Contemporary historians of logic tend to credit Bernard Bolzano with the invention oi the semantic notion of consequence, a full c~ntury before Tarski. ~evertheless, Bolzano's work played no significant rSle in the genesis of modern logical semantics. The purpose of this paper is to point out three highly original, an& still quite relevant themes in Bolzano's work, being a systematic study of possible types of inference, of consistency, as well as their recta-theory. There are certain analogies with Tarski's concerns here, although the main thrust seems to be different, both philosophically and technically. Thus, if only obliquely, we also provide some additional historical perspective on Tarski's achievement. Bernard Bolzano's contributions to logic, largely unnoticed in the 19th century, have been receiving ever more attention from modern logicians (of. [:tO], [~], [6]): As a result, it has already become something of a commonplace to credit Bolzano with the discovery of the notion of logical consequence in the semantic sense. ~ow, this particular attribution, whether justified or not, would nt best establish a historical link between modern logical concerns and Bolzano's work. The purpose of the present note, however, is to bring out three important aspects of that work that are still of contemporary systematic interest. ~o detailed textual study of Bolzano is needed to substantiate our suggestions. We sh~ll refer to well-documented 'public' aspects of the 'Wissensehaitslehre' t [5]), pointing out their more general logical significance.
One w~y or another, the following three themes involve various notions of semantic consequence. At several places, we sh~ll make comparisons with modern orthodoxy on this score, largely due to Tarski. Thus, this paper also contributes, ii only obliquely, to a better understanding of T~rski's ~chievement.