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Errett Bishop’s Followers (2)
Errett Bishop
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Foundations of Constructive Analysis
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published
2012
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3 editions
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Constructive Analysis
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published
1985
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4 editions
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Schizophrenia in contemporary mathematics
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Selected Papers
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published
1986
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Constructive Measure Theory
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Foundations of constructive analysis (McGraw-Hill series in higher mathematics)
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“In the words of Kronecker, the positive integers were created by God. Kronecker would have expressed it even better if he had said that the positive integers were created by God for the benefit of man (and other finite beings). Mathematics belongs to man, not to God. We are not interested in properties of the positive integers that have no descriptive meaning for finite man. When a man proves a positive integer to exist, he should show how to find it. If God has mathematics of his own that needs to be done, let him do it himself.”
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“The primary concern of mathematics is number, and this means the positive integers…. Mathematics belongs to man, not God. We are not interested in properties of the positive integers that have no descriptive meaning for finite man. When a man proves a positive integer exists, he should show how to find it. If God has mathematics of his own that needs to be done, let him do it himself.”
― Constructive Analysis
― Constructive Analysis
“There is a crisis in contemporary mathematics, and anybody who has not noticed it is being willfully blind. The crisis is due to our neglect of philosophical issues. The courses in the foundations of mathematics as taught in our universities emphasize the mathematical analysis of formal systems, at the expense of philosophical substance. Thus it is the mathematical profession that tends to equate philosophy with the study of formal systems, which require knowledge of technical theorems for comprehension. They do not want to learn yet another branch of mathematics and therefore leave the philosophy to the experts. As a consequence, we prove these theorems and we do not know what they mean. The job of proving theorems is not impeded by inconvenient inquires into their meaning or purpose. In order to resolve one aspect of this crisis, emphasis will have to be transferred from the mechanics of the assembly line which keeps grinding out the theorems, to an examination of what is being proved.”
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