- Tytuł:
-
Giuseppe Veronesego konstruktywizm arytmetyczny a poznawalność nieskończoności. Studium wybranych wątków filozofii matematyki we wprowadzeniu do Grundzüge der Geometrie von mehreren Dimensionen
Giuseppe Veronese’s Arithmetical Constructivism and the Cognizability of Infinity: A Study of Selected Aspects of the Philosophy of Mathematics in the Introduction to Grundzüge der Geometrie von mehreren Dimensionen - Autorzy:
- Dadaczyński, Jerzy
- Powiązania:
- https://bibliotekanauki.pl/articles/38429160.pdf
- Data publikacji:
- 2022
- Wydawca:
- Uniwersytet Warszawski. Wydział Filozofii
- Tematy:
-
Giuseppe Veronese
constructivism
natural numbers
infinity
infinite sequences
cognizability - Opis:
- 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.
- Źródło:
-
Filozofia Nauki; 2022, 30, 3; 33-50
1230-6894
2657-5868 - Pojawia się w:
- Filozofia Nauki
- Dostawca treści:
- Biblioteka Nauki
Artykuł