Document Type

Presentation

Presentation Date

Fall 9-12-2016

Conference Name

Colloquium Logicum 2016

Conference Location

Hamburg, Germany

Abstract

We clarify the respective role fixed points, diagonalization, and self- reference play in proofs of G ̈odel’s first incompleteness theorem. We first show that the usual fixed-point construction can be reduced to a double diagonalization; this is done to address widely held views such as that fixed-point are “paradoxical” (Priest), or work by “black magic” (Soare), or that their construction is “intuitively unclear” (Kotlarski). We then discuss three notions of self-reference; this can be seen an extension of a recent study by Halbach and Visser and is meant to show that we do not (yet?) have a robust theory that would allow us to establish a firm link between fixed points and self-reference.

Keywords

Gödel, formalized arithmetic, fixed points, diagonalization, self-reference

Disciplines

Logic and Foundations | Logic and Foundations of Mathematics | Mathematics | Philosophy

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