In the philosophy of mathematics, he became known for the statement that "Mathematics is the science that draws necessary conclusions". Peirce's definition of mathematics was credited by his son, Charles Sanders Peirce, as helping to initiate the consequence-oriented philosophy of pragmatism. Like George Boole, Peirce believed that mathematics could be used to study logic. These ideas were further developed by his son Charles , who noted that logic also includes the study of faulty reasoning. In contrast, the later logicist program of Gottlob Frege and Bertrand Russell attempted to base mathematics on logic.