The problem with the Axiom of Separation is not with the obviousness of the principle; it seems straightforward to accept that if one has a set of objects, one can separate off a subclass of this set by specifying a property, and treat this in turn as a set. The question here is a subtler one, namely that of how to formulate this principle as an axiom. What means of ‘separating off’ are to be accepted? What are allowable as the properties? As a matter of practice, we use a language to state the properties, and in informal mathematics, this is a mixture of natural language and special mathematical language. The Richard Paradox (see Richard 1905 and also the papers of Poincaré 1905, 1906a,b) makes it clear that one has to be careful when defining properties, and that the unregulated use of ‘ordinary language’ can lead to unexpected difficulties.