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

Let's say that I fully know that p$p$ if I know that p$p$, I know that I know that p$p$, I know that I know that I know that p$p$, and so on. Let's say that I partially know that p$p$ if I know that p$p$ but I don't fully know that p$p$. What, if anything, do I fully know? What, if anything, do I partially know? One response in the literature is that I fully know everything that I know; partial knowledge is impossible. This response is in tension with a plausible margin-for-error principle on knowledge. A different response in the literature is that I don't fully know anything; 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 partially 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 possibility of both full knowledge and partial knowledge is consistent with the margin-for-error principle. I also argue that the resulting picture of knowledge is well-motivated.