Non-Humean accounts of the metaphysics of nature posit either laws or powers in order to account for natural necessity and world-order. We argue that such monistic views face fundamental problems. On the one hand, neo-Aristotelians cannot give unproblematic power-based accounts of the functional laws among quantities offered by physical theories, as well as of the place of conservation laws and symmetries in a lawless ontology; in order to capture these characteristics, commitment to governing laws is indispensable. On the other hand, (...) ontologies that entirely exclude some kind of power ascription to worldly entities face what we call the Governing Problem: such ontologies do not have the resources to give an adequate account of how laws play their governing role. We propose a novel dualist model, which, we argue, has the resources to solve the difficulties encountered by its two dominant competitors, without inheriting the problems of either view. According to the dualist model, both laws and powers are equally fundamental and irreducible to each other, and both are needed in order to give a satisfactory account of the nomological structure of the world. The dualist model constitutes thus a promising alternative to current monistic views in the metaphysics of science. (shrink)

We adjust the notion of typicality originated with Russell, which was introduced and studied in a previous paper for general first-order structures, to make it expressible in the language of set theory. The adopted definition of the class ${\rm NT}$ of nontypical sets comes out as a natural strengthening of Russell's initial definition, which employs properties of small (minority) extensions, when the latter are restricted to the various levels $V_\zeta$ of $V$. This strengthening leads to defining ${\rm NT}$ as the (...) class of sets that belong to some countable ordinal definable set. It follows that ${\rm OD}\subseteq {\rm NT}$ and hence ${\rm HOD}\subseteq {\rm HNT}$. It is proved that the class ${\rm HNT}$ of hereditarily nontypical sets is an inner model of ${\rm ZF}$. Moreover the (relative) consistency of $V\neq {\rm NT}$ is established, by showing that in many forcing extensions $M[G]$ the generic set $G$ is a typical element of $M[G]$, a fact which is fully in accord with the intuitive meaning of typicality. In particular it is consistent that there exist continuum many typical reals. In addition it follows from a result of Kanovei and Lyubetsky that ${\rm HOD}\neq {\rm HNT}$ is also relatively consistent. In particular it is consistent that ${\cal P}(\omega)\cap {\rm OD}\subsetneq{\cal P}(\omega)\cap {\rm NT}$. However many questions remain open, among them the consistency of ${\rm HOD}\neq {\rm HNT}\neq V$, ${\rm HOD}={\rm HNT}\neq V$ and ${\rm HOD}\neq {\rm HNT}= V$. (shrink)