On the Concepts of Function and Dependence
This paper briefly traces the evolution of the function concept until its modern settheoretic definition, and then investigates its relationship to the pre-formal notion of variable dependence. I shall argue that the common association of pre-formal dependence with the modern function concept is mi...
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| Format: | Article |
| Language: | English |
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Universidade Federal de Santa Catarina
2015-09-01
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| Series: | Principia: An International Journal of Epistemology |
| Online Access: | https://periodicos.ufsc.br/index.php/principia/article/view/35580 |
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| author | André Bazzoni |
| author_facet | André Bazzoni |
| author_sort | André Bazzoni |
| collection | DOAJ |
| description |
This paper briefly traces the evolution of the function concept until its modern settheoretic definition, and then investigates its relationship to the pre-formal notion of variable dependence. I shall argue that the common association of pre-formal dependence with the modern function concept is misconceived, and that two different notions of dependence are actually involved in the classic and the modern viewpoints, namely effective and functional dependence. The former contains the latter, and seems to conform more to our pre-formal conception of dependence. The idea of effective dependence is further investigated in connection with the notions of function content and intensionality. Finally, the relevance of the distinction between the two kinds of dependence to mathematical practice is considered.
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| format | Article |
| id | doaj-art-efb1e5763d90414d97c013d8e9d037d0 |
| institution | DOAJ |
| issn | 1808-1711 |
| language | English |
| publishDate | 2015-09-01 |
| publisher | Universidade Federal de Santa Catarina |
| record_format | Article |
| series | Principia: An International Journal of Epistemology |
| spelling | doaj-art-efb1e5763d90414d97c013d8e9d037d02025-08-20T02:48:55ZengUniversidade Federal de Santa CatarinaPrincipia: An International Journal of Epistemology1808-17112015-09-0119110.5007/1808-1711.2015v19n1p124360On the Concepts of Function and DependenceAndré Bazzoni0University of California Berkeley This paper briefly traces the evolution of the function concept until its modern settheoretic definition, and then investigates its relationship to the pre-formal notion of variable dependence. I shall argue that the common association of pre-formal dependence with the modern function concept is misconceived, and that two different notions of dependence are actually involved in the classic and the modern viewpoints, namely effective and functional dependence. The former contains the latter, and seems to conform more to our pre-formal conception of dependence. The idea of effective dependence is further investigated in connection with the notions of function content and intensionality. Finally, the relevance of the distinction between the two kinds of dependence to mathematical practice is considered. https://periodicos.ufsc.br/index.php/principia/article/view/35580 |
| spellingShingle | André Bazzoni On the Concepts of Function and Dependence Principia: An International Journal of Epistemology |
| title | On the Concepts of Function and Dependence |
| title_full | On the Concepts of Function and Dependence |
| title_fullStr | On the Concepts of Function and Dependence |
| title_full_unstemmed | On the Concepts of Function and Dependence |
| title_short | On the Concepts of Function and Dependence |
| title_sort | on the concepts of function and dependence |
| url | https://periodicos.ufsc.br/index.php/principia/article/view/35580 |
| work_keys_str_mv | AT andrebazzoni ontheconceptsoffunctionanddependence |