TY - JOUR
T1 - A footnote to The crisis in contemporary mathematics
AU - Katz, Boris
AU - Katz, Mikhail G.
AU - Sanders, Sam
N1 - Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2018/5
Y1 - 2018/5
N2 - We examine the preparation and context of the paper “The Crisis in Contemporary Mathematics” by Errett Bishop, published 1975 in Historia Mathematica. Bishop tried to moderate the differences between Hilbert and Brouwer with respect to the interpretation of logical connectives and quantifiers. He also commented on Robinson's Non-standard Analysis, fearing that it might lead to what he referred to as ‘a debasement of meaning.’ The ‘debasement’ comment can already be found in a draft version of Bishop's lecture, but not in the audio file of the actual lecture of 1974. We elucidate the context of the ‘debasement’ comment and its relation to Bishop's position vis-a-vis the Law of Excluded Middle.
AB - We examine the preparation and context of the paper “The Crisis in Contemporary Mathematics” by Errett Bishop, published 1975 in Historia Mathematica. Bishop tried to moderate the differences between Hilbert and Brouwer with respect to the interpretation of logical connectives and quantifiers. He also commented on Robinson's Non-standard Analysis, fearing that it might lead to what he referred to as ‘a debasement of meaning.’ The ‘debasement’ comment can already be found in a draft version of Bishop's lecture, but not in the audio file of the actual lecture of 1974. We elucidate the context of the ‘debasement’ comment and its relation to Bishop's position vis-a-vis the Law of Excluded Middle.
KW - Constructive mathematics
KW - Infinitesimal analysis
KW - Robinson's framework
UR - http://www.scopus.com/inward/record.url?scp=85045189043&partnerID=8YFLogxK
U2 - 10.1016/j.hm.2018.03.002
DO - 10.1016/j.hm.2018.03.002
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AN - SCOPUS:85045189043
SN - 0315-0860
VL - 45
SP - 176
EP - 181
JO - Historia Mathematica
JF - Historia Mathematica
IS - 2
ER -