Formal resolutions from Words That Echo, expressed under Michael’s Maxim: “There are no true paradoxes; every paradox is resolvable through proper analysis.”
Self-referential truth claims collapse without a temporal or referential offset. A statement cannot fully evaluate itself within the same frame.
Principle: Truth cannot self-evaluate synchronously; define a distinct evaluation frame.
The confusion between meta-sets (rules) and member-sets (objects) generates apparent contradiction. Separate classifier from class.
Principle: No system may classify its own classification rule.
Time travel opens a divergent causal branch rather than negating origin. Identity persists along the traveler’s branch.
Principle: Causality is conserved through divergence, not negation.
Replace universal (“anyone”) claims with probabilistic trend statements; remove the false totality.
Principle: Ambiguous universal quantifiers produce false contradictions.
Rules applied to non-identical subjects generate spurious conclusions. Align rule scope with the actual subject set.
Principle: Misaligned variables create artificial entailment.
Entailment requires contextual relevance; unrelated premises cannot produce meaningful conclusions.
Principle: No entailment without relevance.
Properties of a collective are not properties of each member; probability assertions must respect the level of analysis.
Principle: Do not transfer collective properties to individuals (and vice versa).
Evidence from unrelated domains cannot confirm a universal hypothesis about a specific kind.
Principle: Confirmation requires domain‑relevant evidence.
Imperatives are not truth-apt; they reduce to true/false statements about obligations, dissolving the paradox.
Principle: Imperatives cannot generate contradiction independent of truth conditions.
Perfect foresight is falsely assumed; memory and uncertainty preserve surprise.
Principle: Knowledge cannot fully simulate surprise.
“Unshaven” and “shaved” are sequential states, not simultaneous; the wording collapses time into a single instant.
Principle: Distinguish sequential from simultaneous predicates.
Claims about an entire container of “unnameables” presume illicit total knowledge of that container.
Principle: Do not universalize beyond your classification scope.
Self-referential size descriptions produce recursion errors; resolve by fixing the language game’s ruleset.
Principle: Define meta‑linguistic limits before measuring expressions.
The hidden premise (assumed male surgeon, single meaning of “son”) is false; redefine variables to reflect reality.
Principle: Examine hidden premises about identity.