Whitehead's (Badly) Emended Principia. Issue 2 (2nd April 2016) - Landini, Gregory
Abstract : There are many wonderful puzzles concerning Principia Mathematica, but none are more striking than those arising from the crisis that befell Whitehead in November of 1910. Volume 1 appeared in December of 1910. Volume 2 on cardinal numbers and Russell's relation arithmetic might have appeared in 1911 but for Whitehead's having halted the printing. He discovered that inferences involving the typically ambiguous notation 'Nc' α ' for the cardinal number of α (i.e. the class of all classes similar with α ) might generate fallacies. When the volume appeared in 1912, it was extensively emended by Whitehead and accompanied by a Prefatory Statement of Symbolic Conventions. This paper endeavors to recover from Whitehead's bad emendations—including his bewildering thesis that since ' ' α ' is 'true whenever significant, ' ' α is to be accepted. It is supposedly a fallacy to apply Modus Ponens and infer Nc' α from ' α and ' ' α .