... it would be to doubt one's own existence. Mathematical truths, for instance the assertion that twice two is four, are further examples of ideas that can be clearly and distinctly perceived. This is described in the Fifth Meditation when Descartes considers the properties of a triangle. When one imagines a triangle, one clearly knows that the total of the angles inside equals 180°, whether one "wants to or not", thus he did not invent them yet they remain "obviously true" as they are perceived clearly and distinctly. This, though, begs the question of whether one is born with innate knowledge of all mathematical properties. If one were born knowing clearly and distinctly geometrical and arithmetical propositions, then the study of mathematics would be worthless. A common response to this is that the innate knowledge is untapped, awaiting extraction, but how could one distinguish between the process of learning, and the ...

See this essay or coursework document in full right now