Augustine believed that angels (and demons) possessed ethereal bodies. He reasoned that because angels interact with physical space and assume solid forms to appear to humans, they must possess a semi-material, ethereal nature, rather than being purely incorporeal. He was not alone in this belief, though it eventually fell out of favor in Western Christian theology. Many early Church Fathers (such as St. Basil of Caesarea) and early Christian writers shared this general view, often influenced by contemporary Platonist philosophy, which viewed angels and demons as spiritual beings made of invisible matter.The belief that angels are purely immaterial spirits took over Western theology centuries later, largely championed by St. Thomas Aquinas in the 13th century.
The Fourth Lateran Council of 1215 ended the mainstream acceptance of Augustine's "ethereal body" theory in Western Christianity, But not in the East.
And the text of Lateran IV can be understood in a way that harmonizes with the Eastern Orthodox view.
While Western Catholic theologians (like St. Thomas Aquinas) historically used this text to argue that angels are 100% immaterial, abstract intelligences, the specific wording of Lateran IV'S Firmiter Credimus is broad enough to accommodate the Orthodox concept of "relative corporeality."
The two traditions find common ground within the council text through a 3 distinct avenues:
1.) The council's core purpose was defeating dualism, notot scientific definitions.
When Lateran IV declared that God created two realms—spiritualem et corporalem (spiritual and corporeal)—it was not trying to provide a precise atomic or microscopic breakdown of an angel's nature.
The council's target was dualism. The Cathars believed that God created the spiritual realm, but an evil god (Satan) created the physical realm. By using spiritualem and corporalem, the Council was simply establishing a hierarchy of creation to prove that God is the sole source of everything, whether it is invisible or visible. It does not forbid the idea that the "spiritual" realm contains a higher, refined type of creation ("subtle bodies") that is radically different from our heavy, earthly matter.
2.) The coucil's language could be viewed as relative.
In Latin theology, words like incorporeal (body-less) or immaterial can be interpreted in two ways.
Absolutely: Possessing zero dimensions, zero spatial traits, and zero substance outside of pure mind (the Western Scholastic approach).
Relatively: Completely lacking human flesh, blood, bone, and physical corruption (the Eastern Patristic approach).
Lateran IV uses spiritualem to contrast with our heavy, earthly universe (mundanam). An Orthodox Christian can fully affirm the Latin text of Lateran IV by arguing that angels are spiritualem because they possess no earthly, dense body (corporalem), while still maintaining that only God is "immaterial" in the absolute sense.
3.) Lateran IV describes human beings as being a bridge between the two worlds: "quasi communem ex spiritu et corpore constitutam" (composed as it were of both spirit and body). Both Catholics and Orthodox agree on this text's meaning--hunans have a dual nature (a physical body of this world + a soul). Angels do not share this dual nature. They belong entirely to the celestial order.
Whether that celestial order is completely abstract (West) or composed of invisible matter (East), both views agree with Lateran IV that angels do not possess the corporem (the dense, physical flesh) that humans do.
Because Lateran IV took place in 1215 (after the Great Schism of 1054), the Eastern Orthodox Church does not recognize it as an Ecumenical Council. However, because Lateran IV phrased its definition using broad scriptural categories rather than tight Aristotelian philosophical terms, an Orthodox Christian looking at the Latin text would find very little to disagree with. Both sides firmly confess that angels are entirely above our physical laws, free from fleshly limitations, and created out of nothing by the Holy Trinity.