Understanding and ad hoc Explanation: A Case of Russell’s Reducibility Axiom - V. V. Tselishchev; A. V. Khlebalin (Омский научный вестник: Серия "Общество. История. Современность")
The article examines the common interpretation of the axiom of reducibility in Principia Mathematica according to which the axiom cannot be considered as logical, which casts doubt on the success of the program of logicism. In particular, the ad hoc character attributed to the reducibility axiom is refuted and its explanatory role in substantiating Russell’s uniform approach to resolving set-theoretic and semantic paradoxes is affirmed. The key emphasis in the explanatory nature of the axiom of reducibility is placed on the intensional interpretation of mathematical discourse.