 Due to this definition of truth and due to Bolzano’s doctrine that every proposition has the form \([A\) has \(b]\), every proposition has existential import for Bolzano. (‘Existential’ must here be taken in the sense of Bolzano’s ‘there is’. It must be kept in mind here that Bolzano’s interpretation transfers many propositions to a meta-level and that in such a case the existential import concerns \([A]\) rather than \(A\) itself; the existence of \([A]\), however, is guaranteed even if \([A]\) is empty and \(A\) itself does not exist.) This peculiar kind of an existential presupposition of Bolzano’s logic makes his theory of syllogisms (which he himself saw as a mere section of his whole logic) an intermediate system between Aristotle and Venn: Whereas Aristotle’s theory of categorical syllogisms does not allow empty terms at all, Bolzano’s logic does so, but they cannot be the subject ideas of true propositions in Bolzano’s logic. As a consequence, the so-called conclusio ad subalternatam is logically valid also for Bolzano, i.e., [Some \(A\) have \(b]\) follows logically from [All \(A\) have \(b]\) (WL II, 114, 399 ff.), but [All \(A\) are \(A]\) or — in Bolzano’s notation — [All \(A\) have \(a]\) is not logically true for him; furthermore [All \(A\) have non-\(b]\) is not convertible, i.e., [All \(B\) have non-\(a]\) does not logically follow from [All \(A\) have non-\(b]\) (WL II, 401 f., 526). Therefore exactly two of the 24 valid Aristotelian syllogisms (namely the modi CAMENES — or CALENTES in Bolzano’s terminology — and CAMENOP of form IV) are invalid in Bolzano’s logic as he himself proved by means of counter-examples (WL II, 415, 558), whereas all other Aristotelian modi (including the weakened ones) are logically valid also in Bolzano’s logic.