The descriptive psychological formation of the concept of number

Husserl's pure phenomenology is driven by the goal of making philosophy a rigorous science. By “science” he understood a method of research capable of generating possible true and false propositions on the basis of evidence. By “rigorous” science he understood a science that had advanced to the point of being in the possession of a methodology whose basic concepts and criteria for distinguishing true from false propositions were sufficiently demonstrated to permit an ongoing research agenda available to and embraced by a community of researchers. And by “evidence” he understood the legitimizing source of scientific and philosophical concepts in an experience more original than, but nevertheless related to, their conceptuality. The signal importance of this goal in Husserl's formulation of pure phenomenology cannot be overestimated at any stage of its development. It composes both the most basic intention of his thought and the standard by which he measures the success or failure of its development at any given time.

Husserl did not originally set out to establish a new science whose status as rigorous science would lead to a reform of philosophy. His initial goal was the more modest one of clarifying the most basic concept of arithmetic, number, within the context of a pre-existing philosophical method, that of his teacher Franz Brentano. Brentano's method sought to account for the formation of concepts on the basis of their origin from what appears to perception.