Is a Differentiable Ontology Possible? Representation, Property-Preserving Editing by Gradient Descent and by Language Models, and Scale

An ontology states what exists and how it is classified. In a symbolic ontology, reclassifying the whale from fish to mammal is a jump. We ask whether an ontology can be held as points in a continuous space with a smooth map to answers, so that a category can change gradually and be checked stepwise. We store 81 WordNet concepts and 25 classes in a network that answers each (concept, class) query with one of four values (true, false, both, neither), and test four criteria fixed in advance: representation, property-preserving editing, edits written by gradient descent and by large language models (LLMs) that read the weights as text, and scale. All answers and the class order are recovered on five seeds, and on all sixteen edit paths no sampled point violates disjointness or changes an untouched concept. When a new class requires separating two concepts at the same point, two LLMs (one run each) diagnosed the collapse and changed 25–32 parameters; a gradient with the same permissions succeeded too, changing at least 1,309. In 12 pretrained language models, a gradient-free rank-1 edit that overwrites a subject's representation with that of an existing concept succeeds in 55% of pooled trials, against 3% for random directions of equal norm, a mean per-model difference of 54 points (95% interval 35–72). Its effect is consistent with substituting the subject rather than changing its class; reordering prompt examples lowered success from 90% to 71% in seven re-run pairs. Edit paths inside real models remain unchecked.