Is Iteration an Object of Intuition?

IF 0.8 1区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Bruno Bentzen
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引用次数: 0

Abstract

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.
迭代是直觉的对象吗?
在《直觉、迭代、归纳》一文中,马克-范-阿滕认为迭代是布劳威尔的直觉对象,并从胡塞尔的现象学中解释了迭代行为的直觉特征。我认为这种解读布劳威尔的论据缺乏说服力。在这篇笔记中,我阐述了他关于迭代是直观对象的主张以及他对迭代的胡塞尔式阐释的一些问题。特别是,我认为,由于与布鲁瓦关于二阶数学的评论之间的矛盾,以及胡塞尔并不像布鲁瓦那样理解继承的经验,范阿滕并没有达到他的目的。
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来源期刊
Philosophia Mathematica
Philosophia Mathematica HISTORY & PHILOSOPHY OF SCIENCE-
CiteScore
1.70
自引率
9.10%
发文量
26
审稿时长
>12 weeks
期刊介绍: Philosophia Mathematica is the only journal in the world devoted specifically to philosophy of mathematics. The journal publishes peer-reviewed new work in philosophy of mathematics, the application of mathematics, and computing. In addition to main articles, sometimes grouped on a single theme, there are shorter discussion notes, letters, and book reviews. The journal is published online-only, with three issues published per year.
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