The Primacy of the Universal Quantifier in Frege’s Concept-Script

  • Jongool Kim
Keywords: Universal quantifier, existential quantifier, logicism, the number 0, the number 1, existence

Abstract

This paper presents three explanations of why Frege, the inventor of modern logic, took the universal, rather than the
existential, quantifier as primitive in his formalization of logic. The first two explanations provide technical reasons related to how
Frege formalizes the logic of truth-functions and the logic of quantification. The third, philosophical explanation locates the reason
in Frege’s logicist goal of analyzing arithmetical concepts, including the concepts of 0 and 1, in purely logical terms.

Published
2021-11-02
Section
Articles