AVICENNA ON GRASPING MATHEMATICAL CONCEPTS

IF 0.1 2区哲学 Q3 HISTORY & PHILOSOPHY OF SCIENCE

Arabic Sciences and Philosophy Pub Date : 2021-03-01 DOI:10.1017/S0957423920000090

Mohammad Saleh Zarepour

引用次数: 1

Abstract

Abstract According to Avicenna, some of the objects of mathematics exist and some do not. Every existing mathematical object is a non-sensible connotational attribute of a physical object and can be perceived by the faculty of estimation. Non-existing mathematical objects can be represented and perceived by the faculty of imagination through separating and combining parts of the images of existing mathematical objects that are previously perceived by estimation. In any case, even non-existing mathematical objects should be considered as properties of material entities. They can never be grasped as fully immaterial entities. Avicenna believes that we cannot grasp any mathematical concepts unless we first have some specific perceptual experiences. It is only through the ineliminable and irreplaceable operation of the faculties of estimation and imagination upon some sensible data that we can grasp mathematical concepts. This shows that Avicenna endorses some sort of concept empiricism about mathematics.

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阿维森纳对数学概念的把握

根据阿维森纳的理论，有些数学对象是存在的，有些是不存在的。每一个存在的数学对象都是物理对象的非感性内涵属性，可以通过估计能力感知。不存在的数学对象可以通过想象的能力来表现和感知，通过分离和组合现有的数学对象的图像的部分，这些图像之前是通过估计来感知的。在任何情况下，即使不存在的数学对象也应被视为物质实体的属性。它们永远不能被理解为完全非物质的实体。阿维森纳认为，除非我们首先有一些具体的感知经验，否则我们无法掌握任何数学概念。只有通过估算和想象的能力对一些可感知的数据进行不可消除和不可替代的操作，我们才能掌握数学概念。这表明阿维森纳赞同某种关于数学的概念经验主义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Arabic Sciences and Philosophy Multiple-

CiteScore

0.70

自引率

0.00%

发文量

期刊介绍： Arabic Sciences and Philosophy (ASP) is an international journal devoted to the Arabic sciences, mathematics and philosophy in the world of Islam between the eighth and eighteenth centuries, in a cross-cultural context. In 2009, the journal extended its scope to include important papers on scientific modernization from the nineteenth century in the Islamic world. Together with original studies on the history of all these fields, ASP also offers work on the inter-relations between Arabic and Greek, Indian, Chinese, Latin, Byzantine, Syriac and Hebrew sciences and philosophy. Casting new light on the growth of these disciplines, as well as on the social and ideological context in which this growth took place, ASP is essential reading for those interested in these areas.