Iamblichus broke with his own tradition on the question that decides whether Neoplatonism is a philosophy or a religion, and the tradition followed him rather than his opponent.
Porphyry had raised a set of sceptical objections about the point of ritual: if the gods are impassive, what could a sacrifice do to them, and if the soul ascends by understanding, what is a rite for? The reply that survives under the title On the Mysteries, written by Iamblichus under the persona of an Egyptian priest, argues that the human soul is not merely obscured but genuinely descended, and cannot lift itself by its own contemplation. Theurgy, divine work, is therefore necessary: rites, invocations, symbols, statues and material tokens through which the gods act on the soul from above. The efficacy is the gods', not the operator's, which is precisely what distinguishes theurgy from magic in his account.
This is the philosophical charter for essentially all subsequent Western ceremonial practice. It supplies the justification for using physical materials, names of power and consecrated objects in a system that also holds the divine to be immaterial, the doctrine of correspondences, in which particular stones, plants, hours and figures are linked to particular powers, has its rationale here. Gregory Shaw's study is the standard modern treatment. Iamblichus also gave Neoplatonism its taste for elaborate hierarchy, which Proclus then multiplied.