内容 科学与假设 · 03
Science and Hypothesis · On the Nature of Mathematical Reasoning
Poincare reads mathematical induction as constructive, not merely syllogistic.
庞加莱把数学归纳读成构造性的推理，不只是三段论。
Mathematical reasoning extends a rule while keeping proof responsible.
数学推理会扩展规则，但仍要承担证明责任。
命题
On the Nature of Mathematical Reasoning should be read as a question about how science stabilizes its objects.
卷一 1 · 数学推理的性质 要读成一个问题：科学怎样让自己的对象稳定下来。
读法检查 worked example
题
Why is induction more than checking many examples?
为什么数学归纳不只是检查许多例子？
解
Because it authorizes passage from n to n plus one as a rule.
因为它授权从 n 到 n+1 的规则性过渡。
互链 context
与哈代数学审美 hardy-apology/overview、非欧几何原作 non-euclidean-originals/lobachevsky-overview、分析严密化史 math-meta/topic-calculus-and-analysis-rigor 和拓扑学起源 math-meta/topic-topology-origins 对读。
我的笔记 自动保存