Formal Limits & Impossibility Results

Primes about the boundaries of what formal systems can jointly guarantee: impossibility and incompatibility results (diagonal impossibility, axiomatic incompatibility, trilemma, decidability), and the procedural machinery for checking consistency and termination (consistency models, idempotence, termination conditions, underspecification).

16 primes in this family — primes that sit near one another in abstraction space (k-means over structural-signature embeddings). Each is shown with its short description.

• Axiomatic Incompatibility — A small set of individually plausible axioms is provably jointly unsatisfiable, forcing a chosen trade-off.
• Computability — The in-principle boundary between problems an effective procedure can solve and those none can.
• Consistency — A set of commitments cannot jointly derive a contradiction.
• Consistency Model — An explicit contract over which observations of shared state are legal when updates are concurrent.
• Constraint — Limits possibilities to guide outcomes.
• Contract — A multi-party bundle of obligations, breach criteria, and remedies under an accepted enforcement regime.
• Decidability Computability — A class of yes/no questions admits a finite procedure that always terminates with the correct answer.
• Denormalization — Deliberately re-introduce controlled redundancy against a canonical form, trading a synchronization burden for access-side wins.
• Diagonal Impossibility — In a self-modeling system, a putative total analyzer is refuted by constructing an object engineered to make the analyzer's verdict on it contradict the property it decides.
• Ground Truth — A reference channel designated authoritative for scoring another, itself a fallible construct.
• Idempotence — Repetition yields same result.
• Iteration — Repeats steps to refine outcomes.
• Stasis — Locate the kind of question at issue in a dispute—did it happen, what is it, was it justified, whose call is it—before contesting the substance, since disputants who seem to disagree about the answer are often disagreeing about the question.
• Termination Condition — An explicit, checkable predicate that decides whether an iterative or recursive process stops or continues.
• Trilemma — Three desirable properties that cannot be jointly guaranteed, forcing a pick-any-two choice with a distinct dissolve-or-scope intervention catalogue.
• Underspecification — A selection process treats evidence as if it picked out a single answer when many distinct answers fit it equally well, so a hidden closure silently chooses one representative and the behavior that distinguishes them is left uncontrolled.