La Flèche was the finest school in France, and the Jesuits who ran it taught two incompatible sciences at once. From 1607 to 1614 they gave Descartes Aristotle through the medieval commentators — a cosmos of natural places, substantial forms and real qualities, in which a stone fell because falling was in its nature — and, alongside it, the telescopes finding moons around Jupiter and the mathematicians describing motion with numbers that worked. The physics Europe ran on was quietly failing, and his schooling had shown him where. He took a law degree at Poitiers in 1616, never practised, and enlisted instead.
The turn came in the army. At Breda in 1618 he met Isaac Beeckman, a Dutch mathematician who treated falling bodies and the behaviour of fluids as problems in mathematics, and the meeting left Descartes with the suspicion that would organise the rest of his life: that the whole of nature might yield to a single method. On the night of 10 November 1619, in winter quarters in southern Germany and twenty-three years old, he had three dreams he took as a summons to reform all knowledge. He would spend eighteen years working out what that meant before he published anything at all.
His answer was to stop patching and start again. If the received picture was unsound, the repair was not a better argument inside it but a foundation beneath it, and the way to find one was to throw out whatever admitted the least doubt. The senses deceive, and mathematics goes too if some deceiver arranged the deception; the waking world is indistinguishable from a convincing dream. What survived the demolition was the doubting itself: a thing that is being deceived exists while it is deceived. From that one surviving point he rebuilt — a God who does not deceive, a physical world of extension and motion with nothing in it but geometry, and a mind that is no part of that world at all.
Then Galileo was condemned in 1633, and Descartes withheld The World, his finished physics, because it too had the earth in motion. What he published instead was smaller and stranger: the Discourse on the Method of 1637, anonymous, and in French rather than Latin so that anyone literate could follow it. The Meditations came in 1641, printed with six sets of hostile objections — from Hobbes, from Gassendi, from Arnauld — and his own replies bound in alongside.
The best objection came by letter. In 1643 Princess Elisabeth of Bohemia asked the question his system could not answer: if the mind has no extension, how does it move an arm? His reply reached for an analogy out of the very scholastic physics he had spent his life demolishing, and she said so. The problem is still open.
The costs were real: Voetius had Cartesian teaching banned at Utrecht in 1642 and pressed a charge of atheism, and Descartes, fearing expulsion and the burning of his books, asked the Prince of Orange to intervene. He went to Stockholm in 1649 at Queen Christina's invitation and died there of pneumonia on 11 February 1650, and Rome placed his works on the Index in 1663.
Clear the ground, find one certainty, build outward: that sequence is what modern philosophy has repeated and disputed ever since.