In ‘Intuition, iteration, induction’, Mark van Atten argues that iteration is an object of intuition for Brouwer and explains the intuitive character of the act of iteration drawing from Husserl’s phenomenology. I find the arguments for this reading of Brouwer unconvincing. In this note I set out some issues with his claim that iteration is an object of intuition and his Husserlian explication of iteration. In particular, I argue that van Atten does not accomplish his goals due to tensions with Brouwer’s comments on second-order mathematics and because Husserl does not understand the experience of succession as Brouwer does.

中文翻译：

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迭代是直觉的对象吗？


在《直觉、迭代、归纳》一书中，马克·范·阿滕认为迭代对于布劳威尔来说是直觉的一个对象，并从胡塞尔的现象学中解释了迭代行为的直观特征。我发现对布劳威尔的解读的论据缺乏说服力。在这篇笔记中，我提出了他关于迭代是直觉对象的主张以及他对迭代的胡塞尔解释的一些问题。特别是，我认为范·阿滕没有实现他的目标，是因为他与布劳威尔对二阶数学的评论存在紧张关系，而且因为胡塞尔不像布劳威尔那样理解继承的经验。