The aim of this paper is threefold. Firstly, sections 1 and 2 introduce the novel concept logical akrasia by analogy to epistemic akrasia. If successful, the initial sections will draw attention to an interesting akratic phenomenon which has not received much attention in the literature on akrasia (although it has been discussed by logicians in different terms). Secondly, sections 3 and 4 present a dilemma related to logical akrasia. From a case involving the consistency of Peano Arithmetic and Gödel's Second Incompleteness Theorem, it's shown that either we must be agnostic about the consistency of Peano Arithmetic or akratic in our arithmetical theorizing. If successful, these sections will underscore the pertinence and persistence of akrasia in arithmetic (by appeal to Gödel's seminal work). Thirdly, section 5 concludes by suggesting a way of translating the Dilemma of Arithmetical Akrasia into a case of regular epistemic akrasia; and further how one might try to escape the dilemma when it's framed this way.

Normativism is the (controversial) view that epistemic reasons for belief are really, genuinely normative. Normativists might wonder – and anti-normativists might press the question – why, or in virtue of what, are epistemic reasons normative? Borrowing Korsgaard's metaphor, what's the “source” of their normativity? Here I argue that this question is both highly interesting and subtly distinct from other common questions in the literature. I also propose an initial taxonomy of stance-dependent and stance-independent answers, and I advocate a novel, hybrid type of view as ultimately most promising for (mostly) vindicating normativism.

Can you rationally double-check what you already know? In this paper, I argue that you can. Agents can know that something is true and rationally double-check it at the very same time. I defend my position by considering a wide variety of cases where agents double-check their beliefs to gain epistemic improvements beyond knowledge. These include certainty, epistemic resilience, and sensitivity to error. Although this phenomenon is widespread, my proposal faces two types of challenges. First, some have defended ignorance norms, on which agents are only allowed to inquire about things they don't already know. Second – motivated by strong conceptions of belief or pragmatic encroachment – some have argued that double-checking destroys knowledge. I argue that these competing views fail to capture both the epistemic value of double-checking and the many reasons why agents might double-check. Moreover, they rely on overly strong assumptions about what inquiry, knowledge, or belief requires. Finally, I marshal linguistic data in favor of the compatibility of knowledge and double-checking.

The debate between Uniqueness and Permissivism concerns whether a body of evidence sometimes allows multiple doxastic attitudes towards a proposition. An important motivation for Uniqueness is the so-called ‘arbitrariness argument,’ which says that Permissivism leads to some unacceptable arbitrariness with regard to one's beliefs. An influential response to the argument says that the arbitrariness in beliefs can be avoided by invoking epistemic standards. In this paper, I argue that such a response to the arbitrariness argument is unsuccessful. Then I defend a new response: contrary to common conception, the arbitrariness resulted by Permissivism is acceptable. The basic idea is that the arbitrariness resulted by Permissivism is analogous to the arbitrariness in permissive actions and the latter arbitrariness is intuitively acceptable. I answer three possible objections against this analogy, which are all motivated by the thought that beliefs aim at the truth. In addressing the last objection, I draw inspiration from the recent debate on transformative experience.