Adicity

1997, Robert W. Burch, 13: Peirce's Reduction Thesis, Nathan Houser, Don D. Roberts, James Van Evra (editor), Studies in the Logic of Charles Sanders Peirce, Indiana University Press, page 233, Equivalently, it says that all relations of adicity greater than 3 may be reduced to relations of adicities 1, 2, and/or 3. The negative component of the Thesis says, first, that relations of adicity 2 may not in general be constructed from (reduced to) relations exclusively of adicity 1; and, second, that relations of adicity 3 and greater may not in general be constructed from (equivalently: reduced to) relations exclusively of adicities 1 and/or 2.

What can be predicted is that the adicity of any syntactic predicate is the same: since its adicity is a grammatical and not a thematic fact, semantic differences between predicates cannot affect their grammatical structure.

2007, Helier J. Robinson, Relation Philosophy of Mathematics, Science, and Mind, Sharebooks Publishing, 2nd Edition, page 68, We have seen that every relation, without exception, necessarily has a term set, and the necessary properties of simplicity and an adicity: relations without these are impossible, merely nominal.