Atrichotomy 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[1]—of Tetens's trichotomy of feeling, understanding, and will.[2] In his Logic (113) Kant notes that all "polytomy are empirical" and "cannot be taught in logic".[3]
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.
| Plato's 3 parts of man[4][5] | 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 | The One. The Intellect. The Soul. |
| Shema's 3 elements of man | 1] לב (lev) /Kardia (heart).
2] נפׁש (nephesh) /Psyche (soul). 3] מְאֹד (me'od) /Dynamis (power)[6][7] |
| Saint Paul's tripartite nature of humanity (I Thes. 5:23) | Soma (body). Psyche (soul). Pneuma (spirit). (Paul uses alternative concepts in other passages: kardia [heart], eso kai exo anthropos [inner and outer human being]; nous [mind]; suneidesis [conscience]; sarx [flesh]).[8] |
| Saint Augustine's 3 Laws[9] | Divine Law. Natural Law. Temporal, Positive, or Human Law. |
| Saint Augustine's 3 features of the soul[10] | Intellect. Will. Memory. (Saint John of the Cross, OCD follows this also, but may erroneously identify them as 3 distinct powers.[11]) |
| Saint Albertus Magnus' 3 Universals[12] | 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 principles[13] (based in Aristotle) | Agent. Patient. Act. |
| Aquinas' 3 potencies for intellect[13] (based in Aristotle) | Imagination. Cogitative power (or, in animals, instinct). Memory (and, in humans, reminiscence). |
| Aquinas' 3 acts of intellect[13] (based in Aristotle) | Conception. Judgment. Reasoning. |
| Aquinas' 3 transcendentals of being[13] | Unity. Truth. Goodness. |
| Aquinas' 3 requisites for the beautiful[13] | Wholeness or perfection. Harmony or due proportion. Radiance. |
| Sir Francis Bacon's 3 Tables[14] | 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 knowledgeofDiderot 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[1] | 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[1] | Understanding. Judgment. Reason. |
| Kant's 3 judgments of quantity | Universal. Particular. Singular |
| Kant's 3 categories of quantity | Unity. Plurality. Totality |
| Kant's 3 judgments of quality | Affirmative. Negative. Infinite |
| Kant's 3 categories of quality | Reality. Negation. Limitation. |
| 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. |
| 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[2] | Feeling. Understanding. Will. |
| Hannah Arendt's vita activa | Labor, Work, Action |
| Hegel's 3 Spirits[15] | Subjective Spirit. Objective Spirit. Absolute Spirit. |
| Søren Kierkegaard's 3 stages[16] | 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 sense[17] | The external, public, physical. The internal, private, mental. The Platonic, ideal but objective (to which sentences refer). |
| Sigmund Freud's structural model[5] | 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 stages[18] | Arrest (by wholeness). Fascination (by harmony). Enchantment (by radiance). |
| Jacques Lacan's 3 orders | Real, Symbolic, and Imaginary |
| Karl Popper's 3 worlds[19] | Physical things and processes. Subjective human experience. Culture and objective knowledge |
| Louis Zukofsky's 3 aesthetic elements[20] | Shape. Rhythm. Style. |
| Maurice Merleau-Ponty's 3 fields[21] | Physical. Vital. Human. |
| Maurice Merleau-Ponty's 3 categories[21] | Quantity. Order. Meaning. |
| Eric Berne's transactional analysis | Parent, Adult, Child |
| Alan Watts' 3 world views | Life as machine (Western). Life as organism (Chinese). Life as drama (Indian). |
