…replacement for common or good sense. The very attitude that proof is self-sustaining is as silly as the idea of being able to pull yourself up by your own bootstraps. I encourage you to read Duhem's "German Science" in which he describes exactly the silliness of "science" when it is divorced from common sense. It's not magic, my friend. A man of little good sense will lack a sound place to begin reasoning from.…
……按照他的定性）是错的。关于这个话题有几本挺有意思的书……詹姆斯·富兰克林（James Franklin）的《An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure》，皮埃尔·迪昂（Pierre Duhem）的《German Science》
…he characterizes them) are wrong. Some interesting books on the subject... "An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure" by James Franklin "German Science" by Pierre Duhem
…choose to proceed from. Set theory is a great example. Take Russell's paradox, for instance, and the different responses to it (e.g., ZFC, Lesniewski's mereology). I'm reminded of Duhem's rather humorous "German Science" where he characterizes German mathematics as being disproportionately oriented toward rigorously deducing nonsense from arbitrary axioms as opposed to the French tendency to rely on intuition to arrive…
……无法替代常识或良知。认为“证明”本身就能自给自足的这种态度，简直就跟拽着自己的鞋带把自己提起来一样可笑。我建议你读读迪昂（Duhem）的《German Science》，他在书里精准描绘了当“科学”脱离常识时是多么荒唐。朋友，这可不是什么魔法。缺乏常识的人，连推理都找不到一个靠谱的出发点。……
…replacement for common or good sense. The very attitude that proof is self-sustaining is as silly as the idea of being able to pull yourself up by your own bootstraps. I encourage you to read Duhem's "German Science" in which he describes exactly the silliness of "science" when it is divorced from common sense. It's not magic, my friend. A man of little good sense will lack a sound place to begin reasoning from.…
……按照他的定性）是错的。关于这个话题有几本挺有意思的书……詹姆斯·富兰克林（James Franklin）的《An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure》，皮埃尔·迪昂（Pierre Duhem）的《German Science》
…he characterizes them) are wrong. Some interesting books on the subject... "An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure" by James Franklin "German Science" by Pierre Duhem
……选择从何出发。集合论就是一个极好的例子。拿罗素悖论来说，以及人们对它的不同应对（比如 ZFC、莱斯涅夫斯基的形式部分论 mereology）。这让我想起了迪昂那本挺幽默的《German Science》，他在书里把德国数学描绘成极度偏好从任意公理中严密推导出一堆废话，而法国人则倾向于依靠直觉来得出……
…choose to proceed from. Set theory is a great example. Take Russell's paradox, for instance, and the different responses to it (e.g., ZFC, Lesniewski's mereology). I'm reminded of Duhem's rather humorous "German Science" where he characterizes German mathematics as being disproportionately oriented toward rigorously deducing nonsense from arbitrary axioms as opposed to the French tendency to rely on intuition to arrive…