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

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Mathematical intelligencer ; vol. 38, no. 3, pp. 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 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.
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