Errett Bishop

Errett Bishop (1928-1983) was a mathematical constructivist who, unlike the intuitionist Arend Heyting, held a dim view of classical mathematics in general and Robinson's infinitesimals in particular. Discouraged by the apparent non-constructivity of his early work in functional analysis under Halmos, he believed to have found the culprit in the law of excluded middle (LEM). He spent the remaining 18 years of his life in an effort to expunge the reliance on LEM from analysis, and sought to define meaning itself in mathematics in terms of such LEM-extirpation. Accordingly, he described classical mathematics as both a debasement of meaning and sawdust, and did not hesitate to speak of both crisis and schizophrenia in contemporary mathematics, predicting an imminent demise of classical mathematics. His criticism (subcontracted by Halmos) of calculus pedagogy based on Robinson's infinitesimals was a natural outgrowth of his general opposition to the logical underpinnings of classical mathematics.

Bishop's article "A general language"
Bishop's article "How to compile mathematics into Algol"

See also
MO discussion
Heyting
Bishop Connes Halmos Sergeyev
More on infinitesimals
SPOT as a conservative extension of Zermelo-Fraenkel (MO)
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