This chapter deals with global symmetries and their spontaneous breaking, particularly referring to sigma-models. We consider two theorems about the emergence of Nambu–Goldstone bosons. This takes us to the structure of low-energy effective theories, and to the hierarchy problem in the Higgs sector of the Standard Model. In that context, we further address triviality, the electroweak phase transition in the early Universe, and the extension to two Higgs doublets.

This chapter defends the unorthodox view that metaphysical necessitation is both necessary and sufficient for truthmaking. For x to be a truthmaker for y is for it to be metaphysically necessary that if x exists, then y is true. The necessity of necessitation is defended by considering the truthmakers for truths about truthmaking: facts of the form ‘x is a truthmaker for y’. The sufficiency of necessitation is defended by addressing the many counterexamples that been offered against it (notably those involving necessary truths), and showing how they pose no problem for truthmaking when understood as the task of ontological accounting. It is also shown how this view avoids the triviality challenge posed by Greg Restall.