Our outrageous idea concerns the very core of the Semantic Web { the (lack of) semantics themselves. In Section 1 we claim that the presently used conception of web semantics fails to capture the link between the machine-readable descriptions and their actual meaning (in the sense of a formal grounding in reality). We also argue that this is inherently related to culprits of various difficulties the community has been coping with (e.g., knowledge acquisition bottleneck or data integration challenges). In Section 2 we propose a remedy of this unsatisfactory state of aairs { a broadened notion of emergent web meaning that can be derived in a bottom-up manner from the web data using principles of distributional semantics. Section 3 gives an overview of a preliminary solution [1] we recently implemented with promising results. Finally, we outline directions of future research required to fully realise our vision.