René Descartes uses the chiliagon as an example in his Sixth Meditation to demonstrate the difference between pure intellection and imagination. He says that, when one thinks of a chiliagon, he "does not imagine the thousand sides or see them as if they were present" before him – as he does when one imagines a triangle, for example.

2019年12月1日 · But if I want to think of a chiliagon, although I understand that it is a figure consisting of a thousand sides just as well as I understand the triangle to be a three-sided figure, I do not in the same way imagine the thousand sides …

2018年11月9日 · To demonstrate further, Descartes gives the example of a chiliagon (a thousand-sided polygon) which can be conceived in the mind as pure intellection but cannot be pictured in the imagination.

2017年6月6日 · René Descartes uses the chiliagon as an example in his Sixth Meditation to demonstrate the difference between pure intellection and imagination. He says that, when one thinks of a chiliagon, he "does not imagine the thousand sides or see them as if they were present" before him – as he does when one imagines a triangle, for example.

Descartes argues that the mind is an intellectual substance (64). The senses and imagination are part of the mind, but they are not essential to it in the way that reasoning (“intellection”) is. The idea is that he can imagine thinking without having sensations or mental images.

Nevertheless, there is still the concept of a chiliagon, provided by the intellect: and from the concept we could deduce all kinds of geometrical truths, if we wanted to. This example is given by Descartes to illustrate his point that the imagination is something different to the intellect. Descartes thinks that the fact that our ability to

Descartes continues by explaining what it is to imagine something: Imagining x = Understanding x + intuiting x as present "by my powers of discernment. A triangle can be imagined, but a chiliagon (thousand-sided figure) can only be understood. A "peculiar sort of effort" is required to imagine, beyond what is required to understand.

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The second passage is in First Replies, in which Descartes says that just as we can clearly and distinctly perceive part of a chiliagon if we focus our attention, we can clearly and distinctly perceive a portion of the sea (AT 7:113). This passage can be read as reflecting the Second Meditation view that we can clearly and distinctly perceive a ...

A chiliagon is a polygon with 1000 sides. René Descartes used the chiliagon in his meditations to demonstrate that the intellect is not dependent on imagination, as one can understand a chiliagon without being able to imagine its 1000 sides. Later philosophers also referenced the chiliagon in discussions of ideas versus images and intuition.