0.4 Language as a discovered world

Consider language before considering text. The infant does not receive a curated corpus of sentences. Speech is a temporally extended acoustic stream, mixed with gesture, gaze, repeated routines, and the physical consequences of other people’s actions. Even the boundaries of the candidate units are part of the learning problem. Eight-month-old infants can exploit transitional statistics to segment continuous speech, demonstrating that structure can be recovered before explicit instruction or a mature lexicon [ Saffran et al. , 1996 ] .

Segmentation, however, is only the beginning. A learner must discover units at several scales and the lawful ways in which those units interact. Phonetic contrasts participate in syllables; syllables in words; words in phrases and utterances. Meaning introduces further structure. The expressions “cup,” “blue cup,” and “bring me the blue cup” are not merely three strings of increasing length. They support reusable operations: identifying a kind, restricting a referent, specifying a goal, and recruiting another agent.

An ORACLE declaration of this world might therefore treat linguistic units, meanings, or information states as objects, and grammatical, semantic, or pragmatic transformations as morphisms. Composition records when one transformation can lawfully follow another. Equations record distinct expressions or derivations that are equivalent for the probes currently at issue.

¹1. This is a modeling choice, not a claim that words must always be objects or that sentences must always be morphisms. A different probe language can induce a different, equally useful categorical declaration. ↩

The Piagetian distinction appears immediately. A child assimilates a novel utterance when its pieces and use fit an existing construction. The child accommodates when a familiar form behaves differently from the current schema—when a plural is irregular, a word changes meaning with context, or an apparently grammatical composition fails pragmatically. Accommodation is not simply a larger parameter update. It may revise the inventory of units, the typing of a transformation, or an equation previously taken to hold.

Modern sequence models make the contrast sharp. They can absorb enormous amounts of distributional structure, yet success on familiar mixtures does not by itself establish systematic reuse on novel compositions. The SCAN experiments, for example, were designed to separate interpolation from such systematic compositional generalization [ Lake and Baroni , 2018 ] . For ORACLE, the empirical question is not merely whether the next fragment can be predicted, but whether the learner has identified persistent constructions that continue to work when familiar parts are recombined.