Abstract

In the second volume of his Wissenschaftslehre from 1837, the Bohemian philosopher, theologian, and mathematician Bernard Bolzano introduced his concept of consequence, named derivability, together with a variety of theorems and further considerations. Derivability is an implication relation between sentences in themselves, which are not meant to be linguistic symbols but the contents of declarative sentences as well as of certain mental episodes. When Schmidt utters the sentence ‘Schnee ist weiß’, and Jones judges that snow is white, the sentence in itself expressed by Schmidt is the same as the one to which Jones agrees in thought. This sentence in itself is an abstract entity: in some sense, it exists; but it is unreal insofar as it lacks a position in space and time, does not stand in causal relationships, and is independent of the existence of thinking beings and languages.