adicity

Definitions

1. The number of arguments or operands a function or operation takes. For a relation, the number of domains in the corresponding Cartesian product.
2. Valence.
   obsolete

Equivalents

Examples

“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.”

CEFR level