Marcus R. An Historical Introduction to the Philosophy of Mathematics...2016

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Marcus R. An Historical Introduction to the Philosophy of Mathematics...2016

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Textbook in PDF format A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers Acknowledgments How to use the book Introduction: Terminology and axioms Ancients Introduction to part I Pythagoras, Parmenides, and Zeno’s paradoxes Plato Aristotle Moderns Introduction to part II The rationalists The empiricists Kant Nineteenth and early twentieth centuries Introduction to part III Mill Cantor’s transfinites Logicism Formalism Intuitionism Conventionalism Wittgenstein Gödel’s theorems Contemporary views Introduction to part IV The Benacerraf problem The indispensability argument Benacerraf’s number puzzle and structuralism Modalism Fictionalism Apriorism Maddy’s realism Naturalism Plenitudinous platonism Neo-logicism Experimental mathematics Bibliography Index