If meaning is the minimum that must be grasped in order to understand speech, then meaning is specified when speech is reported. What follows from this hypothesis, and how do constraints on reported speech compare with Frege's 'modes of presentation' as a guide to the concept of meaning? Or take iterated attitudes: two sentence operators may be extensionally equivalent, yet satisfy different principles. Does this phenomenon destroy the celebrated argument against mechanism from Godel's theorem, and what other implications does it have? Or again, does natural language tell for or against second-order logic? For example, is second-order quantification really substitutional, and is our use of plurals best represented in second-order terms? Five philosophers and a linguist debate these issues here. The volume will be of interest to anyone concerned with semantics and logical theory, whether they work in philosophy, logic, or linguistics.