Stairway to Heaven: the abstract method and levels of abstraction in mathematics

The Mathematical Intelligencer 38 (3):41-51 (2016)
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In this paper, following the claims made by various mathematicians, I try to construct a theory of levels of abstraction. I first try to clarify the basic components of the abstract method as it developed in the first quarter of the 20th century. I then submit an explication of the notion of levels of abstraction. In the final section, I briefly explore some of main philosophical consequences of the theory.
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