  On Russell’s view, vagueness is a feature of language, not of the world. In vague language, there is no one-one relation between propositions and facts, so that a vague statement could be considered verified by any one of a range of different facts (Vag, 217). However, in a properly analyzed proposition, there is a clear isomorphism between the structure of the proposition and the structure of the fact that would make it true (PLA, 197); hence a precise and analyzed proposition is capable of being true in one and only one way (Vag, 219). In analyzing a proposition such as “there are a number of people in this room at this moment”, one might obtain a precise statement which would require for its truth that there is a certain class of sensible particulars related to each other in a very definite way constituting the presence of a room, and certain other classes of sensible particulars related to each other in ways constituting people, and that the sensible particulars in the latter classes bear certain definite relations to those in the first class of particulars.  Obviously, nothing like this is clearly in the mind of a person who would ordinarily use the original English expression. It is clear to see in this case that a very specific state of things is required for the truth of the analyzed proposition, and hence the truth of it will be far more doubtful than the truth of the vague assertion with which one began the process (PLA, 179–80). As Russell put the point, “the point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it” (PLA, 193). 