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Giuseppe Veronesego podstawy matematyki

100%
Dadaczyński J.
Zagadnienia Filozoficzne w Nauce
|
2013
|
issue 53
53-92
PL
The aim of this paper is to analyze Veronese’s philosophical principles of mathematics. He tried to begin the construction of mathematics (geometry) with the concept of the Thinking Subject and the phenomenon of thinking, which is discussed in detail. It is very likely that this idea had an impact on Hilbert’s concept of the Mathematical Subject. Some similarities between Veronese’s view and the intuitionistic thinkers are also shown.
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Giuseppe Veronesego konstruktywizm arytmetyczny a poznawalność nieskończoności. Studium wybranych wątków filozofii matematyki we wprowadzeniu do Grundzüge der Geometrie von mehreren Dimensionen

86%
Dadaczyński J.
Filozofia Nauki
|
2022
|
vol. 30
|
issue 3
33-50
EN
In the first part of the article, Giuseppe Veronese’s concept of arithmetical constructivism is reconstructed from his dispersed remarks. It is pointed out that although for Veronese time is a necessary condition for the construction of natural numbers by an individual subject and the subject cognizes time in an a priori way, it is not a (proto-)intuition of the subject. This is a fundamental difference between the concept proposed by Veronese and the constructivism of Kant and Brouwer. Veronese’s justification of the subject’s ability to cognize infinity, represented in his text by infinite sequences, is analyzed in the second part of the paper. The only condition for the cognition of the infinite sequence is to have a rule according to which its successive terms “follow one another.” The price of the ability to cognize the infinitive “whole” (sequence) may be the uncognizability of certain “parts” (terms of sequence). Infinite sequences, cognizable according to Veronese, are allowed as objects of mathematical research, although they do not meet the condition of constructability.
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