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Metoda matematyki według B. Bolzano

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Dadaczyński J.
Zagadnienia Filozoficzne w Nauce
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2006
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issue 38
76-113
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.
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Od wolności do swobody wyboru – formalizacja idei Sena w modelu Arrowa-Debreu

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Mrówka J., Malawski A.
Prakseologia
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2014
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issue 156
157-175
EN
The aim of the paper is to reconstruct the Senian idea of development as a growing range of freedoms in the research program of modelling Schumpeterian evolutionary economics in the dynamical version of the Arrow-Debreu general equilibrium theory. In the context of the Schumpeterian circular flow freedom of choice of consumers and producers is studied in both qualitative and quantitative setting. The static results presented in the form of mathematical theorems are generalized by use of the theory of quasi-semi-dynamical systems, where cumulative extension of economic systems under consideration is preserved over time and models a growing range of freedoms as well as their quality.
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