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Set Theory and its Philosophy
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
The Rise of Analytic Philosophy, 1879–1930
In this book Michael Potter offers a fresh and compelling portrait of the birth of modern analytic philosophy, viewed through the lens of a detailed study of the work of the four philosophers who contributed most to shaping it: Gottlob Frege, Bertrand Russell, Ludwig Wittgenstein, and Frank Ramsey. It covers the remarkable period of discovery that began with the publication of Frege's Begriffsschrift in 1879 and ended with Ramsey's death in 1930. Potter—one of the most influential scholars of this period in philosophy—presents a deep but accessible account of the break with absolute idealism and neo-Kantianism, and the emergence of approaches that exploited the newly discovered methods i...
Wittgenstein's Tractatus
These new studies of Wittgenstein's 'Tractatus' represent a significant step beyond recent polemical debate. They cover a wide range of themes, and show that close investigation into the composition of the work, and into the various influences on it, has much to yield in revealing the complexity and fertility of Wittgenstein's early thought.
Wittgenstein's Notes on Logic
Michael Potter shows, for the first time, that Wittgenstein's early Notes on Logic are a work of philosophical and historical importance. Using a challenging blend of biography and philosophy, he draws new conclusions about the nature of the Notes, the genesis of the Tractatus, and Wittgenstein's working methods.
Sets
This book is an introduction to set theory in which the author develops the subject from first principles and presupposes little more than an elementary grounding in logic. Throughout much attention is paid to the historical and philosophical background which illuminates the subject's development. This book differs from most by providing a particularly elegant and intuitive approach based on Scott's formulation of standard set theory in which sets are built up stage by stage. This approach has the advantage of introducing the axioms of set theory in a natural way and shows how they come to take the form they do. The book covers all the basic tools of set theory: the natural numbers, cardinals, ordinals, and the axiom of choice in some detail. It also provides an account of the representation theory of lattices and how this is closely connected with the various forms of the axiom of choice.
Pioneer Pottery
When he went to West Africa in the 1940s, Michael Cardew found himself in a land where the potter's art had been flourishing for centuries without the use of wheels, or kilns, or glazes. This book grew out of his desire to share all that he had learned from the African pioneers of pottery.
Routledge Philosophy Guidebook to Wittgenstein and the Tractatus Logico-philosophicus
This text presents an introduction to the Tractatus Logico-Philosophicus, the only book Wittgenstein published during his lifetime. Morris introduces & analyses the brief & sometimes cryptic text, including Wittgestein's life, the background to the Tractatus, & the importance of Wittgenstein's work in philosophy today.
The Last Sane Man
British studio potter Michael Cardew (1901-1983) was a man of paradox, a modernist who disliked modernity, a colonial servant who despised Empire, and an intellectual who worked with his hands. After graduating from Oxford in 1923, he made majestic slipware alongside legendary potter Bernard Leach.
The Rise of Analytic Philosophy, 1879–1930
In this book Michael Potter offers a fresh and compelling portrait of the birth of modern analytic philosophy, viewed through the lens of a detailed study of the work of the four philosophers who contributed most to shaping it: Gottlob Frege, Bertrand Russell, Ludwig Wittgenstein, and Frank Ramsey. It covers the remarkable period of discovery that began with the publication of Frege's Begriffsschrift in 1879 and ended with Ramsey's death in 1930. Potter—one of the most influential scholars of this period in philosophy—presents a deep but accessible account of the break with absolute idealism and neo-Kantianism, and the emergence of approaches that exploited the newly discovered methods i...
