Metoda matematyki według B. Bolzano

• Authors: Jerzy Dadaczyński

Title variants

EN

Bernard Bolzano's conception of the mathematical method

• Languages of publication: PL

Abstracts

PL

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 axiomatic-deductive 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.

Keywords

PL

axiomatic method; Bernard Bolzano; methodology of mathematics; philosophy of mathematics

• Publisher: Copernicus Center Press
• Journal: Zagadnienia Filozoficzne w Nauce
• Year: 2006
• Issue: 38
• Pages: 76-113

Dates

published

2006-06-07

Contributors

author

Jerzy Dadaczyński