Merely to say that Peirce was extremely fond of placing things into groups of three, of trichotomies, and of triadic relations, would fail miserably to do justice to the overwhelming obtrusiveness in his philosophy of the number three.
Indeed, he made the most fundamental categories of all “things” of any sort whatsoever the categories of “Firstness,” “Secondness,” and “Thirdness,” and he often described “things” as being “firsts” or “seconds” or “thirds.”
For example, with regard to the trichotomy “possibility,” “actuality,” and “necessity,” possibility he called a first, actuality he called a second, and necessity he called a third. Again: quality was a first, fact was a second, and habit (or rule or law) was a third. Again: entity was a first, relation was a second, and representation was a third. Again: rheme (by which Peirce meant a relation of arbitrary adicity or arity) was a first, proposition was a second, and argument was a third.
The list goes on and on. Let us refer to Peirce’s penchant for describing things in terms of trichotomies and triadic relations as Peirce’s “triadism.”
[Original longer title: Identifying the Conceptual and Practical Power of Christopher Alexander’s Theory and Practice of Wholeness: Clues as Provided by British Philosopher J. G. Bennett’s Systematics of the Triad] David Seamon Department of Architecture Kansas State University Manhattan, KS 66506 email@example.com www.arch.ksu.edu/seamon
Bennett provides a simple example of the triad of interaction in everyday experience: “I am sitting in my study on a cold winter evening and do not notice that the fire has burnt low until my body experiences a sensation of cold. My attention being thus drawn to the fire, I get up, take a poker and poke the fire. When I see that it is burning up, I return to my chair and continue reading.
“The whole event is a cycle of interactions, beginning and ending with the bodily sensations of cold and heat. It can be broken down into a series of triads, starting with my reaction to the sensation of cold. Here the physical sensation links the fall of temperature with my getting up and taking the poker. The environment is active and my body is passive; sensation is the reconciling impulse. When I get up and poke the fire, my body is active, the fire is passive, and the poker transmits the reconciling impulse. When I begin to feel warm again, the fire is active, my body is passive and the radiation of the fire and the wamr air of the room transmit the reconciling impulse.
“The roles of the different objects—air, body, poker, fire—change from one triad to the other. There is neither expansion nor concentration but a change in the distribution of energy. The event can be thus analyzed in greater or less detail, but it will always prove to consist of a nexus of triads in which one entity is acting on another through the medium of a third.
In Ancient Egyptian theology, divine triads were used to express the divine family-unit, usually composed out of Pharaoh (the son) and a divine couple (father & mother), legitimizing his rule as divine king. Pharaoh Akhenaten had introduced a monotheistic triad (exclusive and against all other deities) : Aten, Akhenaten and Nefertiti. In Heliopolis, the original triad was Atum, Shu and Tefnut, in Memphis, Ptah, Sekhmet and Nefertem emerged, whereas Thebes worshipped Amun, Mut and Khonsu. The trinity naturally developed into three or one Ennead.
In Hermetic triad reads as :
God, the Unbegotten One, the essence of being, the Father of All – the “Decad” ;
Nous, the First Intellect, the Self-Begotten One, the Mind or Light of God – the “Ennead” ;
Logos, the “son” from “Nous”, the Begotten One above the Seven Archons – the “Ogdoad”.
The One Entity or God (the “Tenth”) is known to Its creation as the One Mind or Hermes which contains the “noetic” root of every individual existing thing (cf. Plato, Spinoza). This Divine Mind (the attributes or names of the nameless God) allows all things to be sympathetic transformations (adaptations, modi) of God.
Tetraktys (Tetractys) of the Decad, The Monadic Values: There is no doubt that Sethian Gnostics applied the principles of this paradigm. ”Pythagorus considered all things relative to numbers… How he conceived this process has never been satisfactorily explained.” (Bullfinch, pg. 289.) Perhaps this is the secret….
Pythagorus considered the monad as the source of all things. In the case of the tetraktys of the decad, the concepts of form and structure are related in mathematical values. These values work in harmony. They are not just a list, they are a set. The first and most obvious is numerical value is the digital sequence of one through ten. ‘Monad,’ 2. Decad, 3. Triad, 4. Tetrad, 5. Pentad, 6. Hexad, 7. Heptad, 8. Ogdoad, 9. Ennead, and 10. Decad.