Probabilities, Laws, and Structures. Dordrecht: Springer. Structural Invariants, Structural Kinds, Structural Laws

The paper has three parts. In the first part ExtOSR, an extended version of Ontic Structural Realism, will be introduced. ExtOSR considers structural properties as ontological primitives, where structural properties are understood as comprising both relational and structurally derived intrinsic properties or structure invariants. It is argued that ExtOSR is best suited to accommodate gauge symmetry invariants and zero value properties. In the second part, ExtOSR will be given a Humean shape by considering structures as categorical and global. It will be laid out how such structures serve to reconstruct non-essential structural kinds and laws. In the third part Humean structural realism will be defended against the threat of quidditism. Part 1: Structural Realism and Intrinsicality: OSR extended Many structural realists agree on two claims: they prefer ontic over epistemic versions of SR and they don't want to dismiss the idea of relata altogether. Therefore non-eliminative versions of ontic structural realism have become fashionable. They start from the idea that there are relations and relata, but that there is nothing more to the relata than the 'structural properties ' in which they stand. But what are 'structural properties'? Are they all and only relations? Or must we allow for certain intrinsic properties as well? I d