sentences:  In 1925, Frank Plumpton Ramsey argued that it is not needed.However in the second edition of Principia Mathematica (1927, page xiv) and in Ramsey's 1926 paper it is stated that certain theorems about real numbers could not be proved using Ramsey's approach.Most later mathematical formalisms (Hilbert's Formalism or Brower's Intuitionism for example) do not use it.