INCOMPLETE SYMBOLS IN PRINCIPIA MATHEMATICAz AND RUSSELL’S “DEFINITE PROOF”

Early in Principia Mathematicaz Russell presents an argument that “z‘the author of Waverleyz’ means nothing”, an argument that he calls a “deWnite proofz”. He generalizes it to claim that deWnite descriptions are incomplete symbols having meaning only in sentential context. This Principiaz “proofz” went largely unnoticed until Russell reaUrmed a near-identical “proofz” in his philosophical autobiography nearly 50 years later. The “proofz” is important, not only because it grounds our understanding of incomplete symbols in the Principiaz programme, but also because failure to understand it fully has been a source of much unjustiWed criticism of Russell to the eTect that he was wedded to a naïve theory of meaning and prone to carelessness and confusion in his philosophy of logic and language generally. In my paper, I (1) defend Russell’s “proofz” against attacks from several sources over the last half century, (2) examine the implications of the “proofz” for understanding Russell’s treatment of class symbols in Principia, and (3) see how the Principiaz notion of incomplete symbol was carried forward into Russell’s conception of philosophical analysis as it developed in his logical atomist period after 1910.