Toward an Epistemology of Mathematics: Naturalism PDF Download
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Author: Jeffrey Wells Roland
Publisher:
ISBN: 9780496962099
Category :
Languages : en
Pages : 202
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Book Description
Thus, unless this burden can be met (and I strongly suspect that it can't be), neither Mathematical Naturalism nor Naturalistic Constructivism successfully naturalizes the epistemology of mathematics.
Author: Jeffrey Wells Roland
Publisher:
ISBN: 9780496962099
Category :
Languages : en
Pages : 202
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Book Description
Thus, unless this burden can be met (and I strongly suspect that it can't be), neither Mathematical Naturalism nor Naturalistic Constructivism successfully naturalizes the epistemology of mathematics.
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: Sander Verhaegh
Publisher:
ISBN: 0190913150
Category : Philosophy
Languages : en
Pages : 241
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Book Description
Working from Within examines the nature and development of W. V. Quine's naturalism, the view that philosophy ought to be continuous with science. Sander Verhaegh's reconstruction is based on a comprehensive study of Quine's personal and academic archives. Transcriptions of five unpublished papers, letters, and notes are included in the appendix.
Author: Penelope Maddy
Publisher: Oxford University Press
ISBN: 0199596182
Category : Mathematics
Languages : en
Pages : 161
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Book Description
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.
Author: Penelope Maddy
Publisher:
ISBN: 9780191597961
Category : Mathematics
Languages : en
Pages : 254
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Book Description
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.
Author: Mary Leng
Publisher: OUP Oxford
ISBN: 0191527890
Category : Philosophy
Languages : en
Pages : 236
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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.
Author: Woosuk Park
Publisher: Springer
ISBN: 3319951475
Category : Philosophy
Languages : en
Pages : 233
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Book Description
This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand Tarski’s and Gödel’s work, explaining why the problems they discussed are still unsolved. Finally, the book reports on some of the most influential positions in contemporary philosophy of mathematics, i.e., Maddy’s mathematical naturalism and Shapiro’s mathematical structuralism. Last but not least, the book introduces Biancani’s Aristotelian philosophy of mathematics as this is considered important to understand current philosophical issue in the applications of mathematics. One of the main purposes of the book is to stimulate readers to reconsider the Aristotelian position, which disappeared almost completely from the scene in logic and mathematics in the early twentieth century.
Author: Sorin Bangu
Publisher: Routledge
ISBN: 1351998447
Category : Mathematics
Languages : en
Pages : 319
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Book Description
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.
Author:
Publisher: BRILL
ISBN: 9401204365
Category : Philosophy
Languages : en
Pages : 196
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Book Description
Much has happened in the field of contemporary epistemology since Quine’s “Epistemology Naturalized” was published in 1969. Even before Ronald Giere published his article “Philosophy of Science Naturalized,” naturalized philosophy of science had been influenced by the so-called historical approach. Kuhm, Lakatos, Feyerabend and Laudan all contributed importantly to this trend. In this light it has emerged, without a doubt, that philosophy of science is closely related to epistemology. This volume explores some of the relevant relations and will be of interest to epistemologists and philosophers of science.
Author: Penelope Maddy
Publisher: Oxford University Press
ISBN: 0199273669
Category : Mathematics
Languages : en
Pages : 461
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Book Description
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.
