Descartes separates external objects into those that are clear and distinct and those that are confused and obscure. The former group consists of the ideas of extension, duration and movement. These geometrical ideas cannot be misconstrued or combined in a way that makes them false. For example, if the idea of a creature with the head of a giraffe, the body of a lion and tail of a beaver was constructed and the question asked if the creature had a large intestine, the answer would have to be invented. But, no mathematical re-arrangement of a triangle could allow its three internal angles to sum to anything but 180 degrees. Thus, Descartes perceived that truths may have a nature or essence of themselves, independent of the thinker. (In Descartes’ formulation, this is a mathematical truth only pragmatically related to nature; the properties of triangles in Euclidean geometry remain mathematically certain,[8] though it was later discovered that the internal angles in real local triangles sum to more than 180 degrees.)

I find in myself innumerable ideas of things which, though they may not exist outside me, can’t be said to be nothing. While I have some control over my thoughts of these things, I do not make the things up: they have their own real and immutable natures. Suppose, for example, that I have a mental image of a triangle. While it may be that no figure of this sort does exist or ever has existed outside my thought, the figure has a fixed nature (essence or form), immutable and eternal, which hasn’t been produced by me and isn’t dependent of my mind. (Descartes, Meditation V: On the Essence of Material Objects and More on God’s Existence).

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