Frege’s Result: Frege’s Theorem and Related Matters

Abstract

One of the remarkable results of Frege’s Logicism is Frege’s Theorem, which holds that one can derive the main truths of Peano arithmetic from Hume’s Principle (HP) without using Frege’s Basic Law V. This result was rediscovered by the Neo-Fregeans and their allies. However, when applied in developing a more advanced theory of mathematics, their fundamental principles—the abstraction principles—incur some problems, e.g., that of inflation. This paper finds alternative paths for such inquiry in extensionalism and object theory.