[Extract] The idea that there is pragmatic encroachment on knowledge has been vigorously explored in recent literature, but what has been rather less explored is how pragmatic encroachment interacts with another important principle about the structure of knowledge, namely, epistemic closure. In this chapter, we plan to go some way toward remedying that. For the purposes of this chapter, we will focus on single-premise closure, which we will understand as the idea that a proposition competently deduced from something one knows (and believed on that basis) is also known. It is hard to explore the interaction between pragmatic encroachment and closure without some detailed model of how pragmatic encroachment works. To that end, section 1 presents a model for cashing out some standard subject-sensitive ideas. It is a model that we’ve discussed at length elsewhere, and is built on the idea that one knows p only if the gap between one’s strength of epistemic position for p and perfect epistemic position makes no practical difference. In section 2, we explain why that model is antithetical to closure. In section 3, we critically discuss some ways of trying to fix the model so as to restore harmony. In section 4, we discuss the interaction of closure with another idea that is used to motivate pragmatic encroachment, namely the idea that stakes make a difference to whether one knows.
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