by Corry Shores
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[The following is summary. Boldface and bracketed commentary are mine. Proofreading is incomplete, so please forgive my typos.]
Charles Sanders Peirce
Collected Papers of Charles Sanders Peirce
Volume 1: Principles of Philosophy
Book 3: Phenomenology
Chapter 1: Introduction
§3: Monads, Dyads, and Triads [1.293]
Structures of relational bonding between indecomposable parts (“logical relatives”) can only take one of three forms: monadic, dyadic, and triadic. Peirce will now analyze each type as independently as possible from the other forms.
[Logical relatives can only take on of three forms: monad, dyad, and triad. Peirce will now analyze each one.]
Peirce has conducted a thorough study of the logic of relations, and he concludes the following. Logical terms are one of three sorts: monads, dyads, or polyads. But [for some reason] there is no radical difference between triads and other higher valence ‘-ads’ . So there are really just three: monads, dyads, and triads. Peirce will now investigate the monad without reference to dyads and triads. He then will examine dyads, which involve monads, but without reference to triads. And finally he will examine the triad, which involves monads and dyads.
A thorough study of the logic of relatives confirms the conclusions which I had reached before going far in that study. It shows that logical terms are either monads, dyads, or polyads, and that these last do not introduce any radically different elements from those that are found in triads. I therefore divide all objects into monads, dyads, and triads; and the first step in the present inquiry is to ascertain what are the conceptions of the pure monad, free from all dyadic and triadic admixtures; of the dyad (which involves that of the monad) free from all triadic contamination, and what it is that is peculiar which the dyad adds to the monad; and of the triad (which involves those of the monad and dyad) and what it is that is characteristic of the triad.
Peirce, C.S. Collected Papers of Charles Sanders Peirce, Vol 1: Principles of Philosophy. In Collected Papers of Charles Sanders Peirce [Two Volumes in One], Vols. 1 and 2. Edited by Charles Hartshorne and Paul Weiss. Cambridge, Massachusetts: 1965 .