Abstract

The question of whether mathematics depends on experience, including experience of the external world, is problematic because, while it is clear that natural sciences depend on experience, it is not clear that mathematics depends on experience. Indeed, several mathematicians and philosophers think that mathematics does not depend on experience, and this is also the view of mainstream philosophy of mathematics. However, this view has had a deleterious effect on the philosophy of mathematics. This article argues that, in fact, the view is not valid. Mathematics depends on experience because experience influences the making of mathematics, indeed much mathematics arises from experience and is evaluated on the basis of experience.

中文翻译：

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数学与经验

摘要

数学是否依赖于经验，包括外部世界的经验，这个问题是有问题的，因为虽然很明显自然科学依赖于经验，但尚不清楚数学是否依赖于经验。确实，一些数学家和哲学家认为数学不依赖于经验，这也是主流数学哲学的观点。然而，这种观点对数学哲学产生了有害的影响。本文认为，事实上，这种观点是站不住脚的。数学依赖于经验，因为经验影响数学的形成，事实上，许多数学源于经验，并在经验的基础上进行评估。