30 June 2019

René Descartes - Collected Quotes

"Divide each problem that you examine into as many parts as you can and as you need to solve them more easily." (René Descartes, “Discourse on Method”, 1637)

"Each problem that I solved became a rule which served afterwards to solve other problems. [...] thus each truth discovered was a rule available in the discovery of subsequent ones.” (René Descartes, “Discourse on Method”, 1637)

“[…] neither the true roots nor the false are always real; sometimes they are, however, imaginary; namely, whereas we can always imagine as many roots for each equation as I have predicted, there is still not always a quantity which corresponds to each root so imagined. Thus, while we may think of the equation x^3 - 6xx + 13x - 10 = 0 as having three roots, yet there is just one real root, which is 2, and the other two [2+i and 2-i]], however, increased, diminished, or multiplied them as we just laid down, remain always imaginary.” (René Descartes, “Gemetry”, 1637)

"The long chains of simple and easy reasonings by means of which geometers are accustomed to reach the conclusions of their most difficult demonstrations, had led me to imagine that all things, to the knowledge of which man is competent, are mutually connected in the same way, and that there is nothing so far removed from us as to be beyond our reach, or so hidden that we cannot discover it, provided only we abstain from accepting the false for the true, and always preserve in our thoughts the order necessary for the deduction of one truth from another." (René Descartes, "Discourse on the Method", 1637)

“From all this I am beginning to have a rather better understanding of what I am. But it still appears - and I cannot stop thinking this - that the corporeal things of which images are formed in my thought, and which the senses investigate, are known with much more distinctness than this puzzling 'I' which cannot be pictured in the imagination.” (René Descartes, “Meditations” II, 1641)

“In order to seek truth, it is necessary once in the course of our life, to doubt, as far as possible, of all things.” (René Descartes, “Principles of Philosophy”, 1644)

"There is nothing in us which we must attribute to our soul except our thoughts. These are of two principal kinds, some being actions of the soul and others its passions. Those I call its actions are all our volitions […] the various perceptions or modes of knowledge present in us may be called its passions in the general sense, for it is often not our soul which makes them such as they are, and the soul always receives them from the things that are represented by them." (René Descartes, "Les passions de l’âme" ["Passions of the Soul"], 1649)

"The two operations of our understanding [… are] intuition and deduction, on which alone we have said we must rely in the acquisition of knowledge." (René Descartes, "Rules for the Direction of the Mind", 1684)

"When a problem arises, we should be able to see soon whether it will be profitable to examine some other problems first, and which others, and in which order." (René Descartes, "OEuvres" Vol. X, 1897)

"All philosophy is like a tree, the roots are metaphysics, the trunk is physics, and the branches are all the other sciences.” (René Descartes)

"Intuition is the conception of an attentive mind, so clear, so distinct, and so effortless that we cannot doubt what we have so conceived.” (René Descartes)

“It is very helpful to represent these things in this fashion since nothing enters the mind more readily than geometric figures.” (René Descartes)

"The two operations of our understanding, intuition and deduction, on which alone we have said we must rely in the acquisition of knowledge." (René Descartes)

"There have been only Mathematicians who were able to find some proofs, that is to say some sure and certain reasons." (René Descartes)

“We call infinite that thing whose limits we have not perceived, and so by that word we do not signify what we understand about a thing, but rather what we do not understand.” (René Descartes)

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