André Bazzoni
University of Barcelona
This paper briefly traces the evolution of the function concept until its modern set theoretic 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.
Keywords Function concept  philosophy of mathematics  variable dependence  history of mathematics
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DOI 10.5007/1808-1711.2015v19n1p1
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References found in this work BETA

Mathematics, Form and Function.Saunders MacLane - 1986 - Journal of Philosophy 84 (1):33-37.
Intensional Mathematics.Stuart Shapiro - 1991 - Studia Logica 50 (1):161-162.
Intensional Mathematics.Stewart Shapiro - 1989 - Philosophy of Science 56 (1):177-178.
Effectiveness.Stewart Shapiro - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. pp. 37--49.

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