Article ID: CBB001210996

Das Problem der apagogischen Beweise in Bolzanos Beyträgen und seiner Wissenschaftslehre (2012)


This paper analyzes and evaluates Bolzano's remarks on the apagogic method of proof with reference to his juvenile booklet `Contributions to a better founded presentation of mathematics' of 1810 and to his `Theory of science' (1837). I shall try to defend the following contentions: (1) Bolzanos' vain attempt to transform all indirect proofs into direct proofs becomes comprehensible as soon as one recognizes the following facts: (1.1) his attitude towards indirect proofs with an affirmative conclusion differs from his stance to indirect proofs with a negative conclusion; (1.2) by Bolzano's lights arguments via consequentia mirabilis only seem to be indirect. (2) Bolzano does not deny that indirect proofs can be perfect certifications (Gewissmachungen) of their conclusion; what he denies is rather that they can provide grounds for their conclusions. (2.1) They cannot do the latter, since they start from false premises and (2.2) since they make an unnecessary detour. (3) The far-reaching agreement between his early and late assessment of apagogical proofs (in the Beyträge of 1810 and the Wissenschaftslehre of 1837) is partly due to the fact that he develops his own position always against the background of Wolff's and Lambert's views.

Citation URI

Similar Citations

Article Centrone, Stefania; (2012)
Strenge Beweise und das Verbot der metábasis eis állo génos (/isis/citation/CBB001210991/)

Article Eder, Günther; (2013)
Remarks on Independence Proofs and Indirect Reference (/isis/citation/CBB001212142/)

Article Peter Simons; (2015)
Bolzano's Monadology (/isis/citation/CBB137993666/)

Article Tolleya, Clinton; (2012)
Bolzano and Kant on the Nature of Logic (/isis/citation/CBB001210999/)

Article Weltya, Ivan; (2011)
Frege on Indirect Proof (/isis/citation/CBB001210988/)

Article Rusnock, Paul; Burke, Mark; (2010)
Etchemendy and Bolzano on Logical Consequence (/isis/citation/CBB001210969/)

Chapter Edward C. Halper; (2017)
Aristotle’s Scientific Method (/isis/citation/CBB181543613/)

Chapter Marco Zingano; (2017)
Ways of Proving in Aristotle (/isis/citation/CBB121521437/)

Book Yrjönsuuri, Mikko; (2001)
Medieval Formal Logic: Obligations, Insolubles and Consequences (/isis/citation/CBB000102010/)

Chapter Aberdein, Andrew; Read, Stephen; (2009)
The Philosophy of Alternative Logics (/isis/citation/CBB001210355/)

Article Lorenat, Jemma; (2012)
Not Set in Stone: Nineteenth-Century Geometrical Constructions and the Malfatti Problem (/isis/citation/CBB001212294/)

Article Abeles, Francine F.; (2012)
Toward A Visual Proof System: Lewis Carroll's Method of Trees (/isis/citation/CBB001214122/)

Article Centrone, Stefania; (2010)
Functions in Frege, Bolzano and Husserl (/isis/citation/CBB001210980/)

Article Rusnock, Paul; (2013)
On Bolzano's Concept of a Sum (/isis/citation/CBB001212145/)

Chapter Sundholm, Göran; (2009)
A Century of Judgment and Inference, 1837--1936: Some Strands in the Development of Logic (/isis/citation/CBB001210348/)

Article Novy, Luboš; (2008)
Les relations entre la logique et la mathématique dans l'oeuvre de Bernard Bolzano (/isis/citation/CBB001021148/)

Book Parrini, Paolo; Salmon, Wesley C.; Salmon, Merrilee H.; (2003)
Logical Empiricism: Historical and Contemporary Perspectives (/isis/citation/CBB001213664/)

Article Rajan Gurukkal; (2016)
An Introductory Outline of Knowledge Production in Pre-Colonial India (/isis/citation/CBB095195617/)

Article S. N. Venugopalan Nair; Darshan Shankar; (2016)
Knowledge Generation in Āyurveda: Methodological Aspects (/isis/citation/CBB204824703/)

Authors & Contributors
Yrjönsuuri, Mikko
Reada, Stephen
Rusnock, Paul
Centrone, Stefania
Olsson, Erik J.
Pironet, Fabienne
History and Philosophy of Logic
Indian Journal of History of Science
Dianoia: Annali di storia della filosofia
Archives Internationales d'Histoire des Sciences
British Society for the History of Mathematics Bulletin
Logica Universalis
Kluwer Academic
University of Pittsburgh Press
Bolzano, Bernard
Frege, Gottlob
Burley, Walter
Time Periods
19th century
20th century, early
18th century

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment