Remembrances of Errett Bishop

Nerode, Anil; Metakides, George; Constable, R. Todd

doi:10.1090/conm/039/788169

Cited by 1 publication

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“…17 See [12, p. 1] where Bishop states that his general impression was that in those lectures he failed to communicate a real feeling for the philosophical issues involved. Nerode [64] recalls that after his tour of the eastern universities in the USA, Bishop told Nerode that he felt the trip might have been counterproductive, as the audiences did not take his work seriously. Bishop also thought that the difficulties experienced during the lecture tour contributed to the deterioration of his health, resulting in a heart attack [64, p. 80].…”

Section: Persuasion and Dialoguementioning

confidence: 99%

“…We have seen Bishop's concerns in [9] for Brouwer's introduction of free choice sequences and for his inflexible attitude. Furthermore, Bishop in his 1967 book complained that Brouwer was preoccupied 25 See [64]. 26 There has been a recent discussion among constructive mathematicians on two unpublished manuscripts by Bishop, "A general language" and "How to compile mathematics into Algol".…”

Section: Philosophymentioning

confidence: 99%

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Bishop’s Mathematics: A Philosophical Perspective

2023

Handbook of Constructive Mathematics

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Errett Bishop's work in constructive mathematics is overwhelmingly regarded as a turning point for mathematics based on intuitionistic logic. It brought new life to this form of mathematics and prompted the development of new areas of research which witness today's depth and breadth of constructive mathematics. Surprisingly, notwithstanding the extensive mathematical progress since the publication in 1967 of Errett Bishop's Foundations of Constructive Analysis [9], there has been no corresponding advances in the philosophy of constructive mathematics Bishop style.The aim of this paper is to foster the philosophical debate about this form of mathematics. I begin by considering key elements of philosophical remarks by Bishop, especially focusing on Bishop's assessment of Brouwer. I then compare these remarks with "traditional" philosophical arguments for intuitionistic logic and argue that the latter are in tension with Bishop's views. "Traditional" arguments for intuitionistic logic turn out to be also in conflict with significant recent developments in constructive mathematics. This rises pressing questions for the philosopher of mathematics, especially with regard to the possibility of offering alternative philosophical arguments for constructive mathematics. I conclude with the suggestion to look anew at Bishop's own remarks for inspiration.

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Section: Persuasion and Dialoguementioning

confidence: 99%

Section: Philosophymentioning

confidence: 99%