Model Theory And The Philosophy Of Mathematical Practice

Model Theory and the Philosophy of Mathematical Practice PDF
Author: John Baldwin
Publisher: Cambridge University Press
ISBN: 1107189217
Size: 10.44 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 384
View: 5949

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Model Theory And The Philosophy Of Mathematical Practice

by John Baldwin, Model Theory And The Philosophy Of Mathematical Practice Books available in PDF, EPUB, Mobi Format. Download Model Theory And The Philosophy Of Mathematical Practice books, Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.


Metaphysical Myths Mathematical Practice

Metaphysical Myths  Mathematical Practice PDF
Author: Jody Azzouni
Publisher: Cambridge University Press
ISBN: 9780521442237
Size: 60.77 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 249
View: 1665

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Metaphysical Myths Mathematical Practice

by Jody Azzouni, Metaphysical Myths Mathematical Practice Books available in PDF, EPUB, Mobi Format. Download Metaphysical Myths Mathematical Practice books, Jody Azzouni argues in this original and exciting study that mathematical knowledge really is a special kind of knowledge with its own special means of gathering evidence. He analyzes the linguistic pitfalls and misperceptions philosophers in this field are often prone to, and explores the misapplications of epistemic principles from the empirical sciences to the exact sciences. What emerges is a picture of mathematics both sensitive to mathematical practice, and to the ontological and epistemological issues that concern philosophers.


Simplicity Ideals Of Practice In Mathematics And The Arts

Simplicity  Ideals of Practice in Mathematics and the Arts PDF
Author: Roman Kossak
Publisher: Springer
ISBN: 3319533851
Size: 24.47 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 305
View: 4565

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Simplicity Ideals Of Practice In Mathematics And The Arts

by Roman Kossak, Simplicity Ideals Of Practice In Mathematics And The Arts Books available in PDF, EPUB, Mobi Format. Download Simplicity Ideals Of Practice In Mathematics And The Arts books, To find "criteria of simplicity" was the goal of David Hilbert's recently discovered twenty-fourth problem on his renowned list of open problems given at the 1900 International Congress of Mathematicians in Paris. At the same time, simplicity and economy of means are powerful impulses in the creation of artworks. This was an inspiration for a conference, titled the same as this volume, that took place at the Graduate Center of the City University of New York in April of 2013. This volume includes selected lectures presented at the conference, and additional contributions offering diverse perspectives from art and architecture, the philosophy and history of mathematics, and current mathematical practice.


Why Is There Philosophy Of Mathematics At All

Why Is There Philosophy of Mathematics At All  PDF
Author: Ian Hacking
Publisher: Cambridge University Press
ISBN: 1107729823
Size: 27.92 MB
Format: PDF, Docs
Category : Science
Languages : en
Pages : 212
View: 7774

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Why Is There Philosophy Of Mathematics At All

by Ian Hacking, Why Is There Philosophy Of Mathematics At All Books available in PDF, EPUB, Mobi Format. Download Why Is There Philosophy Of Mathematics At All books, This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.


Science After The Practice Turn In The Philosophy History And Social Studies Of Science

Science after the Practice Turn in the Philosophy  History  and Social Studies of Science PDF
Author: Léna Soler
Publisher: Routledge
ISBN: 1317935365
Size: 59.53 MB
Format: PDF, Mobi
Category : Philosophy
Languages : en
Pages : 346
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Science After The Practice Turn In The Philosophy History And Social Studies Of Science

by Léna Soler, Science After The Practice Turn In The Philosophy History And Social Studies Of Science Books available in PDF, EPUB, Mobi Format. Download Science After The Practice Turn In The Philosophy History And Social Studies Of Science books, In the 1980s, philosophical, historical and social studies of science underwent a change which later evolved into a turn to practice. Analysts of science were asked to pay attention to scientific practices in meticulous detail and along multiple dimensions, including the material, social and psychological. Following this turn, the interest in scientific practices continued to increase and had an indelible influence in the various fields of science studies. No doubt, the practice turn changed our conceptions and approaches of science, but what did it really teach us? What does it mean to study scientific practices? What are the general lessons, implications, and new challenges? This volume explores questions about the practice turn using both case studies and theoretical analysis. The case studies examine empirical and mathematical sciences, including the engineering sciences. The volume promotes interactions between acknowledged experts from different, often thought of as conflicting, orientations. It presents contributions in conjunction with critical commentaries that put the theses and assumptions of the former in perspective. Overall, the book offers a unique and diverse range of perspectives on the meanings, methods, lessons, and challenges associated with the practice turn.


Models And Methods In The Philosophy Of Science Selected Essays

Models and Methods in the Philosophy of Science  Selected Essays PDF
Author: Patrick Suppes
Publisher: Springer Science & Business Media
ISBN: 9780792322115
Size: 29.17 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 510
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Models And Methods In The Philosophy Of Science Selected Essays

by Patrick Suppes, Models And Methods In The Philosophy Of Science Selected Essays Books available in PDF, EPUB, Mobi Format. Download Models And Methods In The Philosophy Of Science Selected Essays books, This book publishes 31 of the author's selected papers which have appeared, with one exception, since 1970. The papers cover a wide range of topics in the philosophy of science. Part I is concerned with general methodology, including formal and axiomatic methods in science. Part II is concerned with causality and explanation. The papers extend the author's earlier work on a probabilistic theory of causality. The papers in Part III are concerned with probability and measurement, especially foundational questions about probability. Part IV consists of several papers, including two historical ones, on the foundations of physics, with the main emphasis being on quantum mechanics. Part V, the longest part, is on the foundations of psychology and includes papers mainly on learning and perception. The book is aimed at philosophers of science, scientists concerned with the methodology of the social sciences, and mathematical psychologists interested in theories of learning, perception and measurement.


