Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

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. (shrink)

This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...

The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional philosophies (...) of mathematics indicating how each is prepared to deal with the present problem. It is shown that (the standard formulations of) some views seem to deny outright that there is a relationship between mathematics and any non-mathematical reality; such philosophies are clearly unacceptable. Other views leave the relationship rather mysterious and, thus, are incomplete at best. The final, more speculative section provides the direction of a positive account. A structuralist philosophy of mathematics is outlined and it is proposed that mathematics applies to reality though the discovery of mathematical structures underlying the non-mathematical universe. (shrink)

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 through an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.

One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets.

Bertrand Russell remains one of the greatest philosophers and most complex and controversial figures of the twentieth century. Here, in this frank, humorous and decidedly charming autobiography, Russell offers readers the story of his life – introducing the people, events and influences that shaped the man he was to become. Originally published in three volumes in the late 1960s, _Autobiography_ by Bertrand Russell is a revealing recollection of a truly extraordinary life written with the vivid freshness and clarity that has (...) made Bertrand Russell’s writings so distinctively his own. (shrink)

This paper suggests a new principle for confirmation theory which is called the principle of explanatory surplus. This principle is shown to be non-Bayesian in character, and to lead to a treatment of simplicity in science. Two cases of the principle of explanatory surplus are considered. The first (number of parameters) is illustrated by curve-fitting examples, while the second (number of theoretical assumptions) is illustrated by the examples of Newton's Laws and Adler's Theory of the Inferiority Complex.