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2006 | 38 | 76-113
Article title

BERNARD BOLZANO'S CONCEPTION OF THE MATHEMATICAL METHOD

Authors
Title variants
Languages of publication
PL
Abstracts
EN
The matter under discussion is the methodology of mathematics presented by Bernard Bolzano (1782-1848) in his early pamphlet 'Beitraege zu einer begruendeteren Darstellung der Mathematik' (Prague 1810). Bolzano built, with success, the classical axiomatic­deductive method of nonspacial and atemporal concepts (Begriffe). He abandoned the traditional custom of formulating primitive concepts of deductive theories. Bolzano opposed the traditional conviction that the axioms of mathematical theories should be clear and distinct sentences. He divided the domain of nonspacial and atemporal sentences into the subdomains of objectively provable and objectively nonprovable sentences. In his view, the axioms of mathematical (deductive) theories are only the objectively nonprovable sentences, and each of the objective nonprovable sentences is an axiom of a certain deductive theory. He postulated, at the time when only the (Euclidean) geometry was axiomatized, the axiomatization of all mathematical theories.
Contributors
  • J. Dadaczynski, ul. Lagiewnicka 17, 41-500 Chorzów, Poland
References
Document Type
Publication order reference
Identifiers
CEJSH db identifier
07PLAAAA02735587
YADDA identifier
bwmeta1.element.3664c6b4-6ccd-3774-9ce0-853f36832a7b
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