The paper first discusses the metaphysical framework that allows the soul's integration into the physical world. A close examination of B36, supported by the comparative evidence of some other early theories of the soul, suggests that the word psuchê could function as both a mass term and a count noun for Heraclitus. There is a stuff in the world, alongside other physical elements, that manifests mental functions. Humans, and possibly other beings, show mental functions in so far as they have (...) a portion of that stuff. Turning to the physical characterization of the soul, the paper argues that B36 is entirely consistent with the ancient testimonies that say that psuchê for Heraclitus is exhalation. But exhalations cover all states of matter from the lowest moist part of atmospheric air to the fire of celestial bodies. If so, psuchê for Heraclitus is both air and fire. The fact that psuchê can manifest the whole range of physical properties along the dry-wet axis guarantees that souls can show different intellectual and ethical properties as well. Moreover, Sextus Empiricus, supported by some other sources, provides us with an answer how portions of soul stuff are individuated into individual souls. The paper closes with a brief discussion of the question whether, and if so with what qualifications, we can apply the term 'physicalism' to Presocratic theories of the soul. (shrink)