The Notion of Explanation in Gödel’s Philosophy of Mathematics
DOI: http://doi.org/10.26333/stsen.xxx.05 The article deals with the question of in which sense the notion of explanation (which is rather characteristic of empirical sciences) can be applied to Kurt Gödel’s philosophyof mathematics. Gödel, as a mathematical realist, claims that in mathematics we...
| Format: | Article |
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| Language: | English |
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Polskie Towarzystwo Semiotyczne / The Polish Semiotic Society
2020-05-01
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| Series: | Studia Semiotyczne |
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| Online Access: | http://studiasemiotyczne.pts.edu.pl/index.php/Studiasemiotyczne/article/view/150 |
| _version_ | 1818880208030138368 |
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| collection | DOAJ |
| description | DOI: http://doi.org/10.26333/stsen.xxx.05
The article deals with the question of in which sense the notion of explanation (which is rather characteristic of empirical sciences) can be applied to Kurt Gödel’s philosophyof mathematics. Gödel, as a mathematical realist, claims that in mathematics we are dealing with facts that have an objective character (in particular, they are independent of our activities). One of these facts is the solvability of all well-formulated mathematical problems –and this fact requires a clarification. The assumptions on which Gödel’s position is based are: (1) metaphysical realism: there is a mathematical universe, it is objective and independent of us; (2) epistemological optimism: we are equipped with sufficient cognitive power to gain insight into the universe Gödel’s concept of a solution to a mathematical problem is much broaderthan of a mathematical proof –it is rather about finding reliable axioms that lead to a (formal) solution of the problem. I analyze the problem presented in the article, taking as an example of the continuum hypothesis. |
| first_indexed | 2024-12-19T14:42:18Z |
| format | Article |
| id | doaj.art-99b2f564119e46f6becbf732ea192aa8 |
| institution | Directory Open Access Journal |
| issn | 0137-6608 2544-073X |
| language | English |
| last_indexed | 2024-12-19T14:42:18Z |
| publishDate | 2020-05-01 |
| publisher | Polskie Towarzystwo Semiotyczne / The Polish Semiotic Society |
| record_format | Article |
| series | Studia Semiotyczne |
| spelling | doaj.art-99b2f564119e46f6becbf732ea192aa82022-12-21T20:17:03ZengPolskie Towarzystwo Semiotyczne / The Polish Semiotic SocietyStudia Semiotyczne0137-66082544-073X2020-05-01322The Notion of Explanation in Gödel’s Philosophy of MathematicsDOI: http://doi.org/10.26333/stsen.xxx.05 The article deals with the question of in which sense the notion of explanation (which is rather characteristic of empirical sciences) can be applied to Kurt Gödel’s philosophyof mathematics. Gödel, as a mathematical realist, claims that in mathematics we are dealing with facts that have an objective character (in particular, they are independent of our activities). One of these facts is the solvability of all well-formulated mathematical problems –and this fact requires a clarification. The assumptions on which Gödel’s position is based are: (1) metaphysical realism: there is a mathematical universe, it is objective and independent of us; (2) epistemological optimism: we are equipped with sufficient cognitive power to gain insight into the universe Gödel’s concept of a solution to a mathematical problem is much broaderthan of a mathematical proof –it is rather about finding reliable axioms that lead to a (formal) solution of the problem. I analyze the problem presented in the article, taking as an example of the continuum hypothesis.http://studiasemiotyczne.pts.edu.pl/index.php/Studiasemiotyczne/article/view/150mathematical realismmathematical explanationincompleteness theoremsmathematical universecontinuum hypothesis |
| spellingShingle | The Notion of Explanation in Gödel’s Philosophy of Mathematics Studia Semiotyczne mathematical realism mathematical explanation incompleteness theorems mathematical universe continuum hypothesis |
| title | The Notion of Explanation in Gödel’s Philosophy of Mathematics |
| title_full | The Notion of Explanation in Gödel’s Philosophy of Mathematics |
| title_fullStr | The Notion of Explanation in Gödel’s Philosophy of Mathematics |
| title_full_unstemmed | The Notion of Explanation in Gödel’s Philosophy of Mathematics |
| title_short | The Notion of Explanation in Gödel’s Philosophy of Mathematics |
| title_sort | notion of explanation in godel s philosophy of mathematics |
| topic | mathematical realism mathematical explanation incompleteness theorems mathematical universe continuum hypothesis |
| url | http://studiasemiotyczne.pts.edu.pl/index.php/Studiasemiotyczne/article/view/150 |