Culler writes: “because the sign is arbitrary, because it is the result of dividing a continuum in ways peculiar to the language to which it belongs, we cannot treat the sign as an autonomous entity but must see it as part of a system. It is not just that in order to know the meaning of brown one must understand red, tan, gray, black , and so on. Rather, one could say that the signifieds of color terms are nothing but the product or result of a system of distinctions. Each language, in dividing up the spectrum and distinguishing categories which it calls colors, produces a different system of signifieds: units whose value depends on their relations with one another.”

What makes us say that various uses of bed are “the same”? It’s not, Culler notes, the sounds we make; accents and voices vary. Nor is the identity found in the referent, since the sign can be used to refer to any number of actual beds that differ in many respects. Phonetically, every use of bed is a use of the same sign because the sign bed stands in differentiation from bad, bud, bid, fed, led, bet, and so on - other similar units within the system. Semantically, bed has an identity in differentiation from sofa, couch, mattress, slab, etc.

Culler suggests that the same applies beyond language; identity is relational: “We are willing to grant that in an important sense the 8:25 Geneva-to-Paris Express is the same train each day, even though the coaches, locomotive, and personnel change from one day to the next. What gives the train its identity is its place in the system of trains, as indicated by the timetable. And note that this relational identity is indeed the determining factor: the train remains the same train even if it leaves a half-hour late. In fact, it might always leave late without ceasing to be the 8:25 Geneva-to-Paris Exprerss. What is important is that it be distinguished from, say, the 10:25 Geneva-to-Paris Express, the 8:40 Geneva-to-Dijon Local, and so on.”
In sum: “We began by noting that there was not natural link between signifier and signified, and then, trying to explain the arbitrary nature of the linguistic sign, we saw that both signifier and signified were arbitrary divisions or delimitations of a continuum . . . . This led us to infer that both signifier and signified must be defined in terms of their relations with other signifiers and signifieds, and thus we reached the conclusion that if we are to define the units of a language, we must distinguish between these purely relational and abstract units and their physical realizations.”