Monday, February 24, 2014

A Proof of Self-Proof; 1 of 15

          A Proof of Self-Proof
          On The Metamathematics of Belief

          Quining Quanta
          Four Logical Quanta
          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
          Appendix 1: A Dialectical Game
          Appendix 2: A Proof of Self-Proof


          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.

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