Imagination and the puzzles of iteration

Iteration presents opposing puzzles for a theory of the imagination. The first puzzle, noted by David Lewis, is that when a person pretends to pretend, the iteration is often preserved. Let’s call this the puzzle of ‘preserved iteration’. At the other pole, Gregory Currie has noted that very often when we pretend to pretend, the iteration does collapse. We might call this the puzzle of ‘collapsed iteration’. Somehow a theory of the imagination must be able to address these two puzzles. I argue that an empirically inspired cognitive theory of the imagination (Nichols & Stich 2000) can accommodate both puzzles.