Stairway to Heaven : The abstract method and levels of abstraction in mathematics
Article [Accepted Manuscript]
Is part ofMathematical intelligencer ; vol. 38, no. 3, pp. 41-51.
In this paper, following the claims made by various mathematicians, I try to construct a theory of levels of abstraction. I rst try to clarify the basic components of the abstract method as it developed in the rst quarter of the 20th century. I then submit an explication of the notion of levels of abstraction. In the nal section, I brie y explore some of main philosophical consequences of the theory.