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René Descartes, The Philosopher Mathematician That “Mathematized” Philosophy

April 25, 2022
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By Ashley Langham

René Descartes was best known for creating a mathematical foundation for philosophy. He thought that philosophy could essentially be “mathematicized” because math was created out of certainty and absoluteness. Math was based on universal truths and philosophy could be based on truths that were already determined to be true or accepted to be true. 

He spent the majority of his life isolated, because he had a weakened physique due to illness; and received the benefit of the doubt from others to not expect him out of bed until 11am. While he was lying there, he spent his time in philosophical and mathematical study and deep thought. His fascinating pursuit of truth and the understanding of nature led him to writing one of the most important books of his life: Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences (Discourse on method for rightly conducting the reason and searching for the truth in the sciences). Discourse of Method is seen to be one of the most influential works of modern philosophy, and unlike many philosophers of the time who wrote in Latin, to be read by other scholars; Descartes wrote his book in French to be more accessible to the common people in France. Read on to learn more about his work and life!

René Descartes (1596-1650): The Philosophical Loner

A portrait of René Descartes, created by artist Frans Hals, via Wikimedia

Descartes was born in his grandmother’s house in the commune La Haye en Touraine, France. (The town was later named after him La Haye-Descartes, in 1802, in his honor.)  Unfortunately, his mother, Jeanne, died in childbirth only a year after his birth. His father, a counselor at the court of justice, would remarry when Descartes was only four years old; but he sent his three children, including Descartes, to live with their grandmother while he started a new family with his new wife. 

At age ten, Descartes was sent off to boarding school, La Fleche. Unlike his classmates, who had to be up at 5am to attend their studies; Descartes had the luxury of staying in bed until 11am because he was a sickly child. It was at that point in his life where he developed his practice of meditation, particularly around the subjects of: classical studies, traditional Aristotelian philosophy, math, and science. He developed his deep desire to learn but also wanted to remain perfect, without ever making an error or having doubts in what he was actually learning. He took deep pleasure in learning math because he liked the certainty in mathematical laws and that there was only truth that one could deduce from them. During his hours of deep contemplation, he came to the conclusion that he didn’t like studying books on the laws of nature because he found no use in them. He would later write in his Discourse on Method that he abandoned books because truth could not be determined from them. The only truth he could deduce is the truths he found in himself and his experiences within nature. Hence, his famous line “I think therefore I am” came to be. In this statement he ultimately was saying that we, as humans, cannot doubt our existence because by virtue of doubting, or even thinking, is proof of that existence.

Descartes And His Most Influential Works

Title page of René Descartes' Discourse on Method, via Wikimedia

By 1618, Descartes went to military school in Breda, Netherlands. He kept to his study of mathematics, but also started studying physics in his pursuits to be a military engineer. He spent 8 years traveling to Northern and Southern Europe in both the armies of Maurice of Nassau and Max of Bavaria. He spent most of that time continuing to develop his ideas around “mathematizing” philosophy.  Towards the end of his military tours, his friend from La Fleche, Marin Mersenne, a French priest, encouraged him to publish his new philosophical methods. 

Following his friend's advice, in 1633, he wrote his first physics treatise called Traite du monde de la lumière  (World Treaty of the Light), where he discussed the heliocentric model of the sun and planets developed by the Polish mathematician Copernicus. Unfortunately, he got spooked by learning that Galileo was condemned by the Catholic Church for defending Copernicus’s work; and quickly scrapped his treatise.  

Four years later he created the most influential book in his life, Discourse on Method with three essays to accompany it: Les Meteores (Meteors), La Dioptrique (Dioptric), and La Geometrie (Geometry). In Discourse on Method he created a method for deductive reasoning:  

  1. Accept nothing as true that is not self evident
  2. Divide problems into their simplest parts.
  3. Solve problems by proceeding from simple to complex
  4. Recheck the reasoning

His essay, La Geometrie, was considered his most important work out of the three.  In it, he discovers a method called analytical geometry, whereby he created a coordinate system that defines perpendicular lines and geometric shapes by algebraic equations. Essentially he makes it easier for geometric problems to be solved by algebraic solutions and vice versa. In honor of his work, coordinate systems with perpendicular axes are now called “cartesian coordinates'', Cartesius being his last name in Latin. His work was the stepping stone for Isaac Newton and Gottfried Wilheim to create calculus. The following conventions can also be attributed to him: 

x, y, z = variables

a, b, c = quantities

His other most important work,  Principia Philosophiae (Philosophy Principles), published in 1644, contributed to him becoming one of the most influential philosophers and mathematicians in Europe of his time, even though he didn’t hold any academic positions. It was a comprehensive guide of his mathematical theories on philosophy. 

Descartes’s Unfortunate End

It was his short stint out of isolation that was his downfall. Besides seeing and allowing his friend Mersenne to come visit him at his home, he didn’t see anyone else or had any other friends or visitors. That changed when he was invited by Queen Christina of Sweden to her court in Stockholm as her personal tutor and the organizer of a scientific academy in 1649. 

Where he spent most of his life in bed until 11am, he was forced to wake up even earlier to tutor her at 5am. He was also forced to walk through the dead of winter and the snow to provide her lessons at her palace. A year later, and with a weakened immune system, he caught an infection. Ten days later he died from pneumonia in 1650.

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