Peano's concept of number

Giuseppe Peano's development of the real number system from his postulates for the natural numbers and some of his views on definitions in mathematics are presented in order to clarify his concept of number. They show that his use of the axiomatic method was intended to make mathematical theory clearer, more precise, and easier to learn. They further reveal some of his reasons for not accepting the contemporary “philosophies” of logicism and formalism, thus showing that he never tried to found mathematics on anything beyond our experience of the material world.