Metoda matematyki według B. Bolzano
- Autorzy: Jerzy Dadaczyński
- Czasopismo: Zagadnienia Filozoficzne w Nauce, 38 2006, s. 76
Abstrakt:
The matter under discussion is the methodology of mathematics presented by Bernard Bolzano (17821848) in his early pamphlet Beytraege zu einer begruendeteren Darstel lung 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 ob jective 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.
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 ob jective 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.