This conclusion presents some closing thoughts on the key concepts discussed in the preceding chapters of this book. The book presents with two different accounts of quantity: the class nominalist ‘neo-Ellisonian’ account and the ‘quasi-realist’ BP. It shows what was involved in making such a move and the class nominalist position was contrasted with realism. The book discusses the various positions and proposals have been restricted by qualifiers like “in the classical domain”. The application of mathematics crucially depends on this - hence the emphasis throughout the book on measurement and what this presupposes. The whole idea of ‘new directions’ in the theory of explanation is to allow for different styles and dimensions of explanations. What is then necessary for the instance view to apply to explanation in quantum mechanics is to incorporate the quantum state into the laws that also feature quantities.