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Author | : Charles Parsons |
Publisher | : Harvard University Press |
Total Pages | : 365 |
Release | : 2014-03-10 |
Genre | : Philosophy |
ISBN | : 0674419499 |
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In these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past century: Brouwer, Hilbert, Bernays, Weyl, Gödel, Russell, Quine, Putnam, Wang, and Tait.
Author | : Charles Parsons |
Publisher | : Harvard University Press |
Total Pages | : 331 |
Release | : 2014-03-17 |
Genre | : Philosophy |
ISBN | : 0674419502 |
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In this illuminating collection, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the course of the past century. Parsons begins with a discussion of the Kantian legacy in the work of L. E. J. Brouwer, David Hilbert, and Paul Bernays, shedding light on how Bernays revised his philosophy after his collaboration with Hilbert. He considers Hermann Weyl’s idea of a “vicious circle” in the foundations of mathematics, a radical claim that elicited many challenges. Turning to Kurt Gödel, whose incompleteness theorem transformed debate on the foundations of mathematics and brought mathematical logic to maturity, Parsons discusses his essay on Bertrand Russell’s mathematical logic—Gödel’s first mature philosophical statement and an avowal of his Platonistic view. Philosophy of Mathematics in the Twentieth Century insightfully treats the contributions of figures the author knew personally: W. V. Quine, Hilary Putnam, Hao Wang, and William Tait. Quine’s early work on ontology is explored, as is his nominalistic view of predication and his use of the genetic method of explanation in the late work The Roots of Reference. Parsons attempts to tease out Putnam’s views on existence and ontology, especially in relation to logic and mathematics. Wang’s contributions to subjects ranging from the concept of set, minds, and machines to the interpretation of Gödel are examined, as are Tait’s axiomatic conception of mathematics, his minimalist realism, and his thoughts on historical figures.
Author | : Stuart G. Shanker |
Publisher | : Taylor & Francis |
Total Pages | : 508 |
Release | : 2023-05-09 |
Genre | : Philosophy |
ISBN | : 1000949699 |
Download Philosophy of Science, Logic and Mathematics in the 20th Century Book in PDF, ePub and Kindle
The twentieth century witnessed the birth of analytic philosophy. This volume covers some of its key movements and philosophers, including Frege and Wittgenstein's Tractatus.
Author | : Charles D. Parsons |
Publisher | : Cornell University Press |
Total Pages | : 367 |
Release | : 2018-08-06 |
Genre | : Mathematics |
ISBN | : 1501729322 |
Download Mathematics in Philosophy Book in PDF, ePub and Kindle
This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics. A common point of view, that mathematical thought is central to our thought in general, underlies the essays. In his introduction, Parsons articulates that point of view and relates it to past and recent discussions of the foundations of mathematics. Mathematics in Philosophy is divided into three parts. Ontology—the question of the nature and extent of existence assumptions in mathematics—is the subject of Part One and recurs elsewhere. Part Two consists of essays on two important historical figures, Kant and Frege, and one contemporary, W. V. Quine. Part Three contains essays on the three interrelated notions of set, class, and truth.
Author | : Robert Tubbs |
Publisher | : Johns Hopkins University Press+ORM |
Total Pages | : 276 |
Release | : 2014-07-03 |
Genre | : Mathematics |
ISBN | : 1421414023 |
Download Mathematics in Twentieth-Century Literature & Art Book in PDF, ePub and Kindle
The author of What Is a Number? examines the relationship between mathematics and art and literature of the 20th century. During the twentieth century, many artists and writers turned to abstract mathematical ideas to help them realize their aesthetic ambitions. Man Ray, Marcel Duchamp, and, perhaps most famously, Piet Mondrian used principles of mathematics in their work. Was it coincidence, or were these artists following their instincts, which were ruled by mathematical underpinnings, such as optimal solutions for filling a space? If math exists within visual art, can it be found within literary pursuits? In short, just what is the relationship between mathematics and the creative arts? In this exploration of mathematical ideas in art and literature, Robert Tubbs argues that the links are much stronger than previously imagined and exceed both coincidence and commonality of purpose. Not only does he argue that mathematical ideas guided the aesthetic visions of many twentieth-century artists and writers, Tubbs further asserts that artists and writers used math in their creative processes even though they seemed to have no affinity for mathematical thinking. In the end, Tubbs makes the case that art can be better appreciated when the math that inspired it is better understood. An insightful tour of the great masters of the last century and an argument that challenges long-held paradigms, this book will appeal to mathematicians, humanists, and artists, as well as instructors teaching the connections among math, literature, and art. “Though the content of Tubbs’s book is challenging, it is also accessible and should interest many on both sides of the perceived divide between mathematics and the arts.” —Choice
Author | : Paul Benacerraf |
Publisher | : Cambridge University Press |
Total Pages | : 604 |
Release | : 1984-01-27 |
Genre | : Science |
ISBN | : 1107268133 |
Download Philosophy of Mathematics Book in PDF, ePub and Kindle
The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.
Author | : Stewart Shapiro |
Publisher | : OUP Oxford |
Total Pages | : 323 |
Release | : 2000-07-13 |
Genre | : Philosophy |
ISBN | : 0192893068 |
Download Thinking about Mathematics Book in PDF, ePub and Kindle
Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.
Author | : Stuart G. Shanker |
Publisher | : Psychology Press |
Total Pages | : 461 |
Release | : 2003 |
Genre | : Philosophy |
ISBN | : 9780415308816 |
Download Philosophy of Science, Logic and Mathematics in the Twentieth Century Book in PDF, ePub and Kindle
Contents - Introduction. 1. Philosophy of logic 2. Philosophy of mathematics in the 20th century. 3. Frege 4. Wittgenstein's Tractatus 5. Logical postivism 6. The philosophy of physics 7. The philosophy of science 8. Chance, cause and conduct; probability
Author | : John Stillwell |
Publisher | : Cambridge University Press |
Total Pages | : 77 |
Release | : 2019-06-06 |
Genre | : Science |
ISBN | : 1108456235 |
Download A Concise History of Mathematics for Philosophers . Book in PDF, ePub and Kindle
This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a large extent, the story of philosophy of mathematics.
Author | : David Bostock |
Publisher | : John Wiley & Sons |
Total Pages | : 345 |
Release | : 2009-03-09 |
Genre | : Mathematics |
ISBN | : 1405189924 |
Download Philosophy of Mathematics Book in PDF, ePub and Kindle
Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era. Offers beginning readers a critical appraisal of philosophical viewpoints throughout history Gives a separate chapter to predicativism, which is often (but wrongly) treated as if it were a part of logicism Provides readers with a non-partisan discussion until the final chapter, which gives the author's personal opinion on where the truth lies Designed to be accessible to both undergraduates and graduate students, and at the same time to be of interest to professionals