  Ramsey’s first major self-assigned task in the foundations of mathematics was indeed to revise Whitehead and Russell’s Principia Mathematica, partly in the hope that his version would meet some of Wittgenstein’s criticisms of its axioms and treatment of identity, but also because of some further defects he diagnosed in its treatment of the paradoxes and in its inability properly to account for the ‘extensionality’ of mathematics (1925a, [PP] 177–178). For further details about the content of the following paragraph, see the entry for Principia Mathematica.