Within the depth-psychology corpus, 'Pythagorean' designates not merely a school of ancient mathematics but a primary site where numinous number-experience, soul-doctrine, shamanic religious practice, and cosmological speculation converge. Edinger reads the Pythagoreans as the founders of arithmos as a psychic paradigm — practitioners who experienced numbers as divine disclosures and whose theorem-discoveries carried the character of sacred revelation. Rohde, writing from the history-of-religion perspective, traces the Pythagorean conception of the soul as supra-mundane, radically opposed to nature, and subject to metempsychotic purification — a doctrine he insists cannot be derived from Greek natural science but reflects an independent shamanic stream. Dodds situates Pythagorean catharsis and burial rite within his broader argument about the irrational inheritance of Greek culture, linking Pythagorean transmigration to Orphic and possibly Egyptian influences. Seaford provides an innovative counterpoint, arguing that Pythagorean number-mysticism is intelligible only against the monetisation of the archaic Greek world, which supplied the abstraction necessary for the doctrine that all things are number. The Timaeus passages represent the Platonic assimilation of Pythagorean mathematical cosmology. Vernant and Burkert attend to the political and ritual dimensions of the Pythagorean brotherhood. Across these voices, the term marks the junction of archaic religious psychology and the first systematic mathematisation of reality.
A central concept of the Pythagoreans was arithmos, number. They were responsible for the discovery of numbers as a conceptual paradigm; they were gripped by the numinosity of numbers and experienced them as divine.
Edinger argues that the Pythagorean discovery of number constitutes the inauguration of a genuinely psychic paradigm, rooted in the numinous experience of arithmos as a divine reality.
, The Psyche in Antiquity, Book One: Early Greek Philosophy From Thales to Plotinus, 1999thesis
The practical philosophy of the Pythagorean school is founded upon a conception of the soul as absolutely distinct from 'nature', and, in fact, opposed to it. Its origin is supra-mundane, and so, too, when liberated from the shackles of natural life it will one day be enabled to return to a supernatural existence as a spirit.
Rohde establishes that the Pythagorean soul-doctrine is defined by a radical dualism — the soul's supra-mundane origin and its opposition to the natural world — a position arrived at outside scientific derivation.
, Psyche: The Cult of Souls and the Belief in Immortality among the Greeks, 1894thesis
This discovery was considered a divine disclosure. Pythagoras is said to have sacrificed an ox in gratitude for this revelation. The Pythagorean theorem is part of the discovery of irrational numbers.
Edinger interprets the Pythagorean theorem as a paradigmatic religious event — mathematical discovery experienced as divine revelation — and connects it psychologically to the emergence of irrational numbers as a disturbing confrontation with the unbounded.
, The Psyche in Antiquity, Book One: Early Greek Philosophy From Thales to Plotinus, 1999thesis
For all things to be number, or made of number, it must be the same sort of thing as, and yet ontologically prior to, everything else. The doctrine focuses on the quantitative aspect of things to the exclusion of the qualitative.
Seaford argues that the Pythagorean doctrine of number's ontological priority mirrors the trader's abstraction of quantity from quality, homologising number-mysticism with the logic of monetary value.
, Money and the Early Greek Mind: Homer, Philosophy, Tragedy, 2004thesis
Mathematics, ethical self-restraint, and politics are all attributed by our sources to early Pythagoreanism. The case of Archytas shows how they may have been interrelated.
Seaford demonstrates that early Pythagoreanism integrated mathematical, ethical, and political programmes, with Archytas as the exemplary figure of their synthesis.
, Money and the Early Greek Mind: Homer, Philosophy, Tragedy, 2004supporting
Pythagorean writings clearly show the transition from the primitive to the Hellenic streams of the ancient psyche. A central concept of the Pythagoreans was arithmos, number.
Edinger reads the Pythagorean textual tradition as evidence of a historical psychic transition from primitive shamanic consciousness to the rationalising Hellenic stream.
, The Psyche in Antiquity, Book One Early Greek Philosophy supporting
Its sectaries formed a church rather than a school, a religious order, not an academy of sciences.
Dodds (citing Cumont) characterises Neopythagoreanism as essentially a religious confraternity rather than a philosophical academy, emphasising its eschatological and devotional dimensions.
, The Greeks and the Irrational, 1951supporting
The whole apparatus of ritual dyveia is ascribed to the older Pythagoreans by Alex. Polyh. ap. D.L. viii, 33. This, as a general statement is certainly correct.
