Most substantive (content-bearing) words are polysemous, but polysemy is cross-categorial; for instance, the lexical forms ‘stone’ and ‘front’ are associated with families of interrelated senses and these senses are spread across their manifestations as three words, noun, verb and adjective. So, the ultimate unit underpinning polysemy is not a word but the categoryless root of the related words, which must, in some sense, track the interrelated families of senses. The main topic of this paper is the vexed question of the (...) meaning of roots and the backdrop is a view of words as delineated syntactic domains which allow assignment of atomic content (non-compositional meaning), and whose actual meanings are, in the first instance, pragmatically inferred in the throes of communication, some of them subsequently becoming established, so stored in a lexicon and directly retrieved in comprehension. Three different positions on the meanings of roots are outlined, and their merits and shortcomings are discussed: (a) inherent underspecified meanings; (b) meanings conditioned by grammatical context (allosemy); (c) meaninglessness. I argue that, overall, the current state of the evidence favours the third position: roots are categoryless, meaningless (perhaps phonological) indices. (shrink)