 Bolzano’s logical World 3 includes in addition to ideas and propositions also what we will call ‘arguments’. Bolzano is dealing with arguments at lengths in his Theory of Science (cf., e.g., WL II, 113 ff., 391 ff.), but he does not introduce a name for them. Following the general line of his terminology, he could have called them ‘Schlüsse an sich’ (‘derivations in themselves’ or ‘inferences in themselves’), but he did not; he rather used this term for a certain kind of propositions, namely for propositions stating that a proposition follows (or — in his words — is ableitbar, i.e., derivable) from a set of propositions (WL I, 213, WL II, 200; for another usage of the term ‘Schluß’ by Bolzano cf. section 4.4). A Bolzanian argument consists of two sets of propositions: the set of its premises and the set of its conclusions. In order to simplify matters, we will assume here that an argument has always a single proposition (rather than a whole set of propositions) as its conclusion, and we will identify an argument with an ordered pair \(\langle \sigma , s\rangle\) consisting of a set \(\sigma\) of propositions (i.e., the set of premises) and a single proposition \(s\) (i.e., its conclusion).