A trichotomy is a three-way classificatory division pursued by some philosophers.
History 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 desireKant, Immanuel, The Critique of Judgment, 2007 edition, Cosimo Classics, pp. 10-11.—of Tetens's trichotomy of feeling, understanding, and will.Teo, Thomas (2005), The critique of psychology: from Kant to postcolonial theory, p. 43. In his Logic (113) Kant notes that all "polytomy are empirical" and "cannot be taught in logic".Kant I., (1800), Logic (Logik), tr. J. Richardson London, 1819, p.209. In preparation he states "A division into two members goes under the appelation of dichotomy; but it, when consisting of more than two, takes the name of poytomy".
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.
Examples Plato's 3 parts of manPlato, Timaeus, 30. Nous (mind, intellect). Psyche (soul). Soma (body). Plato's 3 transcendentals Truth (logic, verum). Goodness (ethics, bonum). Beauty (aesthetics, pulchrum). Plato's tripartite soul Logistikon (logical, rational). Thymoeides (spirited, various animal qualities). Epithymetikon (appetitive, volitive, libidinous, desiring). Aristotle's 3 kinds of soul Threptike (nutritive, vegetative). Aisthetike (sensitive, animal). Noetike (rational, human). Aristotle's 3 main modes of persuasion Ethos. Pathos. Logos. Plotinus' three principles (3rd century CE) The One. Nous (mind, intellect). Psyche (soul). Shema'''s 3 elements of man || 1] לב (lev) /Kardia (heart). 2] נפׁש (nephesh) /Psyche (soul). 3] מְאֹד (me'od) /Dynamis (power)Petersen, W.L. 2011. Patristic and Text-Critical Studies: The Collected Essays of William L. Petersen. Brill: Leiden. p. 229. link.Davies, W.D., Allison, D.C. A Critical and Exegetical Commentary on the Gospel According to Saint Matthew. T&T Clark, 1988-1997, 3 vols. link. [vol 3, p. 241.] |- | Saint Paul's tripartite nature of humanity (I Thes. 5:23) || Pneuma (spirit). Psyche (soul). Soma (body).(Paul uses alternative concepts in other passages: kardia [heart], eso kai exo anthropos [inner and outer human being]; nous [mind]; suneidesis [conscience]; sarx [flesh]).Crandall University. Pauline anthropology. . |- | Valentinian gnosticism's three classes of man (2nd century CE) || the , the , and the : "[...] a specifically Valentinian idea is here added in that of the threefold nature of man, who is represented as at once spiritual, psychical and material. In accordance with this there also arise three classes of men, the pneumatici, the psychici and the hylici (van, matter)." |- | Saint Augustine's 3 LawsAugustine through the Ages (1999), p. 582. || Divine Law. Natural Law. Temporal, Positive, or Human Law. |- | Saint Augustine's 3 features of the soulSaint Augustine of Hippo, De Trinitate, 10, 11; Encyclopedia of Christian Theology, Volume 1 (2004), page 54. See Saint Augustine of Hippo, De Trinitate, 14. Saint Thomas Aquinas, OP explains that Saint Augustine does not identify these 3 features as "powers" of the soul. Saint Thomas Aquinas, OP, Summa Theologiae, Prima Pars, Q. 79, A. 7, ad 1. (5th century CE) || Intellect. Will. Memory. (Saint John of the Cross, OCD follows this also, but may erroneously identify them as 3 distinct powers.Saint John of the Cross, OCD, Doctor, The Ascent of Mount Carmel, Book 2, Chapter 6, §1.) |- | Saint Albertus Magnus' 3 Universals"St. Albertus Magnus" in the Catholic Encyclopedia. Eprint.||Ante rem (Idea in God's mind). In re (potential or actual in things). Post rem (mentally abstracted). |- | Saint Thomas Aquinas, O.P.'s 3 causal principlesSee The Pocket Aquinas (1991). (based in Aristotle) || Agent. Patient. Act. |- | Aquinas' 3 potencies for intellect (based in Aristotle) || Imagination. Cogitative power (or, in animals, instinct). Memory (and, in humans, reminiscence). |- | Aquinas' 3 acts of intellect (based in Aristotle) || Conception. Judgment. Reasoning. |- | Aquinas' 3 transcendentals of being|| Unity. Truth. Goodness. |- | Aquinas' 3 requisites for the beautiful|| Wholeness or perfection. Harmony or due proportion. Radiance. |- | Sir Francis Bacon's 3 Tables"Francis Bacon, Viscount Saint Alban", Britannica.com Eprint || Presence. Absence. Degree. |- | Bacon's 3 faculties of mind || Memory. Reason. Imagination. |- | Bacon's 3 branches of knowledge|| History. Philosophy. Poetry. (Inspired the figurative system of human knowledge of Diderot and d'Alembert.) |- | Thomas Hobbes' 3 Fields || Physics. Moral Philosophy. Civil Philosophy. |- | John Dryden's 3 ways of transferring || Metaphrase. Paraphrase. Imitation. |- | Christian Wolff's 3 special metaphysics || Rational psychology. Rational cosmology. Rational theology. |- | Kant's 3 faculties of soul || Faculties of knowledge. Feeling of pleasure or displeasure. Faculty of desire (which Kant regarded also as the will). |- | Kant's 3 higher faculties of cognition || Understanding. Judgment. Reason. |- bgcolor=#eeeeee | Kant's 3 judgments of quantity ||Universal. Particular. Singular |- | Kant's 3 categories of quantity ||Unity. Plurality. Totality |- bgcolor=#eeeeee | Kant's 3 judgments of quality ||Affirmative. Negative. Infinite |- | Kant's 3 categories of quality ||Reality. Negation. Limitation. |- bgcolor=#eeeeee | Kant's 3 judgments of relation ||Categorical. Hypothetical. Disjunctive. |- | Kant's 3 categories of relation || Inherence and subsistence. Causality and dependence. Community. In other words: Substance and accident. Cause and effect. Reciprocity. |- bgcolor=#eeeeee | Kant's 3 judgments of modality ||Problematical. Assertoric. Apodictic |- | Kant's 3 categories of modality ||Possibility. Existence. Necessity |- | Johannes Nikolaus Tetens's 3 powers of mind || Feeling. Understanding. Will. |- |Hannah Arendt's vita activa |Labor, Work, Action |- | Hegel's 3 SpiritsRedding, Paul (1997, 2006), "Georg Wilhelm Friedrich Hegel" in the Stanford Encyclopedia of Philosophy. Eprint. || Subjective Spirit. Objective Spirit. Absolute Spirit. |- | Søren Kierkegaard's 3 stagesMcDonald, William (1996, 2009), "Søren Kierkegaard" in the Stanford Encyclopedia of Philosophy. See Section 6. || Aesthetic. Ethical. Religious. |- | Charles Sanders Peirce's 3 categories || Quality of feeling. Reaction, resistance. Representation, mediation. |- | C. S. Peirce's 3 universes of experience || Ideas. Brute fact. Habit (habit-taking). |- | C. S. Peirce's 3 orders of philosophy || Phenomenology. Normative sciences. Metaphysics. |- | C. S. Peirce's 3 normatives || The good (esthetic). The right (ethical). The true (logical). |- | C. S. Peirce's 3 semiotic elements || Sign (representamen). Object. Interpretant. |- | C. S. Peirce's 3 grades of conceptual clearness || By familiarity. Of definition's parts. Of conceivable practical implications. |- | C. S. Peirce's 3 active principles in the cosmos || Spontaneity, absolute chance. Mechanical necessity. Creative love. |- | Gottlob Frege's 3 realms of senseKlement, Kevin C. (2005), "Gottlob Frege (1848—1925)", Internet Encyclopedia of Philosophy. || The external, public, physical. The internal, private, mental. The Platonic, ideal but objective (to which sentences refer). |- |Sigmund Freud's structural model ||Id, ego, and superego (das „Es“, das „Ich“, das „Über-Ich“'') Edmund Husserl's 3 Reductions Phenomenological. Eidetic. Religious.R. Steiner more threefold aspects.Body, soul and spirit. Imagination, inspiration and intuition. Korzybski's 3 types of life Chemical-binder (i.e. plants). Space-binder (i.e. mammals). Time-binder (i.e. humans). Each one up the scale requires the previous one. James Joyce's 3 aesthetic stagesJoyce, James (1914-1915), A Portrait of the Artist as a Young Man, see Chapter 5, especially (but not only) lines 8215-8221. Arrest (by wholeness). Fascination (by harmony). Enchantment (by radiance).Jacques Lacan's 3 orders Real, Symbolic, and Imaginary Karl Popper's 3 worldsPopper, Karl (1982), The Open Universe: An Argument for Indeterminism. Physical things and processes. Subjective human experience. Culture and objective knowledge Louis Zukofsky's 3 aesthetic elementsZukofsky, Louis, "A" – 12 (1966), and Prepositions (1967, 1981), p. 55. Shape. Rhythm. Style. Maurice Merleau-Ponty's 3 fieldsMerleau-Ponty, Maurice (1942), La structure du comportement, and published in English as The Structure of Behavior. Physical. Vital. Human. Maurice Merleau-Ponty's 3 categories Quantity. Order. Meaning.Eric Berne's transactional analysis (1960s) Parent, Adult, Child Alan Watts' 3 world views Life as machine (Western). Life as organism (Chinese). Life as drama (Indian).
See also Balanced ternary Dichotomy Epistemological pluralism Rule of three (writing) Trilemma Trinity Tripartite motto
Notes
§The list of trichotomies featuring different philosophers was initially influenced by Herb O. Buckland's List which was placed on the Wikipedia years ago but subsequently removed because a complaint was raised about credit not being given to the original author. The original list is here: https://www.threesology.org/3s-poster-5.php. Credit needs to be given where it is due.