Gramatyka nieskończoności. Ludwiga Wittgensteina krytyka teorii mnogości
The paper discusses a relatively underexamined element of Wittgenstein’s philosophy of mathematics associated with his critique of set theory. I outline Wittgenstein’s objections to the theories of Dedekind and Cantor, including the confounding of extension and intension, the faulty definition of th...
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| Format: | Article |
| Language: | deu |
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Wydawnictwo Naukowe Uniwersytetu Szczecińskiego
2023-01-01
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| Series: | Analiza i Egzystencja |
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| Online Access: | https://wnus.usz.edu.pl/aie/pl/issue/1246/article/20012/ |
| _version_ | 1827793285601558528 |
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| author | Piotr Dehnel |
| author_facet | Piotr Dehnel |
| author_sort | Piotr Dehnel |
| collection | DOAJ |
| description | The paper discusses a relatively underexamined element of Wittgenstein’s philosophy of mathematics associated with his critique of set theory. I outline Wittgenstein’s objections to the theories of Dedekind and Cantor, including the confounding of extension and intension, the faulty definition of the infinite set as infinite extension and the critique of Cantor’s diagonal proof. One of Wittgenstein’s major objections to set theory was that the concept of the size of infinite sets, which Cantor expressed by means of symbols אₒ and c, had no application, i.e. that there was no grammatical technique that could show how such expressions were to be used. Notions of set theory are, so to speak, exterior – they find themselves outdoors, outside of what we usually do. They form a discourse that takes us beyond the horizon of everydayness and commonality. They are like an engine idling of the language of mathematics. |
| first_indexed | 2024-03-11T18:16:22Z |
| format | Article |
| id | doaj.art-97228ec38d6444e7b0c2a75ae6a6a68b |
| institution | Directory Open Access Journal |
| issn | 1734-9923 |
| language | deu |
| last_indexed | 2024-03-11T18:16:22Z |
| publishDate | 2023-01-01 |
| publisher | Wydawnictwo Naukowe Uniwersytetu Szczecińskiego |
| record_format | Article |
| series | Analiza i Egzystencja |
| spelling | doaj.art-97228ec38d6444e7b0c2a75ae6a6a68b2023-10-16T07:03:26ZdeuWydawnictwo Naukowe Uniwersytetu SzczecińskiegoAnaliza i Egzystencja1734-99232023-01-016310.18276/aie.2023.63-03Gramatyka nieskończoności. Ludwiga Wittgensteina krytyka teorii mnogościPiotr Dehnel0Pomorska Szkoła Wyższa w Starogardzie GdańskimThe paper discusses a relatively underexamined element of Wittgenstein’s philosophy of mathematics associated with his critique of set theory. I outline Wittgenstein’s objections to the theories of Dedekind and Cantor, including the confounding of extension and intension, the faulty definition of the infinite set as infinite extension and the critique of Cantor’s diagonal proof. One of Wittgenstein’s major objections to set theory was that the concept of the size of infinite sets, which Cantor expressed by means of symbols אₒ and c, had no application, i.e. that there was no grammatical technique that could show how such expressions were to be used. Notions of set theory are, so to speak, exterior – they find themselves outdoors, outside of what we usually do. They form a discourse that takes us beyond the horizon of everydayness and commonality. They are like an engine idling of the language of mathematics.https://wnus.usz.edu.pl/aie/pl/issue/1246/article/20012/CantorDedekindlanguageset theoryinfinitydiagonal proof. |
| spellingShingle | Piotr Dehnel Gramatyka nieskończoności. Ludwiga Wittgensteina krytyka teorii mnogości Analiza i Egzystencja Cantor Dedekind language set theory infinity diagonal proof. |
| title | Gramatyka nieskończoności. Ludwiga Wittgensteina krytyka teorii mnogości |
| title_full | Gramatyka nieskończoności. Ludwiga Wittgensteina krytyka teorii mnogości |
| title_fullStr | Gramatyka nieskończoności. Ludwiga Wittgensteina krytyka teorii mnogości |
| title_full_unstemmed | Gramatyka nieskończoności. Ludwiga Wittgensteina krytyka teorii mnogości |
| title_short | Gramatyka nieskończoności. Ludwiga Wittgensteina krytyka teorii mnogości |
| title_sort | gramatyka nieskonczonosci ludwiga wittgensteina krytyka teorii mnogosci |
| topic | Cantor Dedekind language set theory infinity diagonal proof. |
| url | https://wnus.usz.edu.pl/aie/pl/issue/1246/article/20012/ |
| work_keys_str_mv | AT piotrdehnel gramatykanieskonczonosciludwigawittgensteinakrytykateoriimnogosci |