Sebastian Liu

According to strong verificationism, all truths are known. According to weak verificationism, all truths are knowable. That strong verificationism entails weak verificationism is unsurprising – if all truths are known, then all truths are knowable. That weak verificationism entails strong verificationism, however, is surprising – how could it be that if all truths are knowable, then all truths are in fact known? The collapse of weak verificationism into strong verificationism is at the core of Fitch’s Paradox. Typically, this paradox is taken to suggest that all forms of verificationism must be rejected. But abstractly, the lesson seems to be more general: Given certain properties of a modal operator, the modally qualified weakened form of a principle is not always more defensible than its corresponding strengthened form. The aim of this paper is to apply this lesson and show that Fitch’s Paradox bears on a range of epistemological principles, with a particular focus on closure.

According to the principle of indifference, when a set of possibilities is evidentially symmetric for you – when your evidence no more supports any one of the possibilities over any other – you're required to distribute your credences uniformly among them. Despite its intuitive appeal, the principle of indifference is often thought to be unsustainable due to the problem of multiple partitions: Depending on how a set of possibilities is divided, it seems that sometimes, applying indifference reasoning can require you to assign incompatible credences to equivalent possibilities. This paper defends the principle of indifference from the problem of multiple partitions by offering two guides for how to respond. The first is for permissivists about rationality, and is modeled on permissivists' arguments for the claim that a body of evidence sometimes does not uniquely determine a fully rational credence function. The second is for impermissivists about rationality, and is modeled on impermissivists' arguments for the claim that a body of evidence does always uniquely determine a fully rational credence function. What appears to be a decisive objection against the principle of indifference is in fact an instance of a general challenge taking different forms familiar to both permissivists and impermissivists.

The KK principle states that knowing entails knowing that one knows. This historically popular principle has fallen out of favour among many contemporary philosophers in light of putative counterexamples. Recently, some have defended more palatable versions of KK by weakening the principle. These revisions remain faithful to their predecessor in spirit while escaping crucial objections. This paper examines the prospects of such a strategy. It is argued that revisions of the original principle can be captured by a generalized knowledge iteration principle, Weak-KK, which states that knowing entails the possibility of knowing that one knows. But Weak-KK is vulnerable to an unknowability result and therefore must be rejected. The arguments here suggest that retreating to weaker iteration principles is not an option for the KK enthusiast.