Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs
The Euclidean ideal of mathematics as well as all the foundational schools in the philosophy of mathematics have been contested by the new approach, called the “maverick” trend in the philosophy of mathematics. Several points made by its main representatives are mentioned – from the revisability of...
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| Format: | Article |
| Language: | English |
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Sciendo
2020-10-01
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| Series: | Studia Humana |
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| Online Access: | https://doi.org/10.2478/sh-2020-0034 |
| _version_ | 1819291206199279616 |
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| author | Krajewski Stanisław |
| author_facet | Krajewski Stanisław |
| author_sort | Krajewski Stanisław |
| collection | DOAJ |
| description | The Euclidean ideal of mathematics as well as all the foundational schools in the philosophy of mathematics have been contested by the new approach, called the “maverick” trend in the philosophy of mathematics. Several points made by its main representatives are mentioned – from the revisability of actual proofs to the stress on real mathematical practice as opposed to its idealized reconstruction. Main features of real proofs are then mentioned; for example, whether they are convincing, understandable, and/or explanatory. Therefore, the new approach questions Hilbert’s Thesis, according to which a correct mathematical proof is in principle reducible to a formal proof, based on explicit axioms and logic. |
| first_indexed | 2024-12-24T03:34:57Z |
| format | Article |
| id | doaj.art-c574223685d04d5a8eca84cb869fc12d |
| institution | Directory Open Access Journal |
| issn | 2299-0518 |
| language | English |
| last_indexed | 2024-12-24T03:34:57Z |
| publishDate | 2020-10-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Studia Humana |
| spelling | doaj.art-c574223685d04d5a8eca84cb869fc12d2022-12-21T17:17:06ZengSciendoStudia Humana2299-05182020-10-0193-415416410.2478/sh-2020-0034sh-2020-0034Anti-foundationalist Philosophy of Mathematics and Mathematical ProofsKrajewski Stanisław0University of Warsaw, Krakowskie Przedmieście 3 Street, 00-927Warszawa, PolandThe Euclidean ideal of mathematics as well as all the foundational schools in the philosophy of mathematics have been contested by the new approach, called the “maverick” trend in the philosophy of mathematics. Several points made by its main representatives are mentioned – from the revisability of actual proofs to the stress on real mathematical practice as opposed to its idealized reconstruction. Main features of real proofs are then mentioned; for example, whether they are convincing, understandable, and/or explanatory. Therefore, the new approach questions Hilbert’s Thesis, according to which a correct mathematical proof is in principle reducible to a formal proof, based on explicit axioms and logic.https://doi.org/10.2478/sh-2020-0034mathematical proofaxiomatic proofformal proofphilosophy of mathematicsfoundations of mathematicsmathematical practiceexplanatory proofanalytic proofhilbert’s thesis |
| spellingShingle | Krajewski Stanisław Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs Studia Humana mathematical proof axiomatic proof formal proof philosophy of mathematics foundations of mathematics mathematical practice explanatory proof analytic proof hilbert’s thesis |
| title | Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs |
| title_full | Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs |
| title_fullStr | Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs |
| title_full_unstemmed | Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs |
| title_short | Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs |
| title_sort | anti foundationalist philosophy of mathematics and mathematical proofs |
| topic | mathematical proof axiomatic proof formal proof philosophy of mathematics foundations of mathematics mathematical practice explanatory proof analytic proof hilbert’s thesis |
| url | https://doi.org/10.2478/sh-2020-0034 |
| work_keys_str_mv | AT krajewskistanisław antifoundationalistphilosophyofmathematicsandmathematicalproofs |