Gödel's Incompleteness Theorems

This Element Takes A Deep Dive Into Gdel''S 1931 Paper Giving The First Presentation Of The Incompleteness Theorems Opening Up Completely Passages In It That Might Possibly Puzzle The Student Such As The Mysterious Footnote 48A. It Considers The Main Ingredients Of Gdel''S Proof: Arithmetization Strong Representability And The Fixed Point Theorem In A Layered Fashion Returning To Their Various Aspects: Semantic Syntactic Computational Philosophical And Mathematical As The Topic Arises. It Samples Some Of The Most Important Proofs Of The Incompleteness Theorems E.G. Due To Kuratowski Smullyan And Robinson As Well As Newer Proofs Also Of Other Independent Statements Due To H. Friedman Weiermann And Paris-Harrington. It Examines The Question Whether The Incompleteness Of E.G. Peano Arithmetic Gives Immediately The Undecidability Of The Entscheidungsproblem As Kripke Has Recently Argued. It Considers Set-Theoretical Incompleteness And Finally Considers Some Of The Philosophical Consequences Considered In The Literature.