We know stuff. And we know that we know stuff. But what exactly is the connection between the two?
Epistemic logic is the study of some of the fundamental properties of knowledge and related concepts. For example, one question that bothered philosophers for years: it is true that if I know something, I also know that I know it?
In “Knowledge to Infinity: Full knowledge and the margin-for-error principle” I accept the position that sometimes, I know something without knowing that I know it. But I argue that sometimes, I know something, and I know that I know it, and I know that I know that I know it, and … I show how we can have infinitely many levels of knowledge, without assuming that whenever we know something, we know that we know it.
In “Escaping Zeno’s shadow: A defense of common knowledge”, I use this idea to argue that sometimes, we have common knowledge. A group commonly know something if all its members know it, and they all know that they all know it, and they all know that they all know that they all know it, and … This idea has been used extensively in discussions of rationality, but philosophers have been skeptical of it. I show that there is no reason to think that common knowledge is impossible.
In “Knowledge by choice”, I argue that what we know depends on our choices, and not only on what’s given to us. I use this idea to provide a new response to the lottery paradox. This shows that there’s a problem with the way most philosophers think about the K operator: if Kp means “I can know that p,” then my arguments shows that it doesn’t obey the closure principle, even if closure is true for knowledge itself.
Let’s say that "I fully know that p" if I know that p, I know that I know that p, I know that I know that I know that p, and so on. Let’s say that "I partially know that p" if I know that p but I don’t fully know that 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 (2024, forthcoming) 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.
@article{fiatKnowledgeToInfinity,title={Knowing to infinity: Full knowledge and the margin-for-error principle},author={Fiat, Yonathan},year={forthcoming},journal={Philosophy and Phenomenological Research},}
In progress
Escaping Zeno’s Shadow: A defense of common knowledge
Two agents commonly know that p if they both know that p, they both know that they both know that p, they both know that they both that they both know that p, etc. Common knowledge can in principle arise in many kinds of situations. In this paper, I focus on two extreme kinds of cases: cases where agents can only reach common knowledge by communication, and cases where agents cannot communicate and still apparently have common knowledge. I examine three skeptical arguments to the conclusion that common knowledge is impossible in those cases, and argue that they fail because they make the Zeno Fallacy: the inference from the fact that something needs infinitely many steps to the conclusion that it is impossible to do.