The conceptual divide separating the physical and biological sciences continues to challenge modern science. In this perspective it is proposed that the two sciences can be directly connected through the fundamental concept of stability. Physicochemical stability is shown to have a logical, rather than an empirical basis, and able to manifest itself in two distinct and often contrary ways, one thermodynamic, reflecting energetic considerations, and the other kinetic, reflecting time/persistence considerations. Each stability kind is shown to rest on a particular mathematical truism. Thermodynamic stability, the energetic expression, has a probabilistic/statistical basis due to Boltzmann, and leads to the Second Law of Thermodynamics. Dynamic kinetic stability (DKS), the time/persistence expression, is attributed to the stability associated with persistent replicating systems, and derives from the mathematics of exponential growth. The existence of two distinct stability kinds, each mathematically-based, leads to two distinct organizational forms of matter, animate and inanimate. That understanding offers insight into the reasons for the observation of just those two organizational forms, their different material characteristics, and provides a logical basis for understanding the nature of chemical and biological transformations, both within, and between, the two forms.