Corporations, development organisations and governments have launched ambitious programmes to 'connect the unconnected', reasoning that this creates economic growth and inclusive development. This paper contrasts these actors' discourses with evidence from academic research. The evidence suggests a highly uneven economic impact of Internet connectivity across geographies and social strata. The analysed sources of discourse (African ICT policies and reports by international organisations) instead propose Grand Visions of connectivity, attributing a self-evident positive, widespread, and transformational impact to the Internet. We discuss technological determinism, acontextual modernism, and optimistic simplism as underlying this contrast, calling for more reflexivity towards the opportunities of 'digital development'.