Strenge Beweise und das Verbot der metabasis eis allo genos: Eine Untersuchung zu Bernard Bolzanos Beytragen zu einer begrundeteren Darstellung der Mathematik

摘要

In his booklet ‘Contributions to a better founded presentation of mathematics’ of 1810 Bernard Bolzano made his first serious attempt to explain the notion of a rigorous proof. Although the system of logic he employed at that stage is in various respects far below the level of the achievements in his laterWissenschaftslehre, there is a striking continuity between his earlier and later work as regards the methodological constraints on rigorous proofs. This paper tries to give a perspicuous and critical account of the fragmentary logic of Beytrage, and it shows that there is a tension between that logic and Bolzano’s methodological ban on ‘kind crossing’.