In Stoic philosophy, pneuma (πνεῦμα) is the concept of the "breath of life," a mixture of the elements air (in motion) and fire (as warmth). Originating among Greek medical writers who locate human vitality in the breath, pneuma for the Stoics is the active, generative principle that organizes both the individual and the cosmos. In its highest form, the pneuma constitutes the human soul (psychê), which is a fragment of the pneuma that is the soul of God (Zeus). As a force that structures matter, it exists even in inanimate objects.
Levels of pneuma 
In the Stoic universe, everything is constituted of matter and pneuma. There are three grades or kinds of pneuma, depending on their proportion of fire and air.
- The pneuma of state or tension (tonos). This unifying and shaping pneuma provides stability or cohesion (hexis) to things; it is a force that exists even in objects such as a stone, log, or cup. The 4th-century Christian philosopher Nemesius attributes the power of pneuma in Stoic thought to its "tensile motion" (tonicê kinêsis); that is, the pneuma moves both outwards, producing quantity and quality, and at the same time inwards, providing unity and substance. An individual is defined by the equilibrium of its inner pneuma, which holds it together and also separates it from the world around it.
- The pneuma as life force. The vegetative pneuma enables growth (physis) and distinguishes a thing as alive.
- The pneuma as soul. The pneuma in its most rarefied and fiery form serves as the animal soul (psychê); it pervades the organism, governs its movements, and endows it with powers of perception and reproduction. This concept of pneuma is related to Aristotle's theory that the pneuma in sperm conveys the capacity for locomotion and for certain sensory perceptions to the offspring.
A fourth grade of pneuma may also be distinguished. This is the rational soul (logica psychê) of the mature human being, which grants the power of judgment.
Pneuma and cosmology 
In Stoic cosmology, everything that exists depends on two first principles which can be neither created nor destroyed: matter, which is passive and inert, and the logos, or divine reason, which is active and organizing. The 3rd-century B.C. Stoic Chrysippus regarded pneuma as the vehicle of logos in structuring matter, both in animals and in the physical world. Pneuma in its purest form can thus be difficult to distinguish from logos or the "constructive fire" (pur technikon) that drives the cyclical generation and destruction of the Stoic cosmos. When a cycle reaches its end in conflagration (ekpyrôsis), the cosmos becomes pure pneuma from which it regenerates itself.
The Stoics conceived of the cosmos as a whole and single entity, a living thing with a soul of its own, a spherical continuum of matter held together by the orderly power of Zeus through the causality of the pneuma that pervades it. This divine pneuma that is the soul of the cosmos supplies the pneuma in its varying grades for everything in the world.
- Baltzly, Dirk. "Stoicism." The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. Spring 2008.
- Inwood, Brad, editor. The Cambridge Companion to the Stoics. Cambridge University Press, 2003. ISBN 0-521-77985-5
- Sedley, David. "Stoic Physics and Metaphysics." The Cambridge History of Hellenistic Philosophy. Cambridge University Press, 2005.
- "Stoicism." Routledge Encyclopedia of Philosophy, vol. 9. Taylor & Francis, 1998. ISBN 0-415-07310-3
- Sellars, John. Stoicism. University of California Press, 2006. ISBN 0-520-24907-0
- "Stoicism," Routledge Encyclopedia of Philosophy (Taylor & Francis, 1998), p. 145.
- David Sedley, "Stoic Physics and Metaphysics," The Cambridge History of Hellenistic Philosophy, p. 388.
- John Sellars, Stoicism (University of California Press, 2006), pp. 98-104.
- Michael J. White, "Stoic Natural Philosophy (Physics and Cosmology)," p. 134, and Dorothea Frede, "Stoic Determinism," p. 186, both in The Cambridge Companion to the Stoics (Cambridge University Press, 2003).
- John Sellars, Stoicism, p. 91.
- Friedrich Solmsen, "The Vital Heat, the Inborn Pneuma and the Aether," Journal of Hellenic Studies 77 (1957) 119–123.
- John Sellars, Stoicism, p. 105.
- Dirk Baltzly, "Stoicism," The Stanford Encyclopedia of Philosophy.
- David Sedley, "Stoic Physics and Metaphysics," The Cambridge History of Hellenistic Philosophy, p. 389.
- Michael J. White, "Stoic Natural Philosophy (Physics and Cosmology)," The Cambridge Companion to the Stoics (Cambridge University Press, 2003), p. 136. White suggests that a number of Stoic terms are used interchangeably, or with subtle contextual distinctions, for the principle that acts on and within the physical world: pur, to hêgemonikon, pneuma, theos, nous, sperma, hexis, tonikê kinêsis.
- John Sellars, Stoicism, pp. 98–99.
- David Sedley, "Stoic Physics and Metaphysics," The Cambridge History of Hellenistic Philosophy, p. 447.
- David J. Furley, From Aristotle to Augustine (Routledge, 1999) p. 238; John Sellars, Stoicism, p. 97.