International large-scale assessments like the Programme for the International Assessment of Adult Competences (PIAAC) assess literacy and numeracy proficiency as abstract competences, assuming they are cognitive skills and therefore objectively and universally measurable. However, research into how people's lives are affected by notions of "literacy" and "numeracy" has shown that both are influenced by social conventions and expectations which are embedded in power relations and ideology. Competences and practices are situated in their social context, and they are products of historical processes which include their construction through the way they are referred to by both experts and the general public. The purpose of this article is to look at literacy and numeracy from a post-structural point of view, questioning the individualised understanding of literacy and numeracy as abstract competences which people simply "have". The author explores the possibility of viewing these basic competences as constructed through how they are actively performed (e.g. when someone engages in reading, writing or calculating for a particular purpose in a particular context) and referred to (e.g. when someone is pronounced "literate" or "competent"). The author points out that being acknowledged and addressed as competent and literate opens up possibilities, just as being viewed as lacking these competences can allow access to (learning) opportunities. Simultaneously and ambivalently, constructed notions of competence both liberate and subordinate individuals. They create power relations and vulnerabilities which often remain unacknowledged.