The grammatical paradigm used to be a model for entire areas of cognitive science. Its primary tenet was that theories are axiomatic-like systems. A secondary tenet was that their predictions should be tested quickly and in great detail with introspective judgments. While the grammatical paradigm now often seems passé, we argue that in fact it continues to be as efficient as ever. Formal models are essential because they are explicit, highly predictive, and typically modular. They make numerous critical predictions, which (...) must be tested efficiently; introspective judgments do just this. We further argue that the grammatical paradigm continues to be fruitful. Within linguistics, implicature theory is a recent example, with a combination of formal explicitness, modularity, and interaction with experimental work. Beyond traditional linguistics, the grammatical paradigm has proven fruitful in the study of gestures and emojis; literature (“Free Indirect Discourse”); picture semantics and comics; music and dance cognition; and even reasoning and concepts. We argue, however, that the grammatical paradigm must be adapted to contemporary cognitive science. Computational methods are essential to derive quantitative predictions from formal models (Bayesian pragmatics is an example). And data collection techniques offer an ever richer continuum of options, from introspective judgments to large-scale experiments, which makes it possible to optimize the cost/benefit ratio of the empirical methods that are chosen to test theories. (shrink)