TY - JOUR
ID - 7/2/131.loeb
PY - 2012
TI - Questioning Constructive Reverse Mathematics
AU - Loeb I.
N2 - 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).
UR - http://constructivist.info/7/2/131.loeb
SN - 1782348X
JF - Constructivist Foundations
VL - 7
IS - 2
SP - 131
EP - 140
U1 - conceptual
U3 - Mathematical Constructivism
KW - constructive mathematics
KW - reverse mathematics
KW - mathematical programme
KW - methodology
ER -