 Besides the axiom of infinity, AR is an essential tool for reconstructing classical mathematics, but it is a strong existential principle, apparently in conflict with the philosophical idea that logical and mathematical entities are to be constructively generated according to the vicious circle principle. Nonetheless, it was adopted in the (first edition of the) monumental Principia Mathematica, written in collaboration with A.N. Whitehead and published in 1910 (vol. 1), 1912 (vol. 2) and 1913 (vol. 3).