数学与经验

IF 0.9 4区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE

Foundations of Science Pub Date : 2024-03-13 DOI:10.1007/s10699-024-09943-2

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引用次数: 0

摘要

摘要数学是否依赖于经验，包括外部世界的经验，这个问题很成问题，因为虽然自然科学显然依赖于经验，但数学是否依赖于经验并不清楚。事实上，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影响。本文认为，事实上，这种观点是不成立的。数学依赖于经验，因为经验影响着数学的产生，事实上，许多数学都产生于经验，并在经验的基础上进行评价。

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Mathematics and Experience

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.

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来源期刊

Foundations of Science HISTORY & PHILOSOPHY OF SCIENCE-

CiteScore

2.60

自引率

11.10%

发文量

期刊介绍： Foundations of Science focuses on methodological and philosophical topics of foundational significance concerning the structure and the growth of science. It serves as a forum for exchange of views and ideas among working scientists and theorists of science and it seeks to promote interdisciplinary cooperation. Since the various scientific disciplines have become so specialized and inaccessible to workers in different areas of science, one of the goals of the journal is to present the foundational issues of science in a way that is free from unnecessary technicalities yet faithful to the scientific content. The aim of the journal is not simply to identify and highlight foundational issues and problems, but to suggest constructive solutions to the problems. The editors of the journal admit that various sciences have approaches and methods that are peculiar to those individual sciences. However, they hold the view that important truths can be discovered about and by the sciences and that truths transcend cultural and political contexts. Although properly conducted historical and sociological inquiries can explain some aspects of the scientific enterprise, the editors believe that the central foundational questions of contemporary science can be posed and answered without recourse to sociological or historical methods.