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Mathematics --- Logic of mathematics --- Mathematics, Logic of --- Philosophy --- Mathematics - Philosophy

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A student of Trinity College and a member of the Cambridge Apostles, William Kingdon Clifford (1845-79) graduated as second wrangler in the mathematical tripos, became a professor of applied mathematics at University College London in 1871, and was elected a fellow of the Royal Society in 1874. The present work was begun by Clifford during a remarkably productive period of ill health, yet it remained unfinished at his death. The statistician and philosopher of science Karl Pearson (1857-1936) was invited to edit and complete the work, finally publishing it in 1885. It tackles five of the most fundamental areas of mathematics - number, space, quantity, position and motion - explaining each one in the most basic terms, as well as deriving several original results. Also demonstrating the rationale behind these five concepts, the book particularly pleased a later Cambridge mathematician, Bertrand Russell, who read it as a teenager.

Mathematics --- Logic of mathematics --- Mathematics, Logic of --- Philosophy.

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Tries to refine the philosophy of mathematics to reflect what mathematicians really do, and argues that mathematics must be understood in a social context.

Mathematics --- Logic of mathematics --- Mathematics, Logic of --- Philosophy.

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Hermann Weyl (1885-1955) was one of the twentieth century's most important mathematicians, as well as a seminal figure in the development of quantum physics and general relativity. He was also an eloquent writer with a lifelong interest in the philosophical implications of the startling new scientific developments with which he was so involved. Mind and Nature is a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in any language or translated into English, or that have long been out of print. Complete with Peter Pesic's introduction, notes, and bibliography, these writings reveal an unjustly neglected dimension of a complex and fascinating thinker. In addition, the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished. Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as "a first-class stroke of genius"; two little-known letters by Weyl and Einstein from 1922 that give their contrasting views on the philosophical implications of modern physics; and an essay on time that contains Weyl's argument that the past is never completed and the present is not a point. Also included are two book-length series of lectures, The Open World (1932) and Mind and Nature (1934), each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics. Finally, four retrospective essays from Weyl's last decade give his final thoughts on the interrelations among mathematics, philosophy, and physics, intertwined with reflections on the course of his rich life.

Physics --- Mathematics --- Logic of mathematics --- Mathematics, Logic of --- Philosophy.

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In this introduction to the philosophy of mathematics, Michéle Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics – Platonism, realism, logicism, formalism, constructivism and structuralism – as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. The book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.

Mathematics --- Logic of mathematics --- Mathematics, Logic of --- Philosophy.