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.

中文翻译：

---

掌握数学概念的 AVICENNA

根据阿维森纳的说法，有些数学对象存在，有些则不存在。每个现有的数学对象都是物理对象的非可感知的内涵属性，并且可以被估计能力感知。通过分离和组合先前通过估计感知的现有数学对象的部分图像，想象能力可以表示和感知不存在的数学对象。在任何情况下，即使是不存在的数学对象也应该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特定的感知经验，否则我们无法掌握任何数学概念。只有通过估计和想象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。