Problem solving and construction in the “Rules for the direction of the mind” (c. 1628)
I now turn to the Rules for the direction of the mind (Regulae ad directionem ingenii),1 Descartes’ unfinished attempt to formulate rules of reasoning, dating, in its final form, from c. 1628. The Rules, written in Latin, were not published during his lifetime. The work has great relevance for the understanding of Descartes’ mathematical thought because the rules he formulated were to a large extent inspired by mathematics. The question in what ways mathematics, and in particular the idea of a “universal mathematics” inspired the Rules has been treated extensively in the literature on Descartes2 and I don’t deal with it here. Rather I discuss a more restricted, and in a way reverse question, namely: what do the Rules tell us about Descartes’ mathematical ideas at the time, in particular concerning geometrical construction and the interpretation of exactness.
KeywordsLine Segment Arithmetical Operation Root Extraction Geometrical Construction Reverse Movement
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