This article argues that existing systems on the Web cannot approach human-level intelligence, as envisioned by Descartes, without being able to achieve genuine problem solving on unseen problems. The article argues that this entails committing to a strong intensional logic. In addition to revising extant arguments in favor of intensional systems, it presents a novel mathematical argument to show why extensional systems can never hope to capture the inherent complexity of natural language. The argument makes its case by focusing on (...) representing, with increasing degrees of complexity, knowledge in a first-order language. Nevertheless, the attempts at representation fail to achieve consistency, making the case for an intensional representation system for natural language clear. (shrink)