Abstract
In this paper, I will do preparatory work for a generalized account of applicability, that is, for an account which works for math-to-physics, math-to-math, and physics-to-math application. I am going to present and discuss some examples of these three kinds of application, and I will confront them in order to see whether it is possible to find analogies among them and whether they can be ultimately considered as instantiations of a unique pattern. I will argue that these analogies can be exploited in order to get a better understanding of the applicability of mathematics to physics and of the complex relationship between physics and mathematics.
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Notes
- 1.
Also physicists themselves, such as Jean-Marc Levy-Leblond, argue that this topic deserves some closer attention: <<This inverse relationship, from physics to mathematics, deserves a full study of its own>> (Levy-Leblond 1992, p. 154). Nevertheless, he does not develop this suggestion any further.
- 2.
The first example is also discussed in Bangu (2008).
- 3.
The story is actually a bit more complicate than this. They could prove the existence of the Ω− particle, along with its characteristics—except for its spin. Physicists presumed that its spin was \(\frac {3}{2}\) just because its existence was predicted within the classification symmetry scheme for spin-\(\frac {3}{2}\) baryons, but the actual measurement of its spin was unexpectedly difficult. Although this hyperon was discovered more than 40 years ago, a conclusive measurement of its spin has only recently been obtained by Aubert et al. (2006).
- 4.
As Sir Michael Atiyah said referring to Witten, <<[H]e has made a profound impact on contemporary mathematics. In his hands physics is once again providing a rich source of inspiration and insight in mathematics>> (Atiyah 2003, p. 525).
- 5.
Mathematical optimism can, according to Wilson, take two different forms: lazy and honest. The lazy mathematical optimism is the idea that <<somewhere deep within mathematics’ big bag must lie a mathematical assemblage that is structurally isomorphic to that of the physical world before us, even if it turns out that we will never be able to get our hands on that structure concretely>> (pp. 296–7). As such, lazy mathematical optimism is an a priori thesis. Differently, honest mathematical optimism <<cannot be plausibly regarded as an a priori truth at all, but, from a physical point of view, it can nonetheless prove quite resilient to refutation>> (p. 297). Wilson’s thesis is that <<‘anti-realists’ frequently severely underestimate the difficulties in arguing against honest optimism>> (p. 297).
- 6.
This assumption amounts to saying that the structural similarity between A and B is actually wider than the one circumscribed by the original monomorphism, and can coincide—at its limit—with an isomorphism hypothesis.
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Acknowledgements
I would like to thank Prof. Gabriele Lolli, for his constant support; Prof. Charlotte Werndl for her suggestions on a previous draft of this paper; Prof. Mario Piazza and Prof. Gabriele Pulcini for their work in making this volume possible; an anonimous referee, for their precious comments. Finally, a special thank to Pauline van Wierst, who read the paper and helped me with constant support and important insights.
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Ginammi, M. (2018). Applicability Problems Generalized. In: Piazza, M., Pulcini, G. (eds) Truth, Existence and Explanation. Boston Studies in the Philosophy and History of Science, vol 334. Springer, Cham. https://doi.org/10.1007/978-3-319-93342-9_12
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