Realizability and the varieties of explanation

What realization is has been convincingly presented in relation to the way we determine what counts as the realizers of realized properties. The way we explain a fact of realization includes a reference to what realization should be; therefore it informs in turn our understanding of the nature of realization. Conceptions of explanation are thereby included in the views of realization as a metaphysical property. Recently, several major views of realization such as Polger and Shapiro's or Gillett and Aizawa's, however competing, have relied on the neo-mechanicist theory of explanations (e.g,. Darden and Caver 2013), currently popular among philosophers of science. However, it has also been increasingly argued that some explanations are not mechanistic (e.g., Batterman 2009). Using an account given in Huneman (2017), I argue that within those explanations the fact that some mathematical properties are instantiated is explanatory, and that this defines a specific explanatory type called "structural explanation", whose subtypes could be: optimality explanations (usually found in economics), topological explanations, etc. This paper thereby argues that all subtypes of structural explanation define several kinds of realizability, which are not equivalent to the usual notion of realization tied to mechanistic explanations, onto which many of the philosophical investigations are focused. Then it draws some consequences concerning the notion of multiple realizability.