Colloquium Logicum 2016
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.
Gödel, formalized arithmetic, fixed points, diagonalization, self-reference
Logic and Foundations | Logic and Foundations of Mathematics | Mathematics | Philosophy
Bernd Buldt (2016).
On fixed points, diagonalization, and self-reference. Presented at Colloquium Logicum 2016, Hamburg, Germany.