Mathematics as hammer: the makings of the masters tool
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In an often quoted but not carefully read paper, Wigner (1960) spoke of the unreasonable effectiveness of mathematics in the natural sciences. Mathematics and modern physics in his view presented such fundamentally different branches of knowledge that their close relationship appeared to be puzzling, mysterious and unreasonable.
Missing from Wigner’s analysis is an account of the constitution of mathematics, on the one hand, and its changing relationship with sciences on the other. He adopts uncritically the definition of pure abstract mathematics of the twentieth century and projects it to the mathematics of all areas and all eras. Moreover, the paper is focused almost exclusively on modern theoretical physics (Islami 2016). Thus, critics of Wigner have focused, and with good motivation, on ineffectiveness of mathematics in other sciences (see, for example, Longo and Montévil 2013; Steiner 1998; Velupillai 2005, for responses).
In this spirit, the collection of papers edited by...
- Islami, A. 2016. Match not made in heaven: On the applicability of mathematics in physics. Synthese 87: 1–23.Google Scholar
- Steiner, M. 1998. The applicability of mathematics as a philosophical problem. Cambridge, MA: Harvard University Press.Google Scholar
- Wigner, E. P. 1960. The unreasonable effectiveness of mathematics in the natural sciences. In Symmetries and reflections, 222–237. Woodbridge: Ox Bow Press.Google Scholar