This chapter asks not how, but why a non-equilibrium system like the biosphere should have emerged, and how such a state can be stable. A mathematical theory exists which addresses such questions, familiar from condensed matter and particle physics as the theory of phase transitions. We show why some theory of this kind is needed to make sense of the complex facts and contradictory interpretations that have been given for the origin of life, and then introduce the fundamental concepts of phases and phase transitions in forms appropriate to the phenomena seen in earlier chapters.We introduce phase transitions as a class of mathematical phenomena, which frees us from introducing the subject by analogy, and provides a conceptually more fundamental expression of the main ideas. We show how the concepts of phase transition generalize from familiar equilibrium systems to more complex non-equilibrium cases, and summarize which lessons from equilibrium systems can be expected to generalize and where new ideas will be needed. The thermodynamic theory of stability is an application, in matter, of the method of inference known as Laplace's principle of insufficient reason, which states that when inferring from any observation, we should be as uncommittal as possible given what we have seen. From Laplace's principle, we show how the theory of optimal error correction is of the same kind as the thermal theory of stability of matter. These different versions of the stability perspective are assembled in this and the next chapter to propose that the emergence of the biosphere must be understood as a cascade of non-equilibrium phase transitions away from a lifeless Earth, and this is the origin of their necessity.