Gödel's Incompleteness Theorems

Shows formal systems with self-reference must be incomplete; analogized to Turing's halting problem.

Neighborhood — ranked by edge-count

paper

thinker

Kurt Gödel
introduces
Proved incompleteness theorem showing Principia's formalist program could not succeed; cited for implications on computationalism

concept

Halting Problem
analogous_to
Undecidability of whether an arbitrary program halts, discussed as a self-referential limit of computation.

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Bell's theoremconcept0.729
A result in quantum mechanics asserting deep connectedness in the fabric of space, cited as a theory touching on not-separateness.
Rice's Theoremconcept0.689
No general algorithm decides non-trivial semantic properties of self-modifying trajectories.
Hoel's Causal Emergence Theoryframework0.688
Quantitative emergence theory based on Markov dynamics and effective information (EI).
Every finite non-empty poset has maximal elements.finding0.669
Established property used to characterize down-sets and to relate elements to maximal upper bounds.
Continuous dynamics inhabit real closed fields (complete, decidable); discrete arithmetic is incomplete and uncomputable.claim0.661
Mathematical argument that continuous biological computation operates in a richer formal domain; suggests computational advantages for consciousness-relevant processing.
The centers which exist in a configuration have a real mathematical existence and are actually occurring features of the space itself.claim0.660
Strengthens the claim that centers are not just psychological but physically real.
IIT Five Axioms (Existence, Composition, Information, Integration, Exclusion)concept0.657
Foundational axioms of IIT from which postulates about physical systems are derived; applied to the RN in this study.
Huygens principleconcept0.655
Physical principle used to model tracer effect and traveling wave construction of space in consciousness.