Matematyka nie opisuje świata, lecz wychodzi mu naprzeciw

In everyday experience mathematics rarely appears to us as a whole, and certainly never as a system in the sense of David Hilbert’s considerations from early 20th Century. Mathematical disciplines seem to be independent and autonomous. We do not see that specific deduction goes beyond particular con...

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Bibliographic Details
Published inZagadnienia Filozoficzne w Nauce (Online) Vol. 58; no. 58; pp. 7 - 43
Main Author Mioduszewski, Jerzy
Format Journal Article
LanguagePolish
German
Published Copernicus Center Press 01.06.2015
Subjects
arithmetic
calculus
geometry
incommensurability
Logic
number sense
philosophy of mathematics
Philosophy of Science
Richard Dedekind
transfinite numbers
arithmetic, geometry
transfinite numbers
Richard Dedekind
number sense
incommensurability
philosophy of mathematics
calculus
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Summary:In everyday experience mathematics rarely appears to us as a whole, and certainly never as a system in the sense of David Hilbert’s considerations from early 20th Century. Mathematical disciplines seem to be independent and autonomous. We do not see that specific deduction goes beyond particular convention applicable in given discipline. In the late 19th Century this view was shared by Felix Klein and Richard Dedekind. The latter’s work “What are numbers and what should they be?” (Was Was sind und was sollen die Zahlen?) was the inspiration for writing this article. This essay is an attempt to see mathematics not as a building, but as a living organism seeking its explanation.
ISSN:0867-8286
2451-0602