The idea of philosophy as science expands throughout 19th century philosophy; first instantiated by German Idealism's systems in the shape of absolute science which start from pure subjectivity to further gather deductively the entire world under its categories. This idea is later found within the works of Franz Brentano in the form of philosophy as inductive science that has to work according to the method of natural sciences. However, despite this methodological commitment, Brentano did not give up the metaphysical dimension of philosophical research and accepted natural theology as philosophical science. In this way, his inductive-scientific philosophy is fundamentally different from Comte's and Mill's positive philosophy, which purposely bracketed metaphysical problems in order to focus upon the constant relations of phenomena. Within this framework, the volume starts from Brentano's conception of philosophy as science and aims to analyze the source of this idea in Mill and Comte, its criticism and further development by Marty, Stumpf, Meinong,Twardowski, and Husserl, and also the alternative competing views on the topic of Reinhold, Hegel, Schelling, Nietzsche, Kierkegaard, Paulsen, and Dilthey.