Jan Heylen

Modal-Epistemic Arithmetic and the problem of quantifying in

The subject of this article is Modal-Epistemic Arithmetic (MEA), a theory introduced by Horsten to interpret Epistemic Arithmetic (EA), which in turn was introduced by Shapiro to interpret Heyting Arithmetic. I will show how to interpret MEA in EA such that one can prove that the interpretation of EA is MEA is faithful. Moreover, I will show that one can get rid of a particular Platonist assumption. Then I will discuss models for MEA in light of the problems of logical omniscience and logical competence. Awareness models, impossible worlds models and syntactical models have been introduced to deal with the first problem. Certain conditions on the accessibility relations are needed to deal with the second problem. I go on to argue that those models are subject to the problem of quantifying in, for which I will provide a solution.

Carnap’s Theory of Descriptions and its Problems

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.

The epistemic significance of numerals

The central topic of this article is (the possibility of) de re knowledge about natural numbers and its relation with names for numbers. It is held by several prominent philosophers that (Peano) numerals are eligible for existential quantification in epistemic contexts (‘canonical’), whereas other names for natural numbers are not. In other words, (Peano) numerals are intimately linked with de re knowledge about natural numbers, whereas the other names for natural numbers are not. In this article I am looking for an explanation of this phenomenon. It is argued that the standard induction scheme plays a key role.