The so-called ‘Semantic Web’ is phase II of Tim Berners-Lee’s original vision for the WWW, whereby resources would no longer be indexed merely ‘syntactically’, via opaque character-strings, but via their meanings. We argue that one roadblock to Semantic Web development has been researchers’ adherence to a Cartesian, ‘private’ account of meaning, which has been dominant for the last 400 years, and which understands the meanings of signs as what their producers intend them to mean. It thus strives to build ‘silos of meaning’ which explicitly and antecedently determine what signs on the Web will mean in all possible situations. By contrast, the field is moving forward insofar as it embraces Peirce’s ‘public’, evolutionary account of meaning, according to which the meaning of signs just is the way they are interpreted and used to produce further signs. Given the extreme interconnectivity of the Web, it is argued that silos of meaning are unnecessary as plentiful machine-understandable data about the meaning of Web resources exists already in the form of those resources themselves, for applications that are able to leverage it, and it is Peirce’s account of meaning which can best make sense of the recent explosion in ‘user-defined content’ on the Web, and its relevance to achieving Semantic Web goals.