The training method taught by the Ancient Order of the Culdees of Iona is called the Quaternary or Fourfold Path.

The Quaternary is described by John Scotus Eriugena in his homily called Voice of the Eagle as, ".a certain intelligible world, constituted of its four parts, its four elements. Whose earth, as it were, in the midst, at the lowest point, like a center, is history. Surrounding it, like the waters, is the abyss of moral understanding, that the Greeks are wont to call Ethike. And in this intelligible world, around these two, as it were, lower parts, that I have called history and ethics, floats what I call natural knowledge or knowledge of nature, that the Greeks called physike. Rolled around, outside and beyond all, is the celestial and burning fire of the empyrean heaven, that sublime contemplation that the Greeks named "theology," beyond which no intelligence passes."

The four elements of the Quaternary or Fourfold Path are History, Ethics, Natural Science and Theology.

The first element is History, which has two parts, mundane and divine. Mundane history shows the student the vain and impermanent nature of all temporal activity. Divine history, or the Myths, teaches us useful lessons though example, symbol and allegory that pertain to all four levels of our spiritual experience.

The second element is Ethics wherein we learn through careful training in Reason and the Four Cardinal Virtues, to live and act in natural harmony with the Universe, our fellow creatures, and the Divine. With concentrated training in rational ethics we gain peace of mind and generate in ourselves what Pythagoras called Universal Friendship.