Primacy of the Universal Quantifier in Frege's Concept-Script

Abstract

This paper presents three explanations of why Frege 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---especially the concepts of 0 and 1---in purely logical terms.