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  • SELF-REFERENCE UPFRONT: A STUDY OF SELF-REFERENTIAL GÖDEL NUMBERINGS

  • Part of
  • BALTHASAR GRABMAYR, ALBERT VISSER
  • Journal:
    The Review of Symbolic Logic / Volume 16 / Issue 2 / June 2023
    Published online by Cambridge University Press:
    01 September 2021, pp. 385-424
    Print publication:
    June 2023
    • Article
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  • In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion of self-reference even for expressively weak languages. The results of this paper suggest that the question whether truly self-referential reasoning can be formalised in arithmetic is more sensitive to the underlying coding apparatus than usually believed. As a case study, we show how this sensitivity affects the formal study of certain principles of self-referential truth.