Filozofia i logika intuicjonizmu
At the end of the 19th century in the fundamentals of mathematics appeared a crisis. It was caused by the paradoxes found in Cantor’s set theory. One of the ideas a resolving the crisis was intuitionism – one of the constructivist trends in the philosophy of mathematics. Its creator was Brouwer, the...
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| Format: | Article |
| Language: | English |
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Pontifical University of John Paul II in Krakow, Faculty of Philosophy
2015-09-01
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| Series: | Semina Scientiarum |
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| Online Access: | http://czasopisma.upjp2.edu.pl/seminascientiarum/article/view/1077/1457 |
| _version_ | 1811305621123760128 |
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| author | Marlena Fila |
| author_facet | Marlena Fila |
| author_sort | Marlena Fila |
| collection | DOAJ |
| description | At the end of the 19th century in the fundamentals of mathematics appeared a crisis. It was caused by the paradoxes found in Cantor’s set theory. One of the ideas a resolving the crisis was intuitionism – one of the constructivist trends in the philosophy of mathematics. Its creator was Brouwer, the main representative was Heyting.
In this paper described will be attempt to construct a suitable logic for philosophical intuitionism theses. In second paragraph Heyting system will be present – its axioms and matrices truth-. Later Gödel theorem about the inadequacy of finite dimensional matrices for this system will be explained. At the end this paper an infinite sequence of matrices adequate for Heyting axioms proposed by Jaśkowski will be described. |
| first_indexed | 2024-04-13T08:29:42Z |
| format | Article |
| id | doaj.art-0c78cc720e6947da8bbffb1e73e2fad6 |
| institution | Directory Open Access Journal |
| issn | 1644-3365 2391-6850 |
| language | English |
| last_indexed | 2024-04-13T08:29:42Z |
| publishDate | 2015-09-01 |
| publisher | Pontifical University of John Paul II in Krakow, Faculty of Philosophy |
| record_format | Article |
| series | Semina Scientiarum |
| spelling | doaj.art-0c78cc720e6947da8bbffb1e73e2fad62022-12-22T02:54:17ZengPontifical University of John Paul II in Krakow, Faculty of PhilosophySemina Scientiarum1644-33652391-68502015-09-01143548http://dx.doi.org/10.15633/ss.1077Filozofia i logika intuicjonizmuMarlena Fila0Pedagogical University, KrakowAt the end of the 19th century in the fundamentals of mathematics appeared a crisis. It was caused by the paradoxes found in Cantor’s set theory. One of the ideas a resolving the crisis was intuitionism – one of the constructivist trends in the philosophy of mathematics. Its creator was Brouwer, the main representative was Heyting. In this paper described will be attempt to construct a suitable logic for philosophical intuitionism theses. In second paragraph Heyting system will be present – its axioms and matrices truth-. Later Gödel theorem about the inadequacy of finite dimensional matrices for this system will be explained. At the end this paper an infinite sequence of matrices adequate for Heyting axioms proposed by Jaśkowski will be described.http://czasopisma.upjp2.edu.pl/seminascientiarum/article/view/1077/1457intuitionism; axioms; matrices truth-; Heyting system; Gödel theorem about the inadequacy of finite dimensional matrices for Heyting system; infinite sequence of matrices |
| spellingShingle | Marlena Fila Filozofia i logika intuicjonizmu Semina Scientiarum intuitionism; axioms; matrices truth-; Heyting system; Gödel theorem about the inadequacy of finite dimensional matrices for Heyting system; infinite sequence of matrices |
| title | Filozofia i logika intuicjonizmu |
| title_full | Filozofia i logika intuicjonizmu |
| title_fullStr | Filozofia i logika intuicjonizmu |
| title_full_unstemmed | Filozofia i logika intuicjonizmu |
| title_short | Filozofia i logika intuicjonizmu |
| title_sort | filozofia i logika intuicjonizmu |
| topic | intuitionism; axioms; matrices truth-; Heyting system; Gödel theorem about the inadequacy of finite dimensional matrices for Heyting system; infinite sequence of matrices |
| url | http://czasopisma.upjp2.edu.pl/seminascientiarum/article/view/1077/1457 |
| work_keys_str_mv | AT marlenafila filozofiailogikaintuicjonizmu |