Wittgenstein on mathematical facts

IF 0.4 4区 哲学 0 PHILOSOPHY PHILOSOPHICAL INVESTIGATIONS Pub Date : 2024-08-24 DOI:10.1111/phin.12438
Ásgeir Berg
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Abstract

The status of mathematical facts has long been taken to be unclear in Wittgenstein's philosophy of mathematics, and often, it seems that he wants to eliminate mathematical facts in favour of facts about our beliefs or behaviour. In this paper, I argue that by reading Wittgenstein as a radical conventionalist, we can give a reading of the relevant passages according to which Wittgenstein doesn't deny that there are mathematical facts, but rather denies that one needs a metaphysical account of what mathematical facts are and how they relate to the world that goes beyond the minimal claims of radical conventionalism—that empirical facts about how we would find natural to project our training into new cases and the constitution of concepts by our agreement are enough. At the end of the paper, I discuss the implications of this reading on how to understand a rule's determination of its own application.
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维特根斯坦论数学事实
长期以来,数学事实的地位在维特根斯坦的数学哲学中一直被认为是不明确的,而且他似乎经常想要消除数学事实,而倾向于关于我们的信念或行为的事实。在本文中,我认为通过将维特根斯坦作为一个激进的传统主义者来解读,我们可以对相关段落进行解读,根据这些段落,维特根斯坦并不否认存在数学事实,而是否认人们需要对数学事实是什么以及它们与世界的关系进行形而上学的解释,这种解释超越了激进的传统主义的最低限度的主张--即关于我们如何自然地将我们的训练投射到新的情况中以及我们的约定构成概念的经验事实就足够了。在本文的最后,我将讨论这种解读对于如何理解规则决定其自身应用的意义。
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来源期刊
CiteScore
0.70
自引率
66.70%
发文量
46
审稿时长
45 weeks
期刊介绍: Philosophical Investigations features articles in every branch of philosophy. Whether focusing on traditional or on new aspects of the subject, it offers thought-provoking articles and maintains a lively readership with an acclaimed discussion section and wide-ranging book reviews. Special issues are published on topics of current philosophical interest.
期刊最新文献
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