Of triadic Being the multitude of forms is so terrific that I have usually shrunk from the task of enumerating them;  and for the present purpose such an enumeration would be worse than superfluous:  it would be a great inconvenience.

C.S. Peirce, Collected Papers, CP 6.347

A triadic relation (or ternary relation) is a special case of a polyadic or finitary relation, one in which the number of places in the relation is three.  One may also see the adjectives -adic, -ary, -dimensional, or -place being used to describe these relations.

Mathematics is positively rife with examples of triadic relations and the field of semiotics is rich in its harvest of sign relations, which are special cases of triadic relations.  In either subject, as Peirce observes, the multitude of forms is truly terrific, so it’s best to begin with concrete examples just complex enough to illustrate the distinctive features of each type.  The discussion to follow takes up a pair of simple but instructive examples from each of the realms of mathematics and semiotics.

Resources

• Relation Theory
• Triadic Relations
• Sign Relations
• Survey of Relation Theory
• Peirce’s 1870 Logic Of Relatives

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