Das Problem der apagogischen Beweise in Bolzanos Beyträgen und seiner Wissenschaftslehre

History and Philosophy of Logic 33 (2):127 - 157 (2011)
Abstract
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
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References found in this work BETA
Jan Berg (1962). Bolzano's Logic. Stockholm, Almqvist & Wiksell.
Bernard Bolzano (1969). Bernard Bolzano-Gesamtausgabe. Stuttgart-Bad Cannstatt, Frommann Holzboog.
Ettore Casari (1987). Matematica E Verità. Rivista di Filosofia 78 (3):329-350.
Stefania Centrone (2011). Begründungen bei Bolzano und beim frühen Husserl. Zeitschrift für Philosophische Forschung 65 (1):5-27.

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Paola Cantù, Bolzano Versus Kant: Mathematics as a Scientia Universalis. Philosophical Papers Dedicated to Kevin Mulligan.
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