Articles liés à Elements of Intuitionism
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Synopsis
This first introduction to intuitionistic mathematics concentrates on the fundamental concepts, leading the reader step-by-step through the subject. After a preliminary philosophical orientation, and a sketch of the differences between intuitionistic and classical reasoning, the author outlines the intuitionistic approach to the theory of real numbers. This gives the reader a taste of intuitionistic maths, to motivate the following discussion of the foundations. This begins with the intuitionistic analysis concepts of choice sequences and spreads, and the bar-induction and continuity principles which govern them. The author then gives a much-needed discussion of first-order intuitionistic logic from both proof-theoretic aspect and as handled semantically by Beth and Kripke trees. The section finishes with a comprehensive survey of results concerning the completeness of intuitionistic logic. in detail. The book goes on to look at some metamathematical results, realizability, and at the theory of the creative subject, and ends with an analysis of the philosophical issues. Students of mathematics, logic and philosophy.
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Présentation de l'éditeur
This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an informal but thorough introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics has been completely revised for this second edition. Brouwer's proof of the Bar Theorem has been reworked, the account of valuation systems simplified, and the treatment of generalized Beth Trees and the completeness of intuitionistic first-order logic rewritten. Readers are assumed to have some knowledge of classical formal logic and a general awareness of the history of intuitionism. From reviews of the first edition: This excellent book can be recommended to the student of mathematics or philosophy wishing to get a comprehensive and reliable introduction to modern intuitionism. Zentralblatt für Mathematik The relevance of this book extends well beyond the confines of the philosophy of mathematics, right to the centre of debates in the philosophy of language. Philosophical Books . . . a valuable and original contribution to the philosophy of mathematics. Journal of Symbolic Logic
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