Structuralism And Mathematical Existence
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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 Prehistory Of Mathematical Structuralism
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Author : Erich H. Reck
language : en
Publisher: Oxford University Press
Release Date : 2020
The Prehistory Of Mathematical Structuralism written by Erich H. Reck 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 2020 with Mathematics categories.
This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysical aspects of structuralism.
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.
Philosophy Of Mathematics
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Author : Stewart Shapiro
language : en
Publisher: Oxford University Press
Release Date : 1997-08-07
Philosophy Of Mathematics 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 1997-08-07 with Philosophy categories.
Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.
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.
Scientific Structuralism
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Author : Alisa Bokulich
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-21
Scientific Structuralism written by Alisa Bokulich 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 2011-01-21 with Science categories.
Recently there has been a revival of interest in structuralist approaches to science. Taking their lead from scientific structuralists such as Henri Poincaré, Ernst Cassirer, and Bertrand Russell, some contemporary philosophers and scientists have argued that the most fruitful approach to solving many problems in the philosophy of science lies in focusing on the structural features of our scientific theories. Much of the work in scientific structuralism to date has been focused on the problem of scientific realism, where it has been argued that even in cases of radical theory change the most important structural features of predecessor theories are preserved. These structural realists argue that what our most successful theories get right about the world is these abstract structural features, rather than any particular ontological claims. More recently, philosophers of science have adopted structuralist approaches to many other issues in the philosophy of science, such as scientific explanation and intertheory relations. The nine articles collected in this volume, written by the leading researchers in scientific structuralism, represent some of the most important directions of research in this field. This book will be of particular interest to those philosophers, scientists, and mathematicians who are interested in the foundations of science.
Plato S Problem
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Author : M. Panza
language : en
Publisher: Springer
Release Date : 2013-01-21
Plato S Problem written by M. Panza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-21 with Mathematics categories.
What is mathematics about? And how can we have access to the reality it is supposed to describe? The book tells the story of this problem, first raised by Plato, through the views of Aristotle, Proclus, Kant, Frege, Gödel, Benacerraf, up to the most recent debate on mathematical platonism.
Philosophy Of Mathematics
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Author : Thomas Bedürftig
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-10-26
Philosophy Of Mathematics written by Thomas Bedürftig and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-26 with Mathematics categories.
The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today‘s mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally – First nonstandard steps Retrospection
Reality And Its Structure
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Author : Ricki Bliss
language : en
Publisher: Oxford University Press
Release Date : 2018
Reality And Its Structure written by Ricki Bliss 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 2018 with Philosophy categories.
Reality is a rather large place. It contains protons, economies, headaches, sentences, smiles, asteroids, crimes, numbers, and very many other things. Much of the content of our reality appears to depend on other of its content. Economies, for example, appear to depend upon people and the way they behave, amongst other things. Some of the content of our reality also appears to be, in some significant sense, more important than other of its content. Whilst none of us would wish to deny the very important role that economies play in our lives, most of us would agree that without matter arranged certain ways in space, for example, there could be no economies in the first place. Very many contemporary philosophers are concerned with how exactly we are to fill in the details of this view. What they are inclined to agree on is that reality has an over-arching hierarchical structure ordered by relations of metaphysical dependence, where chains of entities ordered by those dependence relations terminate in something fundamental. It is also commonly taken for granted that what those dependence chains terminate in is merely contingently existent - those things could have failed to exist - and consistent - they have no contradictory properties. This volume brings together fifteen essays from leading and emerging scholars that address these core, yet often under-explored, commitments.
God And Abstract Objects
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Author : William Lane Craig
language : en
Publisher: Springer
Release Date : 2017-09-05
God And Abstract Objects written by William Lane Craig and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-05 with Philosophy categories.
This book is an exploration and defense of the coherence of classical theism’s doctrine of divine aseity in the face of the challenge posed by Platonism with respect to abstract objects. A synoptic work in analytic philosophy of religion, the book engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. It addresses absolute creationism, non-Platonic realism, fictionalism, neutralism, and alternative logics and semantics, among other topics. The book offers a helpful taxonomy of the wide range of options available to the classical theist for dealing with the challenge of Platonism. It probes in detail the diverse views on the reality of abstract objects and their compatibility with classical theism. It contains a most thorough discussion, rooted in careful exegesis, of the biblical and patristic basis of the doctrine of divine aseity. Finally, it challenges the influential Quinean metaontological theses concerning the way in which we make ontological commitments.