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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Main Author: André Bazzoni
Format: Article
Language:English
Published: Universidade Federal de Santa Catarina 2015-09-01
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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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