  Peirce’s so-called “Reduction Thesis” is the thesis that all relations, relations of arbitrary adicity, may be constructed from triadic relations alone, whereas monadic and dyadic relations alone are not sufficient to allow the construction of even a single “non-degenerate” (that is: non-Cartesian-factorable) triadic relation. Although the germ of his argument for the Reduction Thesis lay in his 1873 [1870] paper “Description of a Notation for the Logic of Relatives,” the Thesis was for over a century doubted by many, especially after the publication of a proof by Willard Van Orman Quine that all relations could be constructed exclusively from dyadic ones. As it turns out, both Peirce and Quine were correct: the issue entirely depends on exactly what constructive resources are to be allowed to be used in building relations out of other relations. (Obviously, the more extensive and powerful are the constructive resources, the more likely it is that all relations can be constructed from dyadic ones alone by using them.) An exact exposition and proof of Peirce’s Reduction Thesis was finally accomplished in 1988 (Burch 1991), and it makes clear that Peirce’s constructive resources are to be understood to include only negation, a generalization of de Morgan’s relative product operation, and the use of a particular triadic relation that Peirce called “the teridentity relation” and that we might today write as x = y = z.