Frank Plumpton Ramsey (1903–1930), a brilliant Cambridge philosopher and logician, attempted to give a satisfactory account of the foundations of mathematics in accordance with the method of Frege, Russell, and Whitehead, defending their view that mathematics is logic while proposing revisions in the system of Principia Mathematica suggested by the work of Wittgenstein.

According to Russell, pure mathematics consists of "the class of all propositions of the form 'p implies q' where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants" (The Principles of Mathematics, p. 3). Ramsey agreed with this definition insofar as it characterizes the generality that is a feature of pure mathematics, but he claimed that it takes no account of an equally important mark of mathematics, its tautological character. The term tautological in the relevant sense...