This paper describes a scenario in which a person in his afterlife will with probability 1 spend twice as many days in Heaven as in Hell, but, even though Heaven is as good as Hell is bad, his expected utility for any given day in that afterlife is negative.

An analysis of Moore’s paradox is given in doxastic logic. Logics arising from formalizations of various introspective principles are compared; one logic, K5c, emerges as privileged in the sense that it is the weakest to avoid Moorean belief. Moreover it has other attractive properties, one of which is that it can be justified solely in terms of avoiding false belief. Introspection is therefore revealed as less relevant to the Moorean problem than first appears.

I extend theorems due to Roy Cook (2009) on third- and higher-order versions of abstraction principles and discuss the philosophical importance of results of this type. Cook demonstrated that the satisfiability of certain higher-order analogues of Hume’s Principle is independent of ZFC. I show that similar analogues of Boolos’s NEWV and Cook’s own ordinal abstraction principle SOAP are not satisfiable at all. I argue, however, that these results do not tell significantly against the second-order versions of these principles.

Recently Feferman (Rev. Symb. Logic 6: 6–15, 2013) has outlined a program for the development of a foundation for naive category theory. While Ernst (ibid. 8: 306–327, 2015) has shown that the resulting axiomatic system is still inconsistent, the purpose of this note is to show that nevertheless some foundation has to be developed before naive category theory can replace axiomatic set theory as a foundational theory for mathematics. It is argued that in naive category theory currently a ‘cookbook recipe’ is used for constructing categories, and it is explicitly shown with a formalized argument that this “foundationless” naive category theory therefore contains a paradox similar to the Russell paradox of naive set theory.

Soames’s cognitive propositions are strings of acts to be performed by an agent, such as predicating a property of an individual. King takes these structured propositions to task for proliferating too easily. King’s objection is based on an example that purports to show that three of Soames’s propositions are really just one proposition. I translate the informally stated propositions King attributes to Soames into the intensional λ-calculus. It turns out that they are all β-equivalent to the proposition King claims Soames’s three propositions are identical to. I argue on philosophical grounds against identifying β-equivalent propositions. The reason is that β-conversion obliterates too many of the procedural distinctions that are central to an act-based theory such as Soames’s and which are worth preserving. In fact, β-expansion allows the addition of a fifth proposition that highlights additional procedural distinctions and propositional structure. The welcome conclusion is that we have five procedurally distinct, if equivalent, propositions.

Roger White objects to interval-valued credence theories because they produce a counterintuitive “dilation” effect in a story he calls the Coin Game. We respond that results in the Coin Game were bound to be counterintuitive anyway, because the story involves an agent who learns a biconditional. Biconditional updates produce surprising results whether the credences involved are ranged or precise, so White’s story is no counterexample to ranged credence theories.

Neo-Fregeans have been troubled by the Nuisance Principle (NP), an abstraction principle that is consistent but not jointly (second-order) satisfiable with the favored abstraction principle HP. We show that logically this situation persists if one looks at joint (second-order) consistency rather than satisfiability: under a modest assumption about infinite concepts, NP is also inconsistent with HP.

In a recent paper (2013), Jc Beall has employed what he calls ‘shriek rules’ in a putative solution to the long-standing ‘just false’ problem for glut theory.The purpose of this paper is twofold: firstly, I distinguish the ‘just false’ problem from another problem, with which it is often conflated, which I will call the ‘exclusion problem’. Secondly, I argue that shriek rules do not help glut theorists with either problem.