In his professorial doctoral dissertation , On the Concept of Number ( 1886 ) and in his Philosophy of Arithmetic ( 1891 ) , Husserl sought , by employing Brentano 's descriptive psychology , to define the natural numbers in a way that advanced the methods and techniques of Weierstrass , Dedekind , Georg Cantor , Frege , and other contemporary mathematicians . In his professorial doctoral dissertation , On the Concept of Number ( 1886 ) and in his Philosophy of Arithmetic ( 1891 ) , Husserl sought , by employing Brentano 's descriptive psychology , to define the natural numbers in a way that advanced the methods and techniques of Karl Weierstrass , Richard Dedekind , Georg Cantor , Gottlob Frege , and other contemporary mathematicians .