I argue that philosophical issues concerning reductive explanations help constrain the construction of quantum theories with appropriate state spaces. I illustrate this general proposal with two examples of restricting attention to physical states in quantum theories: regular states and symmetry-invariant states.

2.  Background

2.1.   Physical states

2.2.   Reductive explanations

3.  The Proposed ‘Correspondence Principle’

5.  Example: Symmetry-Invariance

6.  Conclusion: Heuristics and Discovery