 The habilitation thesis is divided into two parts. In the first part, Stumpf examines two antagonistic positions which prevailed at the time, namely J. S. Mill’s empiricism according to which there is no knowledge that is not mediately acquired by induction, and Kantian transcendentalism which claims that our knowledge of the general principles of mathematics is based on synthetic a priori judgments. Stumpf rejects both accounts and seeks to show, in the second part of his thesis, that axioms and mathematical propositions are analytic a priori; they are not acquired through experience but are the result of a process of deduction from concepts.