 The multiple range (“multi–range”) theory is a semantic theory of vagueness that purports to retain classical logic and  bivalence.[8] Here, the vagueness of an expression consists in its having multiple equally permissible, arbitrarily different ways of being applied, relative to a given context (Raffman 2014: ch.4). In a sorites series, the vagueness of a term is reflected in its possession of multiple equally permissible, arbitrarily different places to stop applying it. Any adequate theory of vagueness must acknowledge the existence of permissible stopping places in a sorites series, since competent users of a vague term are required to stop applying it before the end. For example, in a sorites series of ages proceeding from a clearly old age of 90 to a clearly middle-aged (hence not old) age of 50, say for Americans in 2018—make the context as fine-grained as you like—speakers can permissibly stop applying ‘old’ at 70, or at 67, or 65, or 63.5,  etc.[9]  Different speakers will stop at different ages, and the same speaker will stop at different ages on different occasions. Any particular stopping place in the series is arbitrary, hence without legislative force; speakers cannot justifiably charge each other with error when they stop at different places. In contrast, a boundary would be legislative; speakers who failed to stop applying ‘old’ at its boundaries would be making mistakes. The distinction between boundaries and permissible stopping places is a cornerstone of the multi–range approach.