This is a talk about how to compute incremental sub-sentential context. I'll present a result that has clear and significant consequences for the ongoing debate about the role of semantics in phenomena such as presupposition projection and the felicity of epistemic modals. Although I will certainly draw out and discuss those consequences, the first part of the talk will be fairly technical. I'll describe a technique that feels to me a little bit like a magic trick. My goal in the talk will be to show a super slow-motion version that will reveal exactly how the magic happens, as simply as possible.
One of the high points will be a new solution to a presupposition projection timing problem due to Anvari and Blumberg 2021: in "Both children are in high school", standard theories of presupposition (e.g., Schlenker's Transparency theory) predict that the presuppositions of "both" must be satisfied by the (in this example, empty) leftward context. But as Anvari and Blumberg note, we can't decide whether the presupposition of "both" is satisfied until we know what sort of object there must be exactly two of (in this case, children). They propose that assessing presupposition satisfaction must be postponed until presupposition-triggering expressions have combined with at least some of their semantic arguments. On the approach here, the problem dissolves: presupposition satisfaction does in fact depend only on the leftward context, but the content of the presupposition that needs to be satisfied can depend on later expressions.