Pluralism In Mathematics A New Position In Philosophy Of Mathematics

Pluralism in Mathematics  A New Position in Philosophy of Mathematics PDF
Author: Michèle Friend
Publisher: Springer Science & Business Media
ISBN: 9400770588
Size: 54.91 MB
Format: PDF, Docs
Category : Science
Languages : en
Pages : 291
View: 1092

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Pluralism In Mathematics A New Position In Philosophy Of Mathematics

by Michèle Friend, Pluralism In Mathematics A New Position In Philosophy Of Mathematics Books available in PDF, EPUB, Mobi Format. Download Pluralism In Mathematics A New Position In Philosophy Of Mathematics books, This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy’s Naturalism, Shapiro’s Structuralism and Formalism. In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry. In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a strong warning to treat the word ‘pluralism’ with care.


Foundations Of Constructive Mathematics

Foundations of Constructive Mathematics PDF
Author: M.J. Beeson
Publisher: Springer Science & Business Media
ISBN: 3642689523
Size: 44.97 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 466
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Foundations Of Constructive Mathematics

by M.J. Beeson, Foundations Of Constructive Mathematics Books available in PDF, EPUB, Mobi Format. Download Foundations Of Constructive Mathematics books, This book is about some recent work in a subject usually considered part of "logic" and the" foundations of mathematics", but also having close connec tions with philosophy and computer science. Namely, the creation and study of "formal systems for constructive mathematics". The general organization of the book is described in the" User's Manual" which follows this introduction, and the contents of the book are described in more detail in the introductions to Part One, Part Two, Part Three, and Part Four. This introduction has a different purpose; it is intended to provide the reader with a general view of the subject. This requires, to begin with, an elucidation of both the concepts mentioned in the phrase, "formal systems for constructive mathematics". "Con structive mathematics" refers to mathematics in which, when you prove that l a thing exists (having certain desired properties) you show how to find it. Proof by contradiction is the most common way of proving something exists without showing how to find it - one assumes that nothing exists with the desired properties, and derives a contradiction. It was only in the last two decades of the nineteenth century that mathematicians began to exploit this method of proof in ways that nobody had previously done; that was partly made possible by the creation and development of set theory by Georg Cantor and Richard Dedekind.


Making And Breaking Mathematical Sense

Making and Breaking Mathematical Sense PDF
Author: Roi Wagner
Publisher: Princeton University Press
ISBN: 0691171718
Size: 17.69 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 256
View: 3497

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Making And Breaking Mathematical Sense

by Roi Wagner, Making And Breaking Mathematical Sense Books available in PDF, EPUB, Mobi Format. Download Making And Breaking Mathematical Sense books, In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.


Scientific Models In Philosophy Of Science

Scientific Models in Philosophy of Science PDF
Author: Daniela M. Bailer-Jones
Publisher: University of Pittsburgh Pre
ISBN: 0822971232
Size: 64.48 MB
Format: PDF, Kindle
Category : Science
Languages : en
Pages : 248
View: 7235

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Scientific Models In Philosophy Of Science

by Daniela M. Bailer-Jones, Scientific Models In Philosophy Of Science Books available in PDF, EPUB, Mobi Format. Download Scientific Models In Philosophy Of Science books, Scientists have used models for hundreds of years as a means of describing phenomena and as a basis for further analogy. In Scientific Models in Philosophy of Science, Daniela Bailer-Jones assembles an original and comprehensive philosophical analysis of how models have been used and interpreted in both historical and contemporary contexts. Bailer-Jones delineates the many forms models can take (ranging from equations to animals; from physical objects to theoretical constructs), and how they are put to use. She examines early mechanical models employed by nineteenth-century physicists such as Kelvin and Maxwell, describes their roots in the mathematical principles of Newton and others, and compares them to contemporary mechanistic approaches. Bailer-Jones then views the use of analogy in the late nineteenth century as a means of understanding models and to link different branches of science. She reveals how analogies can also be models themselves, or can help to create them. The first half of the twentieth century saw little mention of models in the literature of logical empiricism. Focusing primarily on theory, logical empiricists believed that models were of temporary importance, flawed, and awaiting correction. The later contesting of logical empiricism, particularly the hypothetico-deductive account of theories, by philosophers such as Mary Hesse, sparked a renewed interest in the importance of models during the 1950s that continues to this day. Bailer-Jones analyzes subsequent propositions of: models as metaphors; Kuhn's concept of a paradigm; the Semantic View of theories; and the case study approaches of Cartwright and Morrison, among others. She then engages current debates on topics such as phenomena versus data, the distinctions between models and theories, the concepts of representation and realism, and the discerning of falsities in models.