Foundations of Mathematics and other Logical Essays

Foundations of Mathematics and other Logical Essays
Title Foundations of Mathematics and other Logical Essays PDF eBook
Author Frank Plumpton Ramsey
Publisher Routledge
Pages 312
Release 2013-10-15
Genre Philosophy
ISBN 1134528108

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This is Volume V in a series of eight on the Philosophy of Logic and Mathematics. Originally published in 1931, this study offers a collection of logical essays around the topic of the foundations of mathematics. Though mathematical teaching was Ramsey's profession, philosophy was his vocation. Reared on the logic of Principia Mathematica, he was early to see the importance of Dr. Wittgenstein's work (in the translation of which he assisted); and his own published papers were largely based on this. But the previously unprinted essays and notes collected in this volume show him moving towards a kind of pragmatism, and the general treatise on logic upon which at various times he had been engaged was to have treated truth and knowledge as purely natural phenomena to be explained psychologically without recourse to distinctively logical relations.

The Foundations of Mathematics and Other Logical Essays

The Foundations of Mathematics and Other Logical Essays
Title The Foundations of Mathematics and Other Logical Essays PDF eBook
Author Frank Plumpton Ramsey
Publisher Psychology Press
Pages 312
Release 2000
Genre Mathematics
ISBN 9780415225465

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First Published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Frank Ramsey

Frank Ramsey
Title Frank Ramsey PDF eBook
Author Cheryl Misak
Publisher Oxford University Press
Pages 537
Release 2020-02-13
Genre Philosophy
ISBN 0191074810

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When he died in 1930 aged 26, Frank Ramsey had already invented one branch of mathematics and two branches of economics, laying the foundations for decision theory and game theory. Keynes deferred to him; he was the only philosopher whom Wittgenstein treated as an equal. Had he lived he might have been recognized as the most brilliant thinker of the century. This amiable shambling bear of a man was an ardent socialist, a believer in free love, and an intimate of the Bloomsbury set. For the first time Cheryl Misak tells the full story of his extraordinary life.

Mathematics in Philosophy

Mathematics in Philosophy
Title Mathematics in Philosophy PDF eBook
Author Charles D. Parsons
Publisher Cornell University Press
Pages 367
Release 2018-08-06
Genre Mathematics
ISBN 1501729322

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This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics. A common point of view, that mathematical thought is central to our thought in general, underlies the essays. In his introduction, Parsons articulates that point of view and relates it to past and recent discussions of the foundations of mathematics. Mathematics in Philosophy is divided into three parts. Ontology—the question of the nature and extent of existence assumptions in mathematics—is the subject of Part One and recurs elsewhere. Part Two consists of essays on two important historical figures, Kant and Frege, and one contemporary, W. V. Quine. Part Three contains essays on the three interrelated notions of set, class, and truth.

The Foundations of Mathematics

The Foundations of Mathematics
Title The Foundations of Mathematics PDF eBook
Author Kenneth Kunen
Publisher
Pages 251
Release 2009
Genre Mathematics
ISBN 9781904987147

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Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.

F. P. Ramsey: Philosophical Papers

F. P. Ramsey: Philosophical Papers
Title F. P. Ramsey: Philosophical Papers PDF eBook
Author F. P. Ramsey
Publisher Cambridge University Press
Pages 288
Release 1990-07-27
Genre Philosophy
ISBN 9780521376211

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A compilation of all previously published writings on philosophy and the foundations of mathematics from the greatest of the generation of Cambridge scholars that included G.E. Moore, Bertrand Russell, Ludwig Wittgenstein and Maynard Keynes.

Philosophy of Mathematics in the Twentieth Century

Philosophy of Mathematics in the Twentieth Century
Title Philosophy of Mathematics in the Twentieth Century PDF eBook
Author Charles Parsons
Publisher Harvard University Press
Pages 365
Release 2014-03-10
Genre Philosophy
ISBN 0674419499

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In these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past century: Brouwer, Hilbert, Bernays, Weyl, Gödel, Russell, Quine, Putnam, Wang, and Tait.