Before now, there has been no comprehensive analysis of the multiple relations between A. Comte´s and J.S. Mill´s positive philosophy and Franz Brentano´s work. The present volume aims to fill this gap and to identify Brentano´s position in the context of the positive philosophy of the 19th century by analyzing the following themes: the concept of positive knowledge; philosophy and empirical, genetic and descriptive psychology as sciences in Brentano, Comte and Mill; the strategies for the rebirth of philosophy in these three authors; the theory of the ascending stages of thought, of their decline, of the intentionality in Comte and Brentano; the reception of Comte´s positivism in Whewell and Mill; induction and phenomenalism in Brentano, Mill and Bain; the problem of the "I" in Hume and Brentano; mathematics as a foundational science in Brentano, Kant and Mill; Brentano´s critique of Mach´s positivism; the concept of positive science in Brentano´s metaphysics and in Husserl´s early phenomenology; the reception of Brentano´s psychology in Twardowski; The Brentano Institute at Oxford. The volume also contains the translation of the most significant writings of Brentano regarding philosophy as science.