This study -the opening fragment of a forthcoming book entitled Categorías, intencionalidad y número- is divided into three clearly-distinct sections. The first is a commentary on the introduction to Husserl's On the concept of number, which sets forth the very bases which served as the historical starting-point for the research programme of the creator of phenomenology. The second section discusses the problem of the predication of numbers, showing how the theory of the young Husserl is superior to that of Frege in The fundaments of arithmetic. The third part is an aporetical presentation of the most general problems affecting the notion of totality, as an essential introduction to the ontoIogy of numbers.