 To complete his project Russell needed to find definitions and some “very small number of fundamental logical principles” (Russell 1903, xv) and then produce the required derivations. Finding an adequate definition of classes with the “no-classes theory” and the principles of logic needed to derive the properties of numbers and classes was only completed with Principia Mathematica (Whitehead and Russell 1910–13). This construction of numbers was a clear example of defining entities as classes of others so as to be able to prove certain properties as theorems of logic rather than having to rest with the theft of hypotheses. With the device of contextual definition from the theory of descriptions Russell then eliminated classes too, taking as fundamental the logical notion of a propositional function and so showing that the principles of classes where a part of logic. 