Angels on a pin

Medieval scholars are mocked for asking how many angels fit on a needle's tip. But the mockery misses the point: they were probing real problems — occupancy, individuation, locality, causation for non-material agents — with the only concepts available to them. “Angel questions” are what inquiry looks like when a culture has problem-sensitivity but lacks clean abstractions. The vocabulary may be wrong; the underlying pressure may be profound.

Harman's axes

Graham Harman distinguishes two modes of ontological reduction. Undermining reduces a thing downward to its constituent parts. Overmining reduces a thing upward to its effects, appearances, or relations. These are orthogonal to the underdeveloped/overdetermined axis: an ontology can be underdeveloped AND overmining, or overdetermined AND undermining. The playground estimates a Harman index from axiom type distribution — subtype-heavy axioms lean toward overmining, dependsOn-heavy axioms lean toward undermining.

MDL interpretation

The Minimum Description Length principle says: the best model minimizes the sum of the model's description length $L(O)$ and the residual surprise $L(D|O)$ — how much the phenomena remain unexplained. An underdeveloped ontology has low $L(O)$ but high $L(D|O)$. An overdetermined ontology has bloated $L(O)$ while $L(D|O)$ barely decreases. The playground visualizes this decomposition.

The strongest single test

Does the ontology introduce exactly the distinctions needed to explain stable differences in the world, without multiplying categories beyond independent necessity? That is probably the closest thing to an engineering criterion for ontology.

Model changelog