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Naturalism In Mathematics
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Book Synopsis Naturalism in Mathematics by : Penelope Maddy
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.
Book Synopsis Platonism, Naturalism, and Mathematical Knowledge by : James Robert Brown
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.
Book Synopsis Believing in Dawkins by : Eric Steinhart
Download or read book Believing in Dawkins written by Eric Steinhart and published by Springer Nature. This book was released on 2020-09-16 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dawkin's militant atheism is well known; his profound faith less well known In this book, atheist philosopher Eric Steinhart explores the spiritual dimensions of Richard Dawkins’ books, which are shown to encompass: · the meaning and purpose of life · an appreciation of Platonic beauty and truth · a deep belief in the rationality of the universe · an aversion to both scientism and nihilism As an atheist, Dawkins strives to develop a scientific alternative to theism, and while he declares that science is not a religion, he also proclaims it to be a spiritual enterprise. His books are filled with fragmentary sketches of this ‘spiritual atheism’, resembling a great unfinished cathedral. This book systematises and completes Dawkins’ arguments and reveals their deep roots in Stoicism and Platonism. Expanding on Dawkins’ ideas, Steinhart shows how atheists can develop powerful ethical principles, compelling systems of symbols and images, and meaningful personal and social practices. Believing in Dawkins is a rigorous and potent entreaty for the use of science and reason to support spiritually rich and optimistic ways of thinking and living.
Book Synopsis Second Philosophy by : Penelope Maddy
Download or read book Second Philosophy written by Penelope Maddy and published by Oxford University Press. This book was released on 2007-04-19 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. In this book, Penelope Maddy describes and practises a particularly austere form of naturalism called 'Second Philosophy'. Without a definitive criterion for what counts as 'science' and what doesn't, Second Philosophy can't be specified directly - 'trust only the methods of science!' or some such thing - so Maddy proceeds instead by illustratingthe behaviours of an idealized inquirer she calls the 'Second Philosopher'. This Second Philosopher begins from perceptual common sense and progresses from there to systematic observation, active experimentation, theory formation and testing, working all the while to assess, correct and improve hermethods as she goes. Second Philosophy is then the result of the Second Philosopher's investigations.Maddy delineates the Second Philosopher's approach by tracing her reactions to various familiar skeptical and transcendental views (Descartes, Kant, Carnap, late Putnam, van Fraassen), comparing her methods to those of other self-described naturalists (especially Quine), and examining a prominent contemporary debate (between disquotationalists and correspondence theorists in the theory of truth) to extract a properly second-philosophical line of thought. She then undertakes to practise SecondPhilosophy in her reflections on the ground of logical truth, the methodology, ontology and epistemology of mathematics, and the general prospects for metaphysics naturalized.
Book Synopsis Mathematics and Reality by : Mary Leng
Download or read book Mathematics and Reality written by Mary Leng and published by OUP Oxford. This book was released on 2010-04-22 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. Leng, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.
Book Synopsis Understanding Naturalism by : Jack Ritchie
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 192 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.
Book Synopsis Defending the Axioms by : Penelope Maddy
Download or read book Defending the Axioms written by Penelope Maddy and published by Oxford University Press. This book was released on 2011-01-27 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. The axioms of set theory have long played this role, so the question of how they are properly judged is of central importance. Maddy discusses the appropriate methods for such evaluations and the philosophical backdrop that makes them appropriate.
Book Synopsis Working from Within by : Sander Verhaegh
Download or read book Working from Within written by Sander Verhaegh and published by Oxford University Press, USA. This book was released on 2018-12-05 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past few decades, a radical shift has occurred in how philosophers conceive of the relation between science and philosophy. A great number of analytic philosophers have adopted what is commonly called a "naturalistic" approach, arguing that their inquiries ought to be in some sense continuous with science. Where early analytic philosophers often relied on a sharp distinction between science and philosophy--the former an empirical discipline concerned with fact, the latter an a priori discipline concerned with meaning--philosophers today largely follow Willard Van Orman Quine (1908-2000) in his seminal rejection of this distinction. Sander Verhaegh here offers a comprehensive study of Quine's groundbreaking naturalism. Building on Quine's published corpus as well as a wealth of unpublished letters, notes, lectures, papers, proposals, and annotations from the Quine archives, Verhaegh aims to reconstruct both the nature and the development of his naturalism. As such, Working from Within aims to contribute to the rapidly developing historiography of analytic philosophy, and to provide a better, historically informed, understanding of what is philosophically at stake in the contemporary naturalistic turn. Transcriptions of five unpublished papers, letters, and notes are included in the appendix.
Book Synopsis Naturalism and Normativity by : Mario De Caro
Download or read book Naturalism and Normativity written by Mario De Caro and published by Columbia University Press. This book was released on 2010-08-11 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Normativity concerns what we ought to think or do and the evaluations we make. For example, we say that we ought to think consistently, we ought to keep our promises, or that Mozart is a better composer than Salieri. Yet what philosophical moral can we draw from the apparent absence of normativity in the scientific image of the world? For scientific naturalists, the moral is that the normative must be reduced to the nonnormative, while for nonnaturalists, the moral is that there must be a transcendent realm of norms. Naturalism and Normativity engages with both sides of this debate. Essays explore philosophical options for understanding normativity in the space between scientific naturalism and Platonic supernaturalism. They articulate a liberal conception of philosophy that is neither reducible to the sciences nor completely independent of them yet one that maintains the right to call itself naturalism. Contributors think in new ways about the relations among the scientific worldview, our experience of norms and values, and our movements in the space of reason. Detailed discussions include the relationship between philosophy and science, physicalism and ontological pluralism, the realm of the ordinary, objectivity and subjectivity, truth and justification, and the liberal naturalisms of Donald Davidson, John Dewey, John McDowell, and Ludwig Wittgenstein.
