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Can these universes be mutual subsets? I'm grappling with the incompleteness theorems as they pertain to statements that are not contained in the set of possibi
by datameta 3y ago
Can these universes be mutual subsets? I'm grappling with the incompleteness theorems as they pertain to statements that are not contained in the set of possibilities which they describe, as in Gödel Escher Bach when discussing ideas foundational to Hofstadter's strange loop concept. The self-descriptive nature of information or lack thereof, essentially the existence of recursion without exclusion of the seed itself is stretching my mind. I think I need to start G.E.D. from the beginning (i.e. re-read the 40 pages I made it through).
- mtreis86 3y agoKeep reading it, page 1 really isn't the start. Each thread starts in a different place and we are introduced to some of them in the middle of their story.
- nyssos 3y agoIf you want to understand the incompleteness theorems you need an introductory model theory textbook. GEB doesn't really have anything to do with it.
- markisus 3y agoI recall that GEB gives an informal proof that systems that can formalize arithmetic are incomplete. But a standard textbook would certainly give a terser and more rigorous proof.