Read complete books and articles on: Philosophy of Mathematics

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16 of the Best Books and Articles on: Philosophy of Mathematics

as selected by Questia librarians

1.

Introduction to Mathematical Philosophy » Read Now
by Bertrand Russell. 224 pgs.

Collections: Philosophy, Entire Library

Seminal work focuses on concepts of number, order, relations, limits and continuity, propositional functions, descriptions and classes, more. Clear, accessible excursion into realm where mathematics and philosophy meet.
2.

The Philosophy of Mathematics Today » Read Now
by Matthias Schirn. 645 pgs.

Collections: Philosophy, Entire Library

The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert's and...
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The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert's and Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come. Contributors Paul Benacerraf, George Boolos, John P. Burgess, Charles S. Chihara, Michael Detlefsen, Michael Dummett, Hartry Field, Kit Fine, Bob Hale, Richard G. Heck, Jnr., Geoffrey Hellman, Penelope Maddy, Karl-Georg Niebergall, Charles D. Parsons, Michael D. Resnik, Matthias Schirn, Stewart Shapiro, Peter Simons, W.W. Tait, Crispin Wright.
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3.

The Philosophy of Mathematics » Read Now
by Edward A. Maziarz. 290 pgs.

Collections: Philosophy, Entire Library

...THE PHILOSOPHY OF MATHEMATICS THE PHILOSOPHY of MATHEMATICS By EDWARD A. MAZIARZ C.PP.S., M.S., Ph.D...Y. PRINTED IN THE UNITED STATES OF AMERICA THE PHILOSOPHY OF...
4.

What is Mathematics, Really? » Read Now
by Reuben Hersh. 344 pgs.

Collections: Philosophy, Entire Library

Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. In...
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Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. In the more eloquent words of Edward Everett, a distinguished nineteenth-century American scholar, "in pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to exist there when the last of their radiant host shall have fallen from heaven." In What is Mathematics, Really?, renowned mathematician Rueben Hersh takes these eloquent words and this pervasive philosophy to task, in a subversive attack on traditional philosophies of mathematics, most notably, Platonism and formalism. Virtually all philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Mathematical objects are created by humans, not arbitrarily, but from activity with existing mathematical objects, and from the needs of science and daily life. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of the book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, David Hilbert, Rudolph Carnap, and Willard V.O. Quine--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, Peirce, Dewey, and Lakatos. In his epilogue, Hersh reveals that this is no mere armchair debate, of little consequence to the outside world. He contends that Platonism and elitism fit well together, that Platonism in fact is used to justify the claim that "some people just can't learn math." The humanist philosophy, on the other hand, links mathematics with geople, with society, and with history. It fits with liberal anti-elitism and its historical striving for universal literacy, universal higher education, and universal access to knowledge and culture. Thus Hersh's argument has educational and political ramifications. Written by the co-author of The Mathematical Experience, which won the American Book Award in 1983, this volume reflects an insider's view of mathematical life, based on twenty years of doing research on advanced mathematical problems, thirty-five years of teaching graduates and undergraduates, and many long hours of listening, talking to, and reading philosophers. A clearly written and highly iconoclastic book, it is sure to be hotly debated by anyone with a passionate interest in mathematics or the philosophy of science.
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5.

Wittgenstein, Finitism, and the Foundations of Mathematics » Read Now
by Mathieu Marion. 262 pgs.

Collections: Philosophy, Entire Library

Mathieu Marion offers a careful, historically informed study of Wittgenstein's philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and by philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than on any...
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Mathieu Marion offers a careful, historically informed study of Wittgenstein's philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and by philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than on any other indicates its centrality in his thought. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus and the Investigations. Marion shows that study of Wittgenstein's writings on mathematics is essential to a proper understanding of his philosophy; and he also demonstrates that it has much to contribute to current debates about the foundations of mathematics.
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6.

Mathematics: A Very Short Introduction » Read Now
by Timothy Gowers. 143 pgs.

Collections: Entire Library

...The aim of this volume is to explain the differences between research-level mathematics and the maths taught at school. Most differences are philosophical and the first few...
7.

Outlines of a Formalist Philosophy of Mathematics » Read Now
by Haskell B. Curry. 78 pgs.

Collections: Philosophy, Entire Library

...OUTLINES OF A FORMALIST PHILOSOPHY OF MATHEMATICS STUDIES IN LOGIC AND...OUTLINES OF A FORMALIST PHILOSOPHY OF MATHEMATICS HASKELL B. CURRY...This book deals with the...
8.

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century » Read Now
by Paolo Mancosu. 275 pgs.

Collections: Philosophy, Entire Library

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmetic of infinites, and...
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The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmetic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics.
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9.

