social media is awash with wild conspiracy theories, it is no longer enough for scientists, pundits, and activists to simply ask the public to trust science. Rather, all must better understand how science works, and why science is essential. By exploring many of the odd beliefs embraced by large sections of the public that are rejected by the scientific mainstream, Weirdness! makes a case for science that goes beyond popular slogans. It takes seriously claims that paranormal phenomena, such as psychic abilities and mythical creatures, might be real, but demonstrates how such phenomena would extend beyond the laws of nature. It rejects a sharp boundary between science and religion, while explaining how to negotiate their real differences. Denials of science cause no end of trouble, but so too does placing blind trust in science. As Weirdness! reminds readers, science should not be seen as a mechanism that takes in data and spits out truth—indeed, what we get wrong about how the world works is often as interesting as what we get right.
