The topic of this article is the closure of a priori knowability under a priori knowable material implication: if a material conditional is a priori knowable and if the antecedent is a priori knowable, then the consequent is a priori knowable as well. This principle is arguably correct under certain conditions, but there is at least one counterexample when completely unrestricted. To deal with this, Anderson proposes to restrict the closure principle to necessary truths and Horsten suggests to restrict it (...) to formulas that belong to less expressive languages. In this article it is argued that Horsten’s restriction strategy fails, because one can deduce that knowable ignorance entails necessary ignorance from the closure principle and some modest background assumptions, even if the expressive resources do not go beyond those needed to formulate the closure principle itself. It is also argued that it is hard to find a justification for Anderson’s restricted closure principle, because one cannot deduce it even if one assumes very strong modal and epistemic background principles. In addition, there is an independently plausible alternative closure principle that avoids all the problems without the need for restriction. (shrink)

Carnap's theory of descriptions was restricted in two ways. First, the descriptive conditions had to be non-modal. Second, only primitive predicates or the identity predicate could be used to predicate something of the descriptum . The motivating reasons for these two restrictions that can be found in the literature will be critically discussed. Both restrictions can be relaxed, but Carnap's theory can still be blamed for not dealing adequately with improper descriptions.

In a recent paper Horsten embarked on a journey along the limits of the domain of the unknowable. Rather than knowability simpliciter, he considered a priori knowability, and by the latter he meant absolute provability, i.e. provability that is not relativized to a formal system. He presented an argument for the conclusion that it is not absolutely provable that there is a natural number of which it is true but absolutely unprovable that it has a certain property. The argument depends (...) on a description principle. I will argue that the latter principle implies the knowability of all arithmetical truths. Therefore, Horsten's argument is either sound but its conclusion is trivial, or his argument is unsound. (shrink)