Questioning Constructive Reverse Mathematics

Constructivist Foundations 7 (2):131-140 (2012)
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Abstract

Context: It is often suggested that the methodology of the programme of Constructive Reverse Mathematics (CRM) can be sufficiently clarified by a thorough understanding of Brouwer’s intuitionism, Bishop’s constructive mathematics, and classical Reverse Mathematics. In this paper, the correctness of this suggestion is questioned. Method: We consider the notion of a mathematical programme in order to compare these schools of mathematics in respect of their methodologies. Results: Brouwer’s intuitionism, Bishop’s constructive mathematics, and classical Reverse Mathematics are historical influences upon the origin and development of CRM, but do not give a full “methodological explanation” for it. Implications: Discussion on the methodological issues concerning CRM is needed. Constructivist content: It is shown that the characterisation and comparison of varieties of constructive mathematics should include methodological aspects (as understood from their practices)

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Iris Loeb
VU University Amsterdam

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References found in this work

Constructivism in mathematics: an introduction.A. S. Troelstra - 1988 - New York, N.Y.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.. Edited by D. van Dalen.
The foundations of intuitionistic mathematics.Stephen Cole Kleene - 1965 - Amsterdam,: North-Holland Pub. Co.. Edited by Richard Eugene Vesley.
Equivalents of the (weak) fan theorem.Iris Loeb - 2005 - Annals of Pure and Applied Logic 132 (1):51-66.

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