Relative
Relative
A concept is relative if it is — a word, if it denotes — a polyadic propositional function, or relation, rather than a monadic propositional function. The term relative is applied especially to words which have been or might be thought to denote monadic propositional functions, but for some reason must be taken as denoting relations. Thus the word short or the notion of shortness may be called relative because as a monadic propositional function it is vague, while as a relation (shorter than) it is not vague.
Analogously, the term relative may be applied to words erroneously thought of or used as if denoting binary relations, but which actually must be taken as denoting ternary or quaternary relations, etc. E.g., the Special Theory of Relativity is said to make simultaneity relative because, according to it, simultaneity is a function of two events and a coordinate system or frame of reference — -instead of a function merely of two events, as in the Newtonian or classical theory.
The adjective relative is also used in a less special way, to mean simply relational or pertaining to relations.
In connection with the algebra of relations (see logic, formal, 8), Peirce and Schrder use relative as a noun, in place of relation. For Schrder, a relative (Relativ) is a relation in extension. Peirce makes a distinction between relative and relation, not altogether clear, many passages suggest that relative is a syntactical term, but others approximate the usage adopted by Schrder. — A.C.