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Two short notes on Schlenker's theory of presupposition projection

The format of Theoretical Linguistics is particularly appropriate when one can identify contributions to linguistic theory that – when put in the limelight – are likely to push the field forward in important ways. With this goal in mind, I can’t think of a better choice than Schlenker’s target article, an article which proposes a completely original outlook on a problem that has troubled researchers for decades and – at least in the eyes of some practitioners – has resisted a satisfactory solution. My goal for this commentary is very modest, namely to explain what I find remarkable about Schlenker’s proposal. I will try to achieve this goal by discussing two of Schlenker’s contributions. The first is the identification of a generalization that relates the presupposition of a sentence to what we might call the anti-presupposition of a closely related conjunctive sentence. Although this generalization is predicted by the competing theories that Schlenker considers – namely various versions of dynamic semantics – it suggests a totally new perspective on the problem. The second contribution that I will discuss pertains to the main tool that Schlenker invokes in order to develop his perspective, namely quantification over possible continuations of a sentence at a particular point of sentence processing. I will point out that this new tool could also be used