In its standard formulation, the meaning of a complex expression is determined by the meanings of its parts and the way they are combined. The principle admits two readings: a metaphysical one (the meaning of the whole supervenes on that of the parts) and a psychological one (speakers compute meaning by assembling the parts according to tacit rules). Although it is called "Frege's principle," Frege never stated it explicitly: it was Carnap who formulated it and named it after his teacher (Russin et al., 2025, sec. 2.1).
With Chomsky and Fodor, compositionality moved from formal semantics into cognitive science: it would be what explains productivity (understanding infinitely many new sentences with finite means) and the systematicity of thought. If you understand the dog bites the mailman and know what a cat is, you understand the cat bites the mailman. Classical architectures guarantee this by design; neural networks, which learn statistical regularities without explicit constituent structure, do not (Russin et al., 2025, secs. 2.3, 3).
The issue became experimental with datasets like SCAN, where commands such as jump twice must be mapped to actions and the test set demands new combinations. Early networks failed; later, various transformers reached good or perfect accuracy through architectural tweaks, data augmentation, or meta-learning (Millière & Buckner, 2024a, sec. 3.1). The question of how they do it remains. McCoy et al. (2026) show that the vector representations of several networks, including LLMs working on arithmetic, logic, code, and language, can be approximated by symbolic role–filler structures, and that intervening on those structures changes the model's behavior as predicted.
Buckner (2024) adds a nuance: the hard part of compositionality was never concatenating features, which any associationist can do, but fusing them into a meaningful whole, a part of the problem that classical treatments set aside (2024, p. 218). If a network implicitly realizes symbolic structure, does that vindicate Fodor, or does it show that compositionality does not require explicit symbols?