Kurt Gödel's incompleteness theorems and the limits of knowledge

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Abstract

In this paper a presentation is given of Kurt Gödel’s pathbreaking results on the incompleteness of formal arithmetic. Some biographical details are provided but the main focus is on the analysis of the theorems themselves. An intermediate level between informal and formal has been sought that allows the reader to get a sufficient taste of the technicalities involved and not lose sight of the philosophical importance of the results. Connections are established with the work of Alan Turing and Hao Wang to show the present-day relevance of Gödel’s research and how it relates to the limitations of human knowledge, mathematical knowledge in particular.
Original languageDutch
Pages (from-to)157-182
Number of pages25
JournalAlgemeen Nederlands Tijdschrift voor Wijsbegeerte
Volume113
Issue number1
Publication statusPublished - 2021

Keywords

  • Kurt Gödel
  • Incompleteness theorems
  • Alan Turing
  • Limits

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