LOGICAL ELEMENTS OF J. S. MILL’S EMPIRICAL MATHEMATICS

Abstract

This article examines the relation between logical and mathematical elements in the empiristic doctrine of John Stuart Mill, as it is expounded in his System of Logic. With his understanding of logic as the science of human scientific knowledge based on experience, Mill substituted the idea of a general notion with the idea of a particular name and its connotative and denotative definition, and superimposed inductive over deductive reasoning, asserting the former as a prerequisite of the latter. Establishing the particular as basis of all knowledge facilitates the reevaluation of the status of mathematical knowledge. In Mill’s system, mathematical definitions are just hypothetical names and mathematical postulates are generalizations from all experience. Therefore, there can be no specific mathematical method, and mathematics may only be considered fundamental because it deals with relations that exist between all real objects, not because its laws are neccessary and universal aprioristic truths.