Mill also thought that the basic principles of arithmetic and geometry could be proved by induction. He agreed with Isidore Marie Auguste François Xavier Comte (1798–1857) about a unified view of the social sciences, whereby the laws for more general sciences could be derived from what is known about more specific sciences. For example, observations of individual human behavior could result in a science of psychology, and observations of individual psychology could result in a science of society or sociology. It should be noted that much subsequent theoretical work in mathematics and social science did not find Mill’s ideas useful.

Isidore Marie Auguste François Xavier Comte (1798–1857) was famous and influential in his day as a sociologist, and even coined the word “sociologie.” He was the first Western sociologist. Comte has also endured as the founder of positivism.

Comte taught mathematics for a while at l’École Polytechnique in Paris, where he himself was educated. Although mental illness—to the extent of psychotic episodes that required hospitalization—interfered with his work, his condition stabilized enough for him to complete his major work during a marriage that ended in divorce. After the woman he loved in a subsequent platonic relationship died, he formulated his mission to create a new “religion of humanity.” Comte published Cours de philosophie positive (Course in Positive Philosophy) in six volumes from 1830 to 1832.