Unfolding definitions without hiding cycles
How can a vocabulary be unfolded through its own definitions without concealing circularity?
Expose definitions that reuse other defined objects, and compare compact names with recursively substituted forms.
Status: open problem. Formulation and comparisons: reconstruction. Development: historical branch.
Alternative representations
Named concepts
Affords: Keeps a large definition compact.
Limits or losses: Dependencies remain implicit.
Substituted definitions
Affords: Makes reused definitions visible.
Limits or losses: Recursive substitution may never terminate or may erase useful distinctions.
Tension
Unfolding can clarify a concept or merely move its circularity out of sight.
Challenge
What marks an unresolved cycle, and when is a cycle a valid recursive definition?
This challenge is an editorial prompt, not a claim that the evidence already resolved it.
Proposed next move
Unfold a small vocabulary with a depth bound and explicit cycle markers; compare readers’ interpretations.
Status: new model-proposed experiment or extension; not a reported result.
Related problems
- One structure, several renderings — opens a local operation (corpus_evidence). Changing the representation included substituting defined objects with their definitions.
- The next description becomes another object — exposes a recurrence (retrospective_connection). A definition can become an object for another definition; the analogy does not equate linguistic circularity with every formal limit.
Evidence anchors
- basis-recursive-definitions: The material asks to identify defined objects that appear inside other definitions and replace their names with their definitions. A separate methodological question asks whether internal variants of an idea can help challenge it alongside opposing ideas. [Editorial paraphrase; presence of a proposal does not verify its truth.]
Root evidence and private recovery mappings are not part of this public release.
Open in the reader · All problems
Research editions
- Vertical Infinity and Reflexive Representation (reconstruction).