Non-recursive enumerability of undecidable statements in the OEE knowledge framework

Determine whether the set of undecidable sentences arising in the open-ended evolutionary knowledge framework—i.e., sentences whose truth value cannot be decided within an individual's current theory—is recursively enumerable; specifically, establish or refute that this set is not recursively enumerable.

Background

In discussing frame relativity and Gödelian incompleteness, the paper argues that observers in open-ended systems face an infinite, unlistable collection of undecidable statements. This raises a computability-theoretic question about the enumerability of such undecidable sentences.

If the set of undecidable statements is not recursively enumerable, it would further codify the limits of algorithmic approaches to knowledge mapping and prediction in open-ended evolutionary contexts.