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.
"synopsis" may belong to another edition of this title.
Review
"The present edition satisfies the highest standards of publishing quality...Dummett certainly succeeded in producing an elementary text, accessible to a wide audience, philosophical as well as mathematical." --The Review o f Modern Logic 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 fur 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
"The present edition satisfies the highest standards of publishing quality...Dummett certainly succeeded in producing an elementary text, accessible to a wide audience, philosophical as well as mathematical." --The Review o f Modern Logic 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 fur 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
"The present edition satisfies the highest standards of publishing quality...Dummett certainly succeeded in producing an elementary text, accessible to a wide audience, philosophical as well as mathematical." --The Review o f Modern Logic 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 fur 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
"The present edition satisfies the highest standards of publishing quality...Dummett certainly succeeded in producing an elementary text, accessible to a wide audience, philosophical as well as mathematical." --The Review o f Modern Logic 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 fur 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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