L. WITTGENSTEIN AND F.P. RAMSEY ON IDENTITY (3)
The article examines the concept of a definable class (offered by В. Russell and A. Whitehead in «Principia Mathematica»). Criticism of this concept by F. Ramsey from the point of view of the extensional approach to mathematics is also considered. The practice of mathematical reasoning requires an extensional concept of function and Ramsey replaces defining functions with arbitrary functions. It allows Ramsey to introduce the concept of an extensional function and modify the theory of classes. The Ramsey theory of classes does without the identity sign but is formally equivalent to the system of «Principia Mathematica».