Volume 7 · Number 2 · Pages 131–140

< Previous Paper · Next Paper >

Questioning Constructive Reverse Mathematics

Iris Loeb

Download the full text in
PDF (339 kB)


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).

Key words: constructive mathematics, reverse mathematics, mathematical programme, methodology


Loeb I. (2012) Questioning Constructive Reverse Mathematics. Constructivist Foundations 7(2): 131–140. Available at http://constructivist.info/7/2/131.loeb

Export article citation data: Plain Text · BibTex · EndNote · Reference Manager (RIS)

Similar articles

Müller K. H. (2008) Methodologizing Radical Constructivism. Recipes for RC-Designs in the Social Sciences

Larochelle M. & Désautels J. (2007) Concerning Ernst von Glasersfeld’s Contribution to Intellectual Freedom: One Interpretation, One Example

Umpleby S. A. (2016) Second-Order Cybernetics as a Fundamental Revolution in Science

Bettoni M. C. (2011) Constructing a Beginning in 1985

Bettoni M. C. (2007) The Yerkish Language: From Operational Methodology to Chimpanzee Communication