Knowing to infinity: Full knowledge and the margin‐for‐error principle

Abstract

Let’s say that I fully know that 𝑝 if I know that 𝑝, I knowthat I know that 𝑝, I know that I know that I knowthat 𝑝, and so on. Let’s say that I partially know that 𝑝if I know that 𝑝 but I don’t fully know that 𝑝. What,if anything, do I fully know? What, if anything, do Ipartially know? One response in the literature is that Ifully know everything that I know; partial knowledgeis impossible. This response is in tension with a plausi-ble margin-for-error principle on knowledge. A differentresponse in the literature is that I don’t fully know any-thing; everything that I know, I partially know. Recently,Goldstein (forthcoming, 2024) defended a third view,according to which I fully know some things and I par-tially know other things. While this seems plausible,Goldstein’s account is based on denying the margin-for-error principle. In this paper, I show that the possibilityof both full knowledge and partial knowledge is consis-tent with the margin-for-error principle. I also argue thatthe resulting picture of knowledge is well-motivated.