Rohde establishes that the full apparatus of ritual purity — dietary, textile, and behavioural abstinences — was integral to early Pythagoreanism, affirming the religious character of the brotherhood's praxis.
, Psyche: The Cult of Souls and the Belief in Immortality among the Greeks, 1894supporting
For the members of the sect there was no difference in kind between public preaching aimed at political change, and geometric and astronomical thought.
Vernant argues that for the Pythagoreans political reform, geometry, and cosmology formed a unified project structured around a hierarchical concept of harmonia in the city.
, Myth and Thought Among the Greeks, 1983supporting
Aristotle also knew Pythagorean myths according to which 'any soul can enter any body.' And in a satirical poem, Xenophanes, our earliest witness for Pythagoras, ascribes to him the belief that a human soul, indeed the soul of a friend, could be present in a whipped dog.
Burkert documents the Pythagorean metempsychotic belief in the soul's unlimited bodily mobility, attested already in Xenophanes' earliest satirical reference to Pythagoras.
, Greek Religion: Archaic and Classical, 1977supporting
Given the unreliability of our sources for the history of early Pythagoreanism, this can remain no more than a hypothesis. But it gains support from various considerations.
Seaford situates Pythagoras' emigration from the monetised commercial centre of Samos to Croton within his hypothesis that early Pythagoreanism emerged as a response to rapid monetisation.
, Money and the Early Greek Mind: Homer, Philosophy, Tragedy, 2004supporting
The secrecy and the veneration go together in the punishment of the early Pythagorean Hippasus either for revealing a secret of geometry or for claiming its discovery for himself although it was Pythagoras'.
Seaford reads the case of Hippasus as evidence that Pythagorean secrecy, authority, and veneration of the founder were constitutive features of the early brotherhood's political and intellectual culture.
, Money and the Early Greek Mind: Homer, Philosophy, Tragedy, 2004supporting
There is in my judgement a stronger case for attaching Empedocles to the Pythagorean tradition than for connecting him with anything that is demonstrably and distinctively early-Orphic.
Dodds adjudicates the scholarly debate by aligning Empedocles more firmly with the Pythagorean than with the Orphic tradition, while resisting his classification as a school member.
, The Greeks and the Irrational, 1951supporting
Early Pythagoreans had had a hand in the manufacture of he could appeal to good fifth-century authority, not only to Ion of Chios but also, I think, to Herodotus.
Dodds evaluates the ancient testimony that Pythagoreans were implicated in the transmission of Orphic-Egyptian practices to Greece, finding fifth-century support for this claim.
, The Greeks and the Irrational, 1951supporting
From the point of view of psychology, these early formulations are not only valid for the external world, but are also the projection of pure psychology. They represent the sequence of psychic development in infancy.
Edinger interprets the Pythagorean point-line-plane-solid sequence as a psychological projection — a cosmological diagram of early psychic development from the transcendent Self through to embodied three-dimensional reality.
, The Psyche in Antiquity, Book One Early Greek Philosophy supporting
216 is the cube of 6, and also the sum of 3 cubed, 4 cubed, 5 cubed, the numbers 3, 4, 5 representing the Pythagorean triangle, of which the sides when squared equal the square of the hypotenuse (9 + 16 = 25).
The Republic commentary identifies the Pythagorean right triangle as structurally embedded in Plato's nuptial number 216, confirming the deep penetration of Pythagorean arithmetic into Platonic cosmological and political symbolism.
, Republic, -380supporting
Aristotle says that Plato agrees with the Pythagoreans in making numbers the causes of the reality of other things, but that he differs from them in his 'separation' of numbers from the world.
Seaford rehearses the Aristotelian distinction between Platonic and Pythagorean number-ontology — Pythagoreans apply number to bodies, Plato separates numbers — as context for his monetary-abstraction thesis.
, Money and the Early Greek Mind: Homer, Philosophy, Tragedy, 2004aside
Pythagorean 79, 154, 247
Dodds' index entries for 'Pythagorean' — cross-referencing catharsis, the occult self, and Neopythagoreanism — map the constellation of topics through which the term operates across his study of Greek irrationalism.
, The Greeks and the Irrational, 1951aside
Whether this conclusion should be extended back in time to the earlier Pythagoreans is open to question.
Claus raises the question of whether Empedocles' use of daimōn rather than psychē for the transmigrating self reflects an earlier Pythagorean usage, leaving the matter open as a boundary problem in pre-Platonic soul-terminology.
, Toward the Soul: An Inquiry into the Meaning of Psyche before Plato, 1981aside