The success of pretrained contextual encoders, such as ELMo and BERT, has brought a great deal of interest in what these models learn: do they, without explicit supervision, learn to encode meaningful notions of linguistic structure? If so, how is this structure encoded? To investigate this, we introduce latent subclass learning (LSL): a modification to existing classifier-based probing methods that induces a latent categorization (or ontology) of the probe's inputs. Without access to fine-grained gold labels, LSL extracts emergent structure from input representations in an interpretable and quantifiable form. In experiments, we find strong evidence of familiar categories, such as a notion of personhood in ELMo, as well as novel ontological distinctions, such as a preference for fine-grained semantic roles on core arguments. Our results provide unique new evidence of emergent structure in pretrained encoders, including departures from existing annotations which are inaccessible to earlier methods.