Generative and Evaluative Determination: Guessing, Belief, and Product Questions

Question-sensitive theories of guessing face two closure puzzles. Teague shows that answers selected for a question and a coarsening can conflict; Fang shows that answers permissible on independent factor questions can conjoin into an impermissible product answer. I argue that both puzzles conflate two uses of a determination function relative to a partition. A determination function is generative when it selects an answer from the competitors fixed by a partition, and evaluative when it assesses independently fixed content at the grain supplied by a partition. Uptake bridges these uses, but selection eligibility, permission to adopt, and actual adoption remain distinct. Closure is therefore status-sensitive: local outputs transmit only when the determining procedure preserves the relevant relation, whereas adopted outputs constrain later inquiry through the continuing commitment state. Formally, Binary Dominance permits compatible polar transmission only in the majority region; coarse optimization can discard the global fine optimum; and factor-wise disjunctive answers form rectangles that can violate the staircase produced by direct product Filtering. Teague’s puzzle thus requires an unestablished uptake-and-retention premise. Fang’s natural conjunctive report is explained by joint uptake and commitment closure, but these do not confer fresh product-indexed permission. The distinction also yields separate predictions for the filtering and threshold components of normality.