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Computer science, federal programs, and Nirvana

Published:01 January 1975Publication History
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Abstract

My text this morning comes from a highly regarded German algebraist of the nineteenth century, Leopold Kronecker. He was engaged in a vigorous debate with other mathematicians on exactly this question, what are the foundations of mathematics? What set of axioms can be used as a basis for deriving everything else? Most mathematicians were following directions of thought which invoked the concept of infinity, infinite sequences, infinite sets, infinite classes, and reciprocally, the notion of infinitesimal. By consistent application of logic, their premise inexorably led to further elaborations such as trans-finite numbers which are esoteric in the experience of most of us. Kronecker vigorously asserted that following this path was an error. He claimed that one must begin, and not only begin but remain content with the integers and those things which can be described algorithmically in terms of them. “God made the integers, and all the rest is the work of man.”

References

  1. 1 See, for example, the very readable book entitled G&ohuml;del's Proof, Nagel and Newman, New York University Press, 1958.Google ScholarGoogle Scholar
  2. 2 For a brief but lucid account of the issues and history, see the article on Foundations of Mathematics by S. C. Kleene in the Encyclopedia Britannica, 14th Ed., 1973 printing.Google ScholarGoogle Scholar
  3. 3 Washington Post December 16, 1974, p. A-1 and A-8.Google ScholarGoogle Scholar

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  1. Computer science, federal programs, and Nirvana

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      • Published in

        cover image ACM SIGCSE Bulletin
        ACM SIGCSE Bulletin  Volume 7, Issue 1
        Proceedings of the 5th SIGCSE symposium on Computer science education
        February 1975
        209 pages
        ISSN:0097-8418
        DOI:10.1145/953064
        Issue’s Table of Contents
        • cover image ACM Conferences
          SIGCSE '75: Proceedings of the fifth SIGCSE technical symposium on Computer science education
          January 1975
          221 pages
          ISBN:9781450373982
          DOI:10.1145/800284

        Copyright © 1975 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 1 January 1975

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