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Mathematical Thought and its Objects

Mathematical Thought and its Objects
Author: Charles Parsons
Publisher: Cambridge University Press
Total Pages: 400
Release: 2007-12-24
Genre: Science
ISBN: 1139467271

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Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite.


Greek Mathematical Thought and the Origin of Algebra

Greek Mathematical Thought and the Origin of Algebra
Author: Jacob Klein
Publisher: Courier Corporation
Total Pages: 246
Release: 2013-04-22
Genre: Mathematics
ISBN: 0486319814

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Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th-16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. 1968 edition. Bibliography.


Mathematical Thought

Mathematical Thought
Author: E.W. Beth
Publisher: Springer Science & Business Media
Total Pages: 220
Release: 2013-06-29
Genre: Science
ISBN: 9401722072

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In contributing a foreword to this book I am complying with a wish my husband expressed a few days before his death. He had completed the manuscript of this work, which may be considered a companion volume to his book Formal Methods. The task of seeing it through the press was undertaken by Mr. J. J. A. Mooij, acting director of the Institute for Research in Foundations and the Philosophy of Science (Instituut voor Grondslagenonderzoek en Filoso:fie der Exacte Wetenschappen) of the University of Amsterdam, with the help of Mrs. E. M. Barth, lecturer at the Institute. I wish to thank Mr. Mooij and Mrs. Barth most cordially for the care with which they have acquitted themselves of this delicate task and for the speed with which they have brought it to completion. I also wish to express my gratitude to Miss L. E. Minning, M. A. , for the helpful advice she has so kindly given to Mr. Mooij and Mrs. Barth during the proof reading. C. P. C. BETH-PASTOOR VII PREFACE A few years ago Mr. Horace S.


The Origin of the Logic of Symbolic Mathematics

The Origin of the Logic of Symbolic Mathematics
Author: Burt C. Hopkins
Publisher: Indiana University Press
Total Pages: 593
Release: 2011-09-07
Genre: Philosophy
ISBN: 0253005272

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Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.


The Knot Book

The Knot Book
Author: Colin Conrad Adams
Publisher: American Mathematical Soc.
Total Pages: 330
Release: 2004
Genre: Mathematics
ISBN: 0821836781

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Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.


Mathematics and Mind

Mathematics and Mind
Author: Alexander George
Publisher: Oxford University Press, USA
Total Pages: 218
Release: 1994
Genre: Mathematics
ISBN: 0195079299

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The essays in this volume investigate the conceptual foundations of mathematics illuminating the powers of the mind. Contributors include Alexander George, Michael Dummett, George Boolos, W.W. Tait, Wilfried Sieg, Daniel Isaacson, Charles Parsons, and Michael Hallett.


Philosophy of Mathematics

Philosophy of Mathematics
Author: Ahmet Cevik
Publisher: CRC Press
Total Pages: 352
Release: 2021-11-09
Genre: Mathematics
ISBN: 1000468801

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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


How Not to Be Wrong

How Not to Be Wrong
Author: Jordan Ellenberg
Publisher: Penguin
Total Pages: 482
Release: 2015-05-26
Genre: Mathematics
ISBN: 0143127535

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“Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.


Mathematical Structuralism

Mathematical Structuralism
Author: Geoffrey Hellman
Publisher: Cambridge University Press
Total Pages: 167
Release: 2018-11-29
Genre: Science
ISBN: 110863074X

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The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the Element considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives.


Contemporary Mathematical Thinking

Contemporary Mathematical Thinking
Author: Frédéric Patras
Publisher: Springer Nature
Total Pages: 133
Release: 2023-04-13
Genre: Mathematics
ISBN: 3031275489

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This book deals with the evolution of mathematical thought during the 20th century. Representing a unique point of view combining mathematics, philosophy and history on this issue, it presents an original analysis of key authors, for example Bourbaki, Grothendieck and Husserl. As a product of 19th and early 20th century science, a canon of knowledge or a scientific ideology, mathematical structuralism had to give way. The succession is difficult, still in progress, and uncertain. To understand contemporary mathematics, its progressive liberation from the slogans of "modern mathematics" and the paths that remain open today, it is first necessary to deconstruct the history of this long dominant current. Another conception of mathematical thought emerged in the work of mathematicians such as Hilbert or Weyl, which went beyond the narrow epistemological paths of science in the making. In this tradition, mathematical thought was accompanied by a philosophical requirement. Modernity teaches us to revive it. The book is intended for a varied public: mathematicians concerned with understanding their discipline, philosophers of science, and the erudite public curious about the progress of mathematics.