Arithmos — the Greek term for 'number' as wielded by the Pythagorean brotherhood — occupies a singular position in the depth-psychological corpus as the conceptual bridge between numinous experience and formal structure. Edinger's sustained engagement with the term establishes its primary valence: arithmos was not a mathematical abstraction for the Pythagoreans but a living archetype, the discovery of which constituted a genuine encounter with the divine. The numinosity of number, its capacity to disclose cosmic order, places arithmos at the intersection of shamanic consciousness and nascent rational thought — a transitional figure in the psyche's evolution from primitive participation mystique toward Hellenic logos. Nussbaum's philological excavation of the Homeric andron arithmos illuminates an older stratum: the denumerable as the graspable, the controllable, the narratable, opposed to the apeiron as the boundless and formless. Seaford's materialist reading provocatively grounds Pythagorean number-metaphysics in the monetized economy of early Greece, suggesting that the abstraction of all things into number mirrors the commodity-abstraction of monetary exchange. Von Franz and the broader Jungian tradition treat arithmos as a pre-existent psychic ordering principle, linking it to the constellation of archetypes around the Self. The tension between arithmos as numinous revelation and arithmos as socioeconomic projection constitutes the field's most productive unresolved debate.
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 establishes arithmos as the Pythagorean term for number understood not abstractly but as a numinous, divine archetype — the paradigmatic conceptual discovery of that brotherhood.
, The Psyche in Antiquity, Book One: Early Greek Philosophy From Thales to Plotinus, 1999thesis
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
A parallel passage from Edinger's working text reinforces the claim that arithmos names the Pythagorean experience of number as divine archetype, marking the transition from primitive to Hellenic psychic streams.
, The Psyche in Antiquity, Book One Early Greek Philosophy thesis
For Pythagoras it was arithmos (number) and the tetractys (the divine image of quarternity).
Edinger catalogues arithmos alongside the tetractys as Pythagoras's contribution to the archetypal vocabulary of Greek philosophy, positioning it as one of the religion-creating concepts of the collective unconscious.
, The Psyche in Antiquity, Book One Early Greek Philosophy thesis
The whole universe is harmony and number, arithmos.... The tetractys has withi
Citing Burkert on the Pythagorean tetractys, Edinger demonstrates that arithmos is cosmological: the universe itself is constituted as harmony and number, making arithmos the structural principle of reality.
, The Psyche in Antiquity, Book One: Early Greek Philosophy From Thales to Plotinus, 1999thesis
We find in Homer contrasts between the andron arithmos, the denumerable company of heroes whose story can therefore be told, and the demos apeiron, the mass of the undemarcated, whose lives will never be grasped.
Nussbaum traces arithmos to its Homeric roots, where the denumerable hero-company stands opposed to the boundless undifferentiated mass, establishing number as the condition of definite identity, narrative, and cognitive grasp.
, The Fragility of Goodness: Luck and Ethics in Greek Tragedy and Philosophy, 1986thesis
The diagonal of the square would then be the square root of 2, a result which was termed a logos arithmos, an irrational number. It is a number which cannot be precisely delineated: 1.4142136..., with no conclusion.
Edinger introduces the concept of logos arithmos — the irrational number — as a disturbing limit within the Pythagorean system, where arithmos encounters what resists perfect numerical expression.
, The Psyche in Antiquity, Book One: Early Greek Philosophy From Thales to Plotinus, 1999supporting
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 that all things are number enacts a focus on pure quantity at the expense of quality, a move he links structurally to the logic of monetary valuation in early Greek commerce.
, Money and the Early Greek Mind: Homer, Philosophy, Tragedy, 2004supporting
Philolaus claims that knowing involves limiting (13b) and that 'all things that are known have number. For it is not possible that anything whatsoever be understood or known without this'.
Seaford cites Philolaus to show that within the Pythagorean tradition arithmos is the epistemic condition of all knowledge — to know is to number, and what cannot be numbered cannot be known.
, Money and the Early Greek Mind: Homer, Philosophy, Tragedy, 2004supporting
A world consisting of a pair of basic opposites, informed by harmony and defined by number.
Seaford, citing Burkert on Philolaus, characterizes the Pythagorean cosmos as one in which number (arithmos) is the defining principle ordering a world of opposing limit and unlimited.
, Money and the Early Greek Mind: Homer, Philosophy, Tragedy, 2004supporting
The fifth-century Prometheus Bound calls numbering 'chief of all the stratagems', expressing a popular view that number is somehow a, or even the, chief element in techne, or the techne par excellence.
Nussbaum demonstrates the cultural centrality of arithmos in fifth-century Greek thought, where number is celebrated as the supreme cognitive instrument — the foundation of all techne.
, The Fragility of Goodness: Luck and Ethics in Greek Tragedy and Philosophy, 1986supporting
All number has also an elevating effect; it raises the mind out of the foam and flux of generation to the contemplation of being.
Plato's Republic frames arithmetic — the study of arithmos — as an anagogic discipline that lifts the soul from the flux of becoming toward the stable realm of pure being.
, Republic, -380supporting
arithmos (number), 23. See also Pythagoras
An index entry in Edinger's volume confirms arithmos as a formally designated key term, directing readers to the Pythagorean discussion and cross-referencing it as a technical concept within the work.
, The Psyche in Antiquity, Book One: Early Greek Philosophy From Thales to Plotinus, 1999aside
The mystery of number and the mystery of music were akin. There was a music of rhythm and of harmonious motion everywhere.
Plato's Timaeus commentary articulates the Pythagorean confluence of arithmos and music, placing number at the heart of cosmic harmony and showing its reach across the visible and invisible orders.
, Timaeus, -360supporting
It is in early Pythagoreanism, if anywhere, that we might expect to find sublimation of the concrete plurality inherent in commerce and practical politics.
Seaford proposes that early Pythagoreanism, with its elevation of arithmos, represents a sublimation of the concrete numerical practices of commerce and politics into metaphysical doctrine.
, Money and the Early Greek Mind: Homer, Philosophy, Tragedy, 2004aside