papers

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.

This paper provides a defense of *Parfit’s principle*: when a person’s preferences are unknown, it is wrong to take, on their behalf, some of the risks that they could rationally choose to take. We argue that rejecting the principle leads to a false conclusion when deciding for more than one person. To do that, we prove a pair of theorems that show that all and only risk-seeking attitudes can lead to this result.

Significance testing (ST) is arguably the most widely used tool in statistical analysis. Since its introduction in the early twentieth century, it has led scientists to countless successes. Yet, from the beginning, it has been the target of relentless criticism. Critics - including philosophers, statisticians, meta-scientists, and practitioners - have called it irrational, unmotivated, and fallacious. Even its defenders have often struggled to explain and motivate it. We can do better. In this paper, I show how ST arises naturally from the question "how should we evaluate successful predictions?" Some predictions are more impactful than others. The success of the prediction _it will rain tomorrow_ is somewhat impressive; the success of the prediction _it will rain frogs tomorrow_ is astonishing. I show that if we sharpen and extend this observation, we end up with ST. When a scientist reports that she got a _statistically significant_ result, she reports that she made a prediction and that its success is impressive. If we add the premise that good inquirers are sensitive to impressive successful predictions - a position known as _predictivism_ - we get the conclusion that ST is a rational practice. Moreover, we also get an explanation why it’s a valuable practice, and this explanation can guide us in its application, so we will use it better.

We often think that we can know depends only on what is _given_ to us; on our evidence, for example. In this paper, I argue that this is false. It also depends on our choices. I argue that our choices can change what would be an amazing coincidence, and that typically we can know that amazing coincidences don’t happen. This paper explores three applications of this idea. First, it suggests a new solution to the lottery paradox. Second, it gives us a new understanding of how we can get inductive knowledge. And finally, it shines a new light on _significance testing_, one of the most important statistical practices in science.

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.