Come on baby light my fire...

In the fifth meditation the meditator comes to the conclusion that certain properties of extension are "true and immutable natures" whether they exist outside of her or not. Furthermore, these properties are not an invention of her own intellect. Her reason for concluding this can be found in the consideration of a triangle. A triangle may or may not exist outside of the intellect; however, when considered one notices certain properties of the triangle such as its three angles equaling two right angles. These properties are clearly recognized even if one never thought about them before when imagining a triangle. These properties are what Hatfield calls discoveries as opposed to inventions. That is, these properties are found in a triangle whether one wants to see them or not and whether or not the triangle actually exists.

The discovered properties of a triangle can be compared to the warmth of a fire. The properties come to the meditator whether she wants them to or not in the same way a fire gives her warmth without her choice. The meditator may choose to not think of a triangle at all by thinking on other things; however, when the triangle is in her imagination the properties come to her. The connections found in the triangle reveal themselves to the meditator clearly and distinctly.

The meditator, we can agree, may think of a triangle whether it exists outside of her or not, in the same way she can think of a chimera, which clearly does not exist outside of her. The point to be proven is that the properties of the triangle are not inventions. The idea presented above is that since the meditator has no choice but to see these properties they could not have been invented in her intellect, rather the properties were discovered and furthermore must have preceeded her thinking of the triangle. Not only does this show that uninvented properties may be found whether or not the object of the idea exists outside the intellect, but also it gives a more concrete idea of what it is to have a clear and distinct idea.

I don't know if there is a fire in the room or not, but that definitely makes me feel warm inside...