Whitehead's (Badly) Emended Principia. Issue 2 (2nd April 2016)

• Record Type: Journal Article
• Authors: Landini, Gregory
• Is Part Of: History and philosophy of logic. Volume 37:Issue 2(2016)
• Page Start: 114
• Page End: 169
• Publication Date: 2016-04-02
• Subjects: Logic -- Periodicals; 160.905
• DOI: 10.1080/01445340.2015.1082063
• Languages: English
• ISSNs: 0144-5340

Abstract

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 .