(2005). A proof in this work that a sufficiently strong consistent theory cannot contain its own reference functor is known as the Hilbert–Bernays paradox. In seven papers, published between 1937 and 1954 in the Journal of Symbolic Logic (republished in Müller 1976), Bernays set out an axiomatic set theory whose starting point was a related theory John von Neumann had set out in the 1920s. Von Neumann's theory took the notions of function and argument as primitive. Bernays recast von Neumann's theory so that classes and sets were primitive. Bernays's theory, with modifications by Kurt Gödel, is known as von Neumann–Bernays–Gödel set theory. Publications Notes References . Kneebone, Geoffrey, 1963. Mathematical Logic and the Foundation of Mathematics. Van Nostrand. Dover reprint, 2001. A gentle introduction to some of the ideas in the Grundlagen der Mathematik. External links Hilbert Bernays Project Paul Bernays: A Short Biography (1976) 1888 births 1977 deaths 20th-century Swiss philosophers Institute for Advanced Study visiting scholars Jewish philosophers Jewish scientists Mathematical logicians Philosophers of mathematics Set theorists Swiss Ashkenazi Jews Swiss mathematicians Swiss philosophers Academic staff of ETH Zurich