This chapter draws on insights from non-equilibrium thermodynamics to demonstrate the ontological inadequacy of the machine conception of the organism. The thermodynamic character of living systems underlies the importance of metabolism and calls for the adoption of a processual view, exemplified by the Heraclitean metaphor of the stream of life. This alternative conception is explored in its various historical formulations and the extent to which it captures the nature of living systems is examined. Following this, the chapter considers the metaphysical implications of reconceptualizing the organism from complex machine to flowing stream. What do we learn when we reject the mechanical and embrace the processual? Three key lessons for biological ontology are identified. The first is that activity is a necessary condition for existence. The second is that persistence is grounded in the continuous self-maintenance of form. And the third is that order does not entail design.