No Comment, Quotation — April 3, 2010, 7:09 am

Descartes – The Chain of Reason

vermeergeographer

Ces longues chaînes de raisons, toutes simples et faciles, dont les géomètres ont coutume de se servir pour parvenir à leurs plus difficiles démonstrations, m’avaient donné occasion de m’imaginer que toutes les choses qui peuvent tomber sous la connaissance des hommes s’entresuivent en même façon, et que, pourvu seulement qu’on s’abstienne d’en recevoir aucune pour vraie qui ne le soit, et qu’on garde toujours l’ordre qu’il faut pour les déduire les unes des autres, il n’y en peut avoir de si éloignées auxquelles enfin on ne parvienne, ni de si cachées qu’on ne découvre.

The long chains of reasonings, simple and easy, by which geometricians are wont to achieve their most complex proofs, had led me to suppose that all things, the knowledge of which man may achieve, are strung together in the same way, and that there is nothing so distant as ultimately to be beyond our mental grasp, or so hidden that we cannot uncover it, provided only we avoid accepting falsehoods as true, and always preserve in our thoughts the discipline essential for the deduction of one truth from another.

René Descartes, Le Discours de la méthode pt 2 (1637)(S.H. transl.)


Descartes, a towering figure of the seventeenth century, made no contribution greater than his rules for the discipline of thinking. He comes to compelling conclusions, but he starts from simple premises. In fact, it would be no simplification to say that he starts with Euclidian geometry. He notes how it builds from simple thoughts–first principles and definitions–and steadily develops more and more complex notions from them. In a like manner, Descartes tells us, man can aspire to know even the most complex and distant truths–it requires the patience and resolve to approach the problem in increments. But the key to the success of this approach is the rigorous commitment to truth and willingness to reject whatever is false. Descartes is presenting a cloaked criticism of the great scientific controversy of his time: the trial of Galileo and the posture of the Church, which adhered to Aristotelian precepts about the structure of the universe long after they had been scientifically disproven. A dogmatic adherence to falsehood of the sort frequently claimed by religions which claimed a special knowledge of ultimate questions was, in Descartes’s thinking, one of the greatest challenges to the human species. But for Descartes, the illogical adherence to uttered falsehoods is a human constant which the scientific mind must struggle to overcome. “Since the pressure of things to be done does not always allow us to stop and make such a meticulous check, it must be admitted that in this human life we are often liable to make mistakes about particular things, and we must acknowledge the weakness of our nature.”


Among Descartes’s contemporaries, the Stuttgart-born composer J.J. Froberger assumes a special role as a master of the keyboard and a stylistic conciliator. He mastered the stylus fantasticus of Frescobaldi and the Roman School and merged this with the North German and French styles, and he developed the notion of the keyboard suite. But he was also an early experimenter with programmatic music. Froberger also approaches the task of composition as an essentially mathematical exercise in which each chord has a relationship to the one that proceeded and the one that followed it.

Listen to Johann Jakob Froberger’s Tombeau fait à Paris sur la mort de Monsieur Blancrocher (1652) performed by Blandine Verlet on a Ruckers II harpsichord from 1624:

And then listen to the Lamentation faite sur la mort très douloureuse de Sa Majesté Impériale, Ferdinand III (1657), a work composed in the unusual key of F (for obvious reasons), and particularly the three notes of F struck at the conclusion, which fade off into eternity, a notion that Froberger stressed in his extraordinary manuscript of the score:

Share
Single Page

More from Scott Horton:

Conversation August 5, 2016, 12:08 pm

Lincoln’s Party

Sidney Blumenthal on the origins of the Republican Party, the fallout from Clinton’s emails, and his new biography of Abraham Lincoln

Conversation March 30, 2016, 3:44 pm

Burn Pits

Joseph Hickman discusses his new book, The Burn Pits, which tells the story of thousands of U.S. soldiers who, after returning from Iraq and Afghanistan, have developed rare cancers and respiratory diseases.

