One of the traditional assumptions of CS is the non-existence of polysemy, which is explored the article "Monosemy, homonymy and polysemy" (pp. 93-129) by Wallis Reid. The prepositions 'at', 'in' and 'on' are chosen for an exemplification of the reduction of traditionally polysemous signs to one single-meaning items. Each of them is postulated to have one single abstract meaning (similar to the schematic meanings suggested by CG) based on the number of dimensions that they conceptualize: in encompasses three dimensions in location, on more than zero and less than three, and at involves zero dimensions. Through the application of metaphor as described by cognitive grammarians, these meanings are transferred to the temporal sphere and to abstract domains. The abundant examples and discussions clarify the suitability of the meanings sketched and how they can account for the description of the three prepositions without resorting to polysemy. This article also illustrates some bridges of cooperation between CG and CS, such as the adoption of CG's view of metaphor (Asunción Villamil)