Brentano's mathematical foundation of science

I examine Brentano's strategic positioning between German Idealism and British Empiricism, exemplified by Kant and Mill, focusing on the idea of mathematics as foundational science. For Brentano mathematics is both logically and chronologically prior to all other sciences. However, the 1874 Psychologie vom empirischen Standpunkte does not give a complete enough picture of Brentano's philosophy of mathematics, discussion of which must be based on textual evidence from his lecture notes and manuscripts, particularly Megethologie. Here Brentano clarifies that mathematics is not inductive, but a purely deductive and a priori science. Against Mill, Brentano argues that induction in the sciences is justified by the calculus of probability, which is founded on a priori mathematical deduction. Through the analysis of Brentano's mathematical foundations of science and comparative analysis of his critique of Kant and Mill, we can better understand Brentano's project of philosophy as science.