This article describes aspects of classroom discourse, illustrated through vignettes, that reveal the complex relationship between the forms in which mathematical objects exist and their ostensive representations. We illustrate various aspects of the process through which students come to consider the reality of mathematical objects that are different to their representations, as well as the use of these different representations. We assume that speaking about the existence of mathematical objects is an essentially metaphorical question and that, under certain circumstances, this metaphorical discourse can pose problems for students' understanding. We draw on some theoretical notions from the onto-semiotic approach and the cognitive science of mathematics.