Following Hale & Reiss' paper on the Subset Principle (SP) in phonology, we draw attention here to some unsolved problems in the application of SP to syntax acquisition. While noting connections to formal results in computational linguistics, our focus is on how SP could be implemented in a way that is both linguistically well-grounded and psychologically feasible. We concentrate on incremental learning (with no memory for past inputs), which is now widely assumed in psycholinguistics. However, in investigating its interactions with SP, we uncover the rather startling fact that incremental learning and SP are incompatible, given other standard assumptions. We set out some ideas for ways in which they might be reconciled. Some seem more promising than others, but all appear to carry severe costs in terms of computational load, learning speed or memory resources. The penalty for disobeying SP has long been understood. In future language acquisition research it will be important to address the costs of obeying SP.
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