1. SELF-REFERENCE UPFRONT: A STUDY OF SELF-REFERENTIAL GÖDEL NUMBERINGS.
- Author
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GRABMAYR, BALTHASAR and VISSER, ALBERT
- Subjects
ARITHMETIC ,NUMBER theory - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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