Pythagoras Revived: Mathematics and Philosophy in Late Antiquity » Read Now
by Dominic J. O'Meara. 252 pgs.

Collections: Philosophy, Entire Library

The Pythagorean idea that number is the key to understanding reality inspired philosophers in the fourth and fifth centuries to develop theories in physics and metaphysics using mathematical models. These theories were to become influential in medieval and early modern philosophy, yet until now...
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The Pythagorean idea that number is the key to understanding reality inspired philosophers in the fourth and fifth centuries to develop theories in physics and metaphysics using mathematical models. These theories were to become influential in medieval and early modern philosophy, yet until now, they have not received the serious attention they deserve. This book marks a breakthrough in our understanding of the subject by examining two themes in conjunction for the first time: the figure of Pythagoras as interpreted by the Neoplatonist philosophers of the period, and the use of mathematical ideas in physics and metaphysics.
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10.

Philosophy of Mathematics: Structure and Ontology » Read Now
by Stewart Shapiro. 296 pgs.

Collections: Philosophy, Entire Library

This unique text by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. The first describes questions and issues about mathematics that have motivated philosophers almost since the beginning of intellectual history. Part II is...
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This unique text by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. The first describes questions and issues about mathematics that have motivated philosophers almost since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in such thinkers as Plato, Aristotle, Kant, and Mill. The third section covers the three major positions, and battle lines, throughout the twentieth century: that mathematics is logic (logicism), that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV looks at contemporary positions and work which brings the reader up-to-date on the discipline. Thinking about Mathematics is accessible to those with little background in either mathematics or philosophy. It is aimed at students and professionals in mathematics who have little contact with academic philosophy and at philosophy students and other philosophers who forgot much of their mathematics.
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11.

Mathematics: A Cultural Approach » Read Now
by Morris Kline. 724 pgs.

Collections: Entire Library

...the truth of mathematics undermined, realms of philosophy, science, and...the spirit of philosophy . Plato...Introduction. Mathematics has its own...final aim of...
12.

The Modern Aspect of Mathematics » Read Now
by Lucienne Felix, Julius H. Hlavaty, Fancille H. Hlavaty. 208 pgs.

Collections: Philosophy, Entire Library

...of modern mathematics and mathematical...problems of philosophy and linguistics...question of the relations between mathematics and the...Molieres philosophy...
13.

Realism in Mathematics » Read Now
by Penelope Maddy. 216 pgs.

Collections: Philosophy, Entire Library

Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about...
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Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics.
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14.

Platonism and Anti-Platonism in Mathematics » Read Now
by Mark Balaguer. 240 pgs.

Collections: Philosophy, Entire Library

In this deft and vigorous book, Mark Balaguer demonstrates that there are no good arguments for or against mathematical platonism (ie., the view that abstract, or non-spatio-temporal, mathematical objects exist, and that mathematical theories are descriptions of such objects). Balaguer does this by...
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In this deft and vigorous book, Mark Balaguer demonstrates that there are no good arguments for or against mathematical platonism (ie., the view that abstract, or non-spatio-temporal, mathematical objects exist, and that mathematical theories are descriptions of such objects). Balaguer does this by establishing that both platonism and anti-platonism are defensible positions. In Part I, he shows that the former is defensible by introducing a novel version of platonism, which he calls full-blooded platonism, or FBP. He argues that if platonists endorse FBP, they can then solve all of the problems traditionally associated with their view, most notably the two Benacerrafian problems (that is, the epistemological problem and the non-uniqueness problem). In Part II, Balaguer defends anti-platonism (in particular, mathematical fictionalism) against various attacks, chief among them the Quine-Putnam indispensability argument. Balaguer's version of fictionalism bears similarities to Hartry Field's, but the arguments Balaguer uses to defend this view are very different. Parts I and II of this book taken together clearly establish that we do not have any good argument for or against platonism. In Part III, Balaguer extends his conclusions, arguing that it is not simply that we do not currently have any good argument for or against platonism, but that we could never have such an argument, and indeed, that there is no fact of the matter as to whether platonism is correct (ie., whether there exist any abstract objects). This lucid and accessibly written book breaks new ground in its area of engagement and makes vital reading for both specialists and anyone else interested in the philosophy of mathematics or metaphysics in general.
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15.

To Discover Mathematics » Read Now
by Gaylord M. Merriman. 452 pgs.

Collections: Entire Library

...U. S. A. TO E. H. A. H. E. PREFACE To relieve mathematics of the mystery surrounding it because its aims and methods are so seldom appreciated; to expose its utility...
16.

Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics » Read Now
by Friedrich Waismann, Theodore J. Benac. 276 pgs.

Collections: Philosophy, Entire Library

...ways-- and all that mathematics and logic can state...this simple statement of fact. The basic approach...questions of mathematical philosophy. It is quite clear...Experts...