Book Synopsis The Applicability of Mathematics as a Philosophical Problem by : Mark Steiner
Download or read book The Applicability of Mathematics as a Philosophical Problem written by Mark Steiner and published by Harvard University Press. This book was released on 2009-07-01 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis--the success of mathematical physics appears to assign the human mind a special place in the cosmos. Mark Steiner distinguishes among the semantic problems that arise from the use of mathematics in logical deduction; the metaphysical problems that arise from the alleged gap between mathematical objects and the physical world; the descriptive problems that arise from the use of mathematics to describe nature; and the epistemological problems that arise from the use of mathematics to discover those very descriptions. The epistemological problems lead to the thesis about the mind. It is frequently claimed that the universe is indifferent to human goals and values, and therefore, Locke and Peirce, for example, doubted science's ability to discover the laws governing the humanly unobservable. Steiner argues that, on the contrary, these laws were discovered, using manmade mathematical analogies, resulting in an anthropocentric picture of the universe as "user friendly" to human cognition--a challenge to the entrenched dogma of naturalism.
Book Synopsis Strict Finitism and the Logic of Mathematical Applications by : Feng Ye
Download or read book Strict Finitism and the Logic of Mathematical Applications written by Feng Ye and published by Springer Science & Business Media. This book was released on 2011-07-06 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book intends to show that radical naturalism (or physicalism), nominalism and strict finitism account for the applications of classical mathematics in current scientific theories. The applied mathematical theories developed in the book include the basics of calculus, metric space theory, complex analysis, Lebesgue integration, Hilbert spaces, and semi-Riemann geometry (sufficient for the applications in classical quantum mechanics and general relativity). The fact that so much applied mathematics can be developed within such a weak, strictly finitistic system, is surprising in itself. It also shows that the applications of those classical theories to the finite physical world can be translated into the applications of strict finitism, which demonstrates the applicability of those classical theories without assuming the literal truth of those theories or the reality of infinity. Both professional researchers and students of philosophy of mathematics will benefit greatly from reading this book.
Book Synopsis Mathematical Knowledge by : Mary Leng
Download or read book Mathematical Knowledge written by Mary Leng and published by OUP Oxford. This book was released on 2007-11-15 with total page 236 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.
Book Synopsis Philosophical Naturalism by : David Papineau
Download or read book Philosophical Naturalism written by David Papineau and published by Wiley-Blackwell. This book was released on 1993-01-01 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Naturalism written by Stewart Goetz and published by Wm. B. Eerdmans Publishing. This book was released on 2008-04-29 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This inaugural Interventions volume introduces readers to the dominant scientifically oriented worldview called naturalism. Stewart Goetz and Charles Taliaferro examine naturalism philosophically, evaluating its strengths and weaknesses. Whereas most other books on naturalism are written for professional philosophers alone, this one is aimed primarily at a college-educated audience interested in learning about this pervasive worldview. Read a related blog post by the authors on EerdWord.
Book Synopsis An Introduction to the Philosophy of Mathematics by : Mark Colyvan
Download or read book An Introduction to the Philosophy of Mathematics written by Mark Colyvan and published by Cambridge University Press. This book was released on 2012-06-14 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.
Book Synopsis Naturalizing Logico-Mathematical Knowledge by : Sorin Bangu
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.
Book Synopsis Wittgenstein and Naturalism by : Kevin M. Cahill
Download or read book Wittgenstein and Naturalism written by Kevin M. Cahill and published by Routledge. This book was released on 2018-01-17 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wittgenstein was centrally concerned with the puzzling nature of the mind, mathematics, morality and modality. He also developed innovative views about the status and methodology of philosophy and was explicitly opposed to crudely "scientistic" worldviews. His later thought has thus often been understood as elaborating a nuanced form of naturalism appealing to such notions as "form of life", "primitive reactions", "natural history", "general facts of nature" and "common behaviour of mankind". And yet, Wittgenstein is strangely absent from much of the contemporary literature on naturalism and naturalising projects. This is the first collection of essays to focus explicitly on the relationship between Wittgenstein and naturalism. The volume is divided into four sections, each of which addresses a different aspect of naturalism and its relation to Wittgenstein's thought. The first section considers how naturalism could or should be understood. The second section deals with some of the main problematic domains—consciousness, meaning, mathematics—that philosophers have typically sought to naturalise. The third section explores ways in which the conceptual nature of human life might be continuous in important respects with animals. The final section is concerned with the naturalistic status and methodology of philosophy itself. This book thus casts a fresh light on many classical philosophical issues and brings Wittgensteinian ideas to bear on a number of current debates-for example experimental philosophy, neo-pragmatism and animal cognition/ethics-in which naturalism is playing a central role.
