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

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The Mathematical Intelligencer 38 (3):41-51 (2016)
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Abstract

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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Jean-Pierre Marquis
Université de Montréal

Citations of this work

Conceptual and Computational Mathematics†.Nicolas Fillion - 2019 - Philosophia Mathematica 27 (2):199-218.

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References found in this work

Who were the American Postulate Theorists?Michael Scanlan - 1991 - Journal of Symbolic Logic 56 (3):981-1002.
Who were the american postulate theorists?Michael Scanlan - 1991 - Journal of Symbolic Logic 56 (3):981-1002.
Facets and Levels of Mathematical Abstraction.Hourya Benis Sinaceur - 2014 - Philosophia Scientiae 18 (1):81-112.
Mathematical Abstraction, Conceptual Variation and Identity.Jean-Pierre Marquis - 2014 - In Peter Schroeder-Heister, Gerhard Heinzmann, Wilfred Hodges & Pierre Edouard Bour (eds.), Logic, Methodology and Philosophy of Science, Proceedings of the 14th International Congress. London, UK: pp. 299-322.

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