“A trichotomy is a three-way classificatory division. Some philosophers pursued trichotomies.
Important trichotomies discussed by Aquinas include the causal principles (agent, patient, act), the potencies for the intellect (imagination, cogitative power, and memory and reminiscence), and the acts of the intellect (concept, judgment, reasoning), with all of those rooted in Aristotle; also the transcendentals of being (unity, truth, goodness) and the requisites of the beautiful (wholeness, harmony, radiance).
Kant expounded a table of judgments involving four three-way alternatives, in regard to (1) Quantity, (2) Quality, (3) Relation, (4) Modality, and, based thereupon, a table of four categories, named by the terms just listed, and each with three subcategories. Kant also adapted the Thomistic acts of intellect in his trichotomy of higher cognition—(a) understanding, (b) judgment, (c) reason—which he correlated with his adaptation in the soul’s capacities—(a) cognitive faculties, (b) feeling of pleasure or displeasure, and (c) faculty of desire—of Tetens’s trichotomy of feeling, understanding, will. In his Logic Kant notes that all “polytomy are empirical” and “cannot be taught in logic”.
Hegel held that a thing’s or idea’s internal contradiction leads in a dialectical process to a new synthesis that makes better sense of the contradiction. The process is sometimes described as thesis, antithesis, synthesis. It is instanced across a pattern of trichotomies (e.g. being-nothingness-becoming, immediate-mediate-concrete, abstract-negative-concrete); such trichotomies are not just three-way classificatory divisions; they involve trios of elements functionally interrelated in a process. They are often called triads (but ‘triad’ does not have that as a fixed sense in philosophy generally).
Charles Sanders Peirce built his philosophy on trichotomies and triadic relations and processes, and framed the “Reduction Thesis” that every predicate is essentially either monadic (quality), dyadic (relation of reaction or resistance), or triadic (representational relation), and never genuinely and irreducibly tetradic or larger.”
“…a series of 12 papers Freud composed during World War I, only some of which were published in his lifetime. Their general findings appeared in two books in the 1920s: Jenseits des Lustprinzips (1920; Beyond the Pleasure Principle) and Das Ich und das Es (1923; The Ego and the Id).
In these works, Freud attempted to clarify the relationship between his earlier topographical division of the psyche into the unconscious, preconscious, and conscious and his subsequent structural categorization into id, ego, and superego…
…The last component in Freud’s trichotomy, the superego, develops from the internalization of society’s moral commands through identification with parental dictates during the resolution of the Oedipus complex. Only partly conscious, the superego gains some of its punishing force by borrowing certain aggressive elements in the id, which are turned inward against the ego and produce feelings of guilt. But it is largely through the internalization of social norms that the superego is constituted, an acknowledgement that prevents psychoanalysis from conceptualizing the psyche in purely biologistic or individualistic terms…”