Before its discovery there was just one geometry and mathematics; the idea that another geometry existed was considered improbable. When Gauss discovered hyperbolic geometry, it is said that he did not publish anything about it out of fear of the "uproar of the Boeotians ", which would ruin his status as princeps mathematicorum Latin, "the Prince of Mathematicians". Main article: Begriffsschrift Begriffsschrift German for, roughly, "concept-script" is a book on logic by Gottlob Frege , published in , and the formal system set out in that book. Begriffsschrift is usually translated as concept writing or concept notation; the full title of the book identifies it as "a formula language , modeled on that of arithmetic , of pure thought.
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In a note about writing the book, Kleene notes that up to , about 17, copies of the English version of his text were sold, as were thousands of various translations including a sold-out first print run of of the Russian translation. So this is a book with a quite pivotal influence on the education of later logicians, and on their understanding of the fundamentals of recursive function theory and the incompleteness theorems in particular.
It is indeed still a pleasure to read or at least, it ought to be a pleasure for anyone interested enough in logic to be reading these pages. The Introduction to Metamathematics remains a really impressive achievement: and not one to be admired only from afar, either.
Some details Chs. This is all very attractively done. In Ch. And the final Ch. Summary verdict This book can still be warmly recommended as an enjoyable and illuminating presentation of fundamental material, written by someone who was himself so closely engaged in the early developments back in the glory days.
It should be entirely accessible if you have managed e.
Stephen Cole Kleene
Samusar Summary verdict This book can still be warmly recommended as an enjoyable and illuminating presentation of fundamental material, written by someone who was himself so closely engaged in the early developments back in the glory days. This is all very attractively done. Request removal from index. Thomas Andrews k 11 Metamathematics and the Philosophy of Mind. History of Western Philosophy. The proof of most of the formulae from to is only hinted: There are more recent books that in my opinion are better.
He was awarded the Ph. In , he joined the mathematics department at the University of Wisconsin—Madison , where he spent nearly all of his career. After two years as an instructor, he was appointed assistant professor in While a visiting scholar at the Institute for Advanced Study in Princeton, —, he laid the foundation for recursion theory , an area that would be his lifelong research interest. In , he returned to Amherst College, where he spent one year as an associate professor of mathematics. He was an instructor of navigation at the U. In , Kleene returned to Wisconsin , becoming a full professor in and the Cyrus C.