It is argued that signed communication systems differ from spoken ones in having not one but two structured systems of representation. In addition to the linguistic mode (which is shared with spoken communication, and which appears to be fundamentally identical across spoken and signed modalities), signers also command distinctive, formal systems of schematic visual representation. These are the forms of signing known as classifier predicates. For the past two decades, signed classifier predicates have been modeled as linguistic. However, the basic formal units of such signing, the combination of these units, and their breakdown, all differ both from patterns seen in other signed forms that have long been recognized as linguistic, and from the classic patterns of language in general. Classifier predicates continue to be modeled as linguistic mostly on the basis of assumptions about alternatives, specifically about the form and acquisition of systems of visual-spatial representation. These assumptions are shown to be incorrect. Signed classifiers are shown to correspond in many respects not merely to visual representation, but to a particular strategy of depiction known as schematic visual representation. This is the mode of depiction that appears to be most natural for both children and adults to master, and that is commonly seen in drawing. There is thus strong evidence that in signed language classifiers we have what, from the point of view of traditional (spoken-language based) linguistics, is a qualitatively new communication mode: formal, structured systems of visual representation that exist side-by-side with linguistic modalities, within the total signed communication system.