Mediator: Tsvi Tlusty, Princeton Institute for Advanced Studies

Organization: 3 half-days, End of May 2013

Credits: 9h

Synopsis:
Self-reference is a very old idea and an even older myth: Ouroboros, the self-eating serpent, was an icon of ancient religions. Self-reflexivity occurs very naturally when we think or talk about ourselves, for example the first person pronoun "I". It is frequently used in the arts, for example in Don Quixote or in Magritte's painting "ceci n'est pas une pipe". The idea of self-reference is central in the foundations of mathematics, philosophy, linguistics and computation. All these fields are related to the basic liar paradox that we encounter when reading the phrase "this sentence is wrong" and asking whether it is true or false. This paradox lead to Gödel's theorem and to Turing's formulation of computability through the use of recursive functions. The same ideas are linked to self-reproducing machines, and in particular to the molecular machinery of living systems and to the emergence of Life. In the lectures we will review these concepts and relations from various formal and informal angles.
- Lecture 1 - Logic paradoxes and computation (recursive functions, Gödel, Turing, Church).
- Lecture 2 - Self-reproducing machines in technology and Life (von Neumann's machines, origins of life).
- Lecture 3 - Self-reference in language and mind (dictionaries, consciousness etc.)

References:
- Smullyan, Diagonalization and Self-Reference.
- Rogers, Theory of Recursive functions.
- Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid.
- Nagel & Newman, Gödel's proof.