Proof vs Truth in Mathematics
Two crucial concepts of the methodology and philosophy of mathematics are considered: proof and truth. We distinguish between informal proofs constructed by mathematicians in their research practice and formal proofs as defined in the foundations of mathematics (in metamathematics). Their role, feat...
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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-2020-0025 |
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doaj-7dfae74865444413b5818d3ffdf1a4d12021-10-02T19:14:51ZengSciendoStudia Humana2299-05182020-10-0193-4101810.2478/sh-2020-0025sh-2020-0025Proof vs Truth in MathematicsMurawski Roman0Adam Mickiewicz University, Uniwersytetu Poznańskiego 4 Street, 61-614Poznań, PolandTwo crucial concepts of the methodology and philosophy of mathematics are considered: proof and truth. We distinguish between informal proofs constructed by mathematicians in their research practice and formal proofs as defined in the foundations of mathematics (in metamathematics). Their role, features and interconnections are discussed. They are confronted with the concept of truth in mathematics. Relations between proofs and truth are analysed.https://doi.org/10.2478/sh-2020-0025formal proofinformal prooftruthmathematicslogicincompletenessjan woleński |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Murawski Roman |
| spellingShingle |
Murawski Roman Proof vs Truth in Mathematics Studia Humana formal proof informal proof truth mathematics logic incompleteness jan woleński |
| author_facet |
Murawski Roman |
| author_sort |
Murawski Roman |
| title |
Proof vs Truth in Mathematics |
| title_short |
Proof vs Truth in Mathematics |
| title_full |
Proof vs Truth in Mathematics |
| title_fullStr |
Proof vs Truth in Mathematics |
| title_full_unstemmed |
Proof vs Truth in Mathematics |
| title_sort |
proof vs truth in mathematics |
| publisher |
Sciendo |
| series |
Studia Humana |
| issn |
2299-0518 |
| publishDate |
2020-10-01 |
| description |
Two crucial concepts of the methodology and philosophy of mathematics are considered: proof and truth. We distinguish between informal proofs constructed by mathematicians in their research practice and formal proofs as defined in the foundations of mathematics (in metamathematics). Their role, features and interconnections are discussed. They are confronted with the concept of truth in mathematics. Relations between proofs and truth are analysed. |
| topic |
formal proof informal proof truth mathematics logic incompleteness jan woleński |
| url |
https://doi.org/10.2478/sh-2020-0025 |
| work_keys_str_mv |
AT murawskiroman proofvstruthinmathematics |
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