Constructibility And Mathematical Existence
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Constructibility And Mathematical Existence
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Author : Charles S. Chihara
language : en
Publisher: Oxford University Press
Release Date : 1990
Constructibility And Mathematical Existence written by Charles S. Chihara and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
Concerned with the problem of existence in mathematics, this volume develops a mathematical system in which there are no existence assertions but only assertions of constructibility. It explores the philosophical implications of such an approach in the writings of Field, Burgess, Maddy and Kitcher.
Constructibility And Mathematical Existence
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Author : Charles S. Chihara
language : en
Publisher: Clarendon Press
Release Date : 1990-04-12
Constructibility And Mathematical Existence written by Charles S. Chihara and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-04-12 with Philosophy categories.
This book is concerned with `the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach in an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.
Constructibility And Mathematical Existence The Constructibility Theory 1 The Problem Of Existence In Mathematics 2 The Constructibility Quantifiers 3 Constructibility And Open Sentences 4 The Deductive System 5 Cardinality And Number Theory 6 Measurable Quantities And Analysis Part Ii Philosophical Developments 7 Mathematical Structuralism 8 Science Without Numbers 9 Why Burgess Is A Moderate Realist 10 Maddy S Solution To The Problem Of Reference 10 Kitcher S Ideal Agent 12 Deflationism And Mathematical Truth
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Author : Charles S. Chihara
language : en
Publisher:
Release Date : 1990
Constructibility And Mathematical Existence The Constructibility Theory 1 The Problem Of Existence In Mathematics 2 The Constructibility Quantifiers 3 Constructibility And Open Sentences 4 The Deductive System 5 Cardinality And Number Theory 6 Measurable Quantities And Analysis Part Ii Philosophical Developments 7 Mathematical Structuralism 8 Science Without Numbers 9 Why Burgess Is A Moderate Realist 10 Maddy S Solution To The Problem Of Reference 10 Kitcher S Ideal Agent 12 Deflationism And Mathematical Truth written by Charles S. Chihara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Structuralism And Mathematical Existence
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Author : Timothy Garrick Murphy
language : en
Publisher:
Release Date : 2007
Structuralism And Mathematical Existence written by Timothy Garrick Murphy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
The Oxford Handbook Of Philosophy Of Mathematics And Logic
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Author : Stewart Shapiro
language : en
Publisher: Oxford University Press
Release Date : 2005-02-10
The Oxford Handbook Of Philosophy Of Mathematics And Logic written by Stewart Shapiro and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-10 with Mathematics categories.
Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.
Le Niewski S Systems Of Logic And Foundations Of Mathematics
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Author : Rafal Urbaniak
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-24
Le Niewski S Systems Of Logic And Foundations Of Mathematics written by Rafal Urbaniak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-24 with Science categories.
This meticulous critical assessment of the ground-breaking work of philosopher Stanislaw Leśniewski focuses exclusively on primary texts and explores the full range of output by one of the master logicians of the Lvov-Warsaw school. The author’s nuanced survey eschews secondary commentary, analyzing Leśniewski's core philosophical views and evaluating the formulations that were to have such a profound influence on the evolution of mathematical logic. One of the undisputed leaders of the cohort of brilliant logicians that congregated in Poland in the early twentieth century, Leśniewski was a guide and mentor to a generation of celebrated analytical philosophers (Alfred Tarski was his PhD student). His primary achievement was a system of foundational mathematical logic intended as an alternative to the Principia Mathematica of Alfred North Whitehead and Bertrand Russell. Its three strands—‘protothetic’, ‘ontology’, and ‘mereology’, are detailed in discrete sections of this volume, alongside a wealth other chapters grouped to provide the fullest possible coverage of Leśniewski’s academic output. With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great pioneers.
Proof And Other Dilemmas
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Author : Bonnie Gold
language : en
Publisher: MAA
Release Date : 2008
Proof And Other Dilemmas written by Bonnie Gold and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
During the first 75 years of the twentieth century almost all work in the philosophy of mathematics concerned foundational questions. In the last quarter of the century, philosophers of mathematics began to return to basic questions concerning the philosophy of mathematics such as, what is the nature of mathematical knowledge and of mathematical objects, and how is mathematics related to science? Two new schools of philosophy of mathematics, social constructivism and structuralism, were added to the four traditional views (formalism, intuitionalism, logicism, and platonism). The advent of the computer led to proofs and the development of mathematics assisted by computer, and to questions of the role of the computer in mathematics. This book of 16 essays, all written specifically for this volume, is the first to explore this range of new developments in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers are not yet discussing. The other half, written by philsophers of mathematics, summarize the discussion in that community during the last 35 years. In each case, a connection is made to issues relevant to the teach of mathematics.
A Structural Account Of Mathematics
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Author : Charles S. Chihara
language : en
Publisher: OUP Oxford
Release Date : 2003-11-20
A Structural Account Of Mathematics written by Charles S. Chihara and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-20 with Philosophy categories.
Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems are applied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. Chihara builds upon his previous work, in which he presented a new system of mathematics, the constructibility theory, which did not make reference to, or presuppose, mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show how such systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by Willard Quine and Hilary Putnam. And Chihara presents a rationale for the nominalistic outlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings. A Structural Account of Mathematics will be required reading for anyone working in this field.
Philosophy S Loss Of Logic To Mathematics
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Author : Woosuk Park
language : en
Publisher: Springer
Release Date : 2018-07-12
Philosophy S Loss Of Logic To Mathematics written by Woosuk Park and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-12 with Philosophy categories.
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.
A World Without Time
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Author : Palle Yourgrau
language : en
Publisher: Hachette UK
Release Date : 2009-03-04
A World Without Time written by Palle Yourgrau and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-04 with Science categories.
It is a widely known but little considered fact that Albert Einstein and Kurt Godel were best friends for the last decade and a half of Einstein's life. The two walked home together from Princeton's Institute for Advanced Study every day; they shared ideas about physics, philosophy, politics, and the lost world of German science in which they had grown up. By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist . Einstein endorsed this result-reluctantly, since it decisively overthrew the classical world-view to which he was committed. But he could find no way to refute it, and in the half-century since then, neither has anyone else. Even more remarkable than this stunning discovery, however, was what happened afterward: nothing. Cosmologists and philosophers alike have proceeded with their work as if Godel's proof never existed -one of the greatest scandals of modern intellectual history. A World Without Time is a sweeping, ambitious book, and yet poignant and intimate. It tells the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue from undeserved obscurity the brilliant work they did together.