A Proof of Self-Proof; 1 of 15

          A Proof of Self-Proof

          On The Metamathematics of Belief

          Introduction

          Notation

          Quining Quanta

          Four Logical Quanta

          Dualities

          Evaluating Four Quanta

          Some Tables

          The Miracle of Doubt

          The Failure of Shame

          The Fall of Pride

          The Vanity of Faith

          How heavy is your theory?

          Paradoxes of Orthodoxy

          Do I exist?

          Cosmos from Chaos

          Summary

          Appendix 1: A Dialectical Game

          Appendix 2: A Proof of Self-Proof

          Introduction

          This paper is about the mathematical logic of belief systems. I  discuss four forms of self-reference, and their paradoxical properties. These imply Gödel’s Incompleteness Theorems, which in turn imply Löb’s Theorem.

          Löb’s Theorem says that any statement that asserts just its own provability is, in fact, provable. It is a logical bootstrap; by declaring itself necessary, it makes itself necessary. A Löbian statement, by its perfect faith in itself, attains truth.

          But why? How can anything so vain as self-belief attain absolute certainty? Read on, and I shall prove it to you.