Creating new concepts in mathematics: freedom and limitations. The case of Category Theory
In the paper we discuss the problem of limitations of freedom in mathematics and search for criteria which would differentiate the new concepts stemming from the historical ones from the new concepts that have opened unexpected ways of thinking and reasoning. We also investigate the emergence of...
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Copernicus Center Press
2020-12-01
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| Series: | Zagadnienia Filozoficzne w Nauce |
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| Online Access: | https://zfn.edu.pl/index.php/zfn/article/view/512 |
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doaj-c836ad92896b4f279b2eedfdededff642020-12-30T16:40:29ZdeuCopernicus Center PressZagadnienia Filozoficzne w Nauce0867-82862451-06022020-12-01693365512Creating new concepts in mathematics: freedom and limitations. The case of Category TheoryZbigniew Semadeni0University of WarsawIn the paper we discuss the problem of limitations of freedom in mathematics and search for criteria which would differentiate the new concepts stemming from the historical ones from the new concepts that have opened unexpected ways of thinking and reasoning. We also investigate the emergence of category theory (CT) and its origins. In particular we explore the origins of the term functor and present the strong evidence that Eilenberg and Carnap could have learned the term from Kotarbiński and Tarski.https://zfn.edu.pl/index.php/zfn/article/view/512categoriesfunctorseilenberg-mac lane programmathematical cognitive transgressionsphylogenyplatonism |
| collection |
DOAJ |
| language |
deu |
| format |
Article |
| sources |
DOAJ |
| author |
Zbigniew Semadeni |
| spellingShingle |
Zbigniew Semadeni Creating new concepts in mathematics: freedom and limitations. The case of Category Theory Zagadnienia Filozoficzne w Nauce categories functors eilenberg-mac lane program mathematical cognitive transgressions phylogeny platonism |
| author_facet |
Zbigniew Semadeni |
| author_sort |
Zbigniew Semadeni |
| title |
Creating new concepts in mathematics: freedom and limitations. The case of Category Theory |
| title_short |
Creating new concepts in mathematics: freedom and limitations. The case of Category Theory |
| title_full |
Creating new concepts in mathematics: freedom and limitations. The case of Category Theory |
| title_fullStr |
Creating new concepts in mathematics: freedom and limitations. The case of Category Theory |
| title_full_unstemmed |
Creating new concepts in mathematics: freedom and limitations. The case of Category Theory |
| title_sort |
creating new concepts in mathematics: freedom and limitations. the case of category theory |
| publisher |
Copernicus Center Press |
| series |
Zagadnienia Filozoficzne w Nauce |
| issn |
0867-8286 2451-0602 |
| publishDate |
2020-12-01 |
| description |
In the paper we discuss the problem of limitations of freedom in mathematics and search for criteria which would differentiate the new concepts stemming from the historical ones from the new concepts that have opened unexpected ways of thinking and reasoning.
We also investigate the emergence of category theory (CT) and its origins. In particular we explore the origins of the term functor and present the strong evidence that Eilenberg and Carnap could have learned the term from Kotarbiński and Tarski. |
| topic |
categories functors eilenberg-mac lane program mathematical cognitive transgressions phylogeny platonism |
| url |
https://zfn.edu.pl/index.php/zfn/article/view/512 |
| work_keys_str_mv |
AT zbigniewsemadeni creatingnewconceptsinmathematicsfreedomandlimitationsthecaseofcategorytheory |
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1724365685363048448 |