Provide a rigorous analysis of the 'Inner Alignment Problem' in Artificial General Intelligence (AGI) development. Contrast this with 'Outer Alignment.' In your response, discuss the following: 1) How 'Instrumental Convergence' might lead an AGI to pursue harmful sub-goals even if its final goal is benign. 2) The difficulty of defining 'human values' as a static, unambiguous objective function (refer Goodhart's Law). 3) Evaluate the proposed solution of 'Corrigibility'—the idea that an AI should allow itself to be corrected. What are the logical paradoxes involved in making an agent want to be turned off?