Notation Systems

A notation system, in Goodman's rigorous definition, is a symbolic scheme that satisfies five requirements: syntactic disjointness (every mark belongs to exactly one character), syntactic differentiation (theoretically possible to determine which character any mark belongs to), semantic disjointness (every character's compliance-class is distinct), semantic differentiation (theoretically possible to determine whether an object complies), and unambiguity (every object complies with at most one character). Musical scores and alphabetic writing approximate these requirements; painting and sculpture do not. The function of a notation is to preserve a work's identity across multiple instances—a score allows Beethoven's Ninth to be the same work whether played in Berlin or Vienna, a text allows Hamlet to be the same work in every correctly printed copy. Notation makes allographic art possible by specifying identity-determining features precisely enough that compliance can be determined independently of the work's productive history. The requirements are strict because the function is demanding: if identity is to be preserved across instances, the notation must eliminate ambiguity about what counts as a correct instance. Any looseness in the notation—any