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  • Hansen, Kaj Börge, 1946- (author)
  • Conceptual Foundations of Operational Set Theory
  • 2010
  • In: Danish Yearbook of Philosophy. - Copenhagen : Museum Tusculanum Press. - 0070-2749 .- 2468-9300. ; 45:1, s. 29-50
  • Journal article (peer-reviewed)abstract
    • I formulate the Zermelo-Russell paradox for naive set theory. A sketch is given of Zermelo’s solution to the paradox: the cumulative type structure. A careful analysis of the set formation process shows a missing component in this solution: the necessity of an assumed imaginary jump out of an infinite universe. Thus a set is formed by a suitable combination of concrete and imaginary operations all of which can be made or assumed by a Turing machine. Some consequences are drawn from this improved analysis of the concept of set, for the theory of sets and for the philosophy and foundations of mathematics.
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Type of publication
journal article (1)
Type of content
peer-reviewed (1)
Author/Editor
Hansen, Kaj Börge, 1 ... (1)
University
Uppsala University (1)
Language
English (1)
Year
2016 (1)

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