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Author: James Robert Brown
Publisher: Routledge
ISBN: 1136580387
Category : Philosophy
Languages : en
Pages : 195
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Book Description
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.
Author: James Robert Brown
Publisher: Routledge
ISBN: 1136580387
Category : Philosophy
Languages : en
Pages : 195
Get Book Here
Book Description
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.
Author: Mario De Caro
Publisher: Columbia University Press
ISBN: 0231508875
Category : Philosophy
Languages : en
Pages : 378
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Book Description
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.
Author: Penelope Maddy
Publisher: Clarendon Press
ISBN: 0191518972
Category : Philosophy
Languages : en
Pages : 265
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Book Description
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.
Author: Jack Ritchie
Publisher: Routledge
ISBN: 1317493575
Category : Philosophy
Languages : en
Pages : 208
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Book Description
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.
Author: Ahmet Cevik
Publisher: CRC Press
ISBN: 1000468801
Category : Mathematics
Languages : en
Pages : 352
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Book Description
The philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge. With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic. Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, consequences, reasons, etc. This book fills this gap. The book can be used as a textbook for a one-semester or even one-year course on philosophy of mathematics. "Other textbooks on the philosophy of mathematics are aimed at philosophers. This book is aimed at mathematicians. Since the author is a mathematician, it is a valuable addition to the literature." - Mark Balaguer, California State University, Los Angeles "There are not many such texts available for mathematics students. I applaud efforts to foster the dialogue between mathematics and philosophy." - Michele Friend, George Washington University and CNRS, Lille, France
Author: J. Franklin
Publisher: Springer
ISBN: 1137400730
Category : Mathematics
Languages : en
Pages : 316
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Book Description
Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.
Author: C. S. Jenkins
Publisher: OUP Oxford
ISBN: 0191552402
Category : Philosophy
Languages : en
Pages : 306
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Book Description
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.
Author: Scott Berman
Publisher: Bloomsbury Publishing
ISBN: 1350080225
Category : Philosophy
Languages : en
Pages : 193
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Book Description
What are the objects of science? Are they just the things in our scientific experiments that are located in space and time? Or does science also require that there be additional things that are not located in space and time? Using clear examples, these are just some of the questions that Scott Berman explores as he shows why alternative theories such as Nominalism, Contemporary Aristotelianism, Constructivism, and Classical Aristotelianism, fall short. He demonstrates why the objects of scientific knowledge need to be not located in space or time if they are to do the explanatory work scientists need them to do. The result is a contemporary version of Platonism that provides us with the best way to explain what the objects of scientific understanding are, and how those non-spatiotemporal things relate to the spatiotemporal things of scientific experiments, as well as everything around us, including even ourselves.
Author: Lloyd P. Gerson
Publisher: Cornell University Press
ISBN: 1501747274
Category : Philosophy
Languages : en
Pages : 0
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Book Description
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.
Author: Mary Leng
Publisher: Oxford University Press, USA
ISBN: 0199228248
Category : Language Arts & Disciplines
Languages : en
Pages : 199
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Book Description
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.