Context, No Comment August 28, 2015, 12:16 pm

Beltway Secrecy

In five easy lessons

Get access to 165 years of
Harper’s for only $45.99

United States Canada

CATEGORIES

THE CURRENT ISSUE

March 2017

City of Gilt

= Subscribers only.
Sign in here.
Subscribe here.

Tyranny of the Minority

= Subscribers only.
Sign in here.
Subscribe here.

Texas is the Future

= Subscribers only.
Sign in here.
Subscribe here.

Family Values

= Subscribers only.
Sign in here.
Subscribe here.

Itchy Nose

= Subscribers only.
Sign in here.
Subscribe here.

Black Like Who?

= Subscribers only.
Sign in here.
Subscribe here.

view Table Content

FEATURED ON HARPERS.ORG

Article
Texas is the Future·

= Subscribers only.
Sign in here.
Subscribe here.

I first heard the name Barack Obama in the spring of 2004, while visiting my mother in Chicago. As we sat around the kitchen table early one spring morning, I noticed a handsome studio portrait among the pictures, lists, cards, and other totems of family life fastened to the refrigerator door. “Who’s the guy with the ears?” I asked, assuming he was some distant relative or family friend I didn’t know or else had forgotten. “Barack Obama,” she answered with a broad smile. “He’s running for Senate, but he’s going to be the first black president.”

Illustration (detail) by John Ritter
Post
The Forty-Fifth President·

= Subscribers only.
Sign in here.
Subscribe here.

I first heard the name Barack Obama in the spring of 2004, while visiting my mother in Chicago. As we sat around the kitchen table early one spring morning, I noticed a handsome studio portrait among the pictures, lists, cards, and other totems of family life fastened to the refrigerator door. “Who’s the guy with the ears?” I asked, assuming he was some distant relative or family friend I didn’t know or else had forgotten. “Barack Obama,” she answered with a broad smile. “He’s running for Senate, but he’s going to be the first black president.”

Photograph (detail) by Philip Montgomery
Article
Itchy Nose·

= Subscribers only.
Sign in here.
Subscribe here.

I first heard the name Barack Obama in the spring of 2004, while visiting my mother in Chicago. As we sat around the kitchen table early one spring morning, I noticed a handsome studio portrait among the pictures, lists, cards, and other totems of family life fastened to the refrigerator door. “Who’s the guy with the ears?” I asked, assuming he was some distant relative or family friend I didn’t know or else had forgotten. “Barack Obama,” she answered with a broad smile. “He’s running for Senate, but he’s going to be the first black president.”

Artwork (detail) © The Kazuto Tatsuta/Kodansha Ltd
Article
A Matter of Life·

= Subscribers only.
Sign in here.
Subscribe here.

I first heard the name Barack Obama in the spring of 2004, while visiting my mother in Chicago. As we sat around the kitchen table early one spring morning, I noticed a handsome studio portrait among the pictures, lists, cards, and other totems of family life fastened to the refrigerator door. “Who’s the guy with the ears?” I asked, assuming he was some distant relative or family friend I didn’t know or else had forgotten. “Barack Obama,” she answered with a broad smile. “He’s running for Senate, but he’s going to be the first black president.”

Photograph (detail) by Edwin Tse
Article
Black Like Who?·

= Subscribers only.
Sign in here.
Subscribe here.

I first heard the name Barack Obama in the spring of 2004, while visiting my mother in Chicago. As we sat around the kitchen table early one spring morning, I noticed a handsome studio portrait among the pictures, lists, cards, and other totems of family life fastened to the refrigerator door. “Who’s the guy with the ears?” I asked, assuming he was some distant relative or family friend I didn’t know or else had forgotten. “Barack Obama,” she answered with a broad smile. “He’s running for Senate, but he’s going to be the first black president.”

Photograph © Jon Lowenstein/NOOR

Ratio of the average cost of a gallon of gas in Britain last September to that of a gallon of Starbucks coffee:

1:4

The faculty of embarrassment was located in the pregenual anterior cingulate cortex by neurologists who made brain-damaged subjects sing along to “My Girl” and then listen to their own singing played back without musical accompaniment.

Greece evacuated 72,000 people from the town of Thessaloniki while an undetonated World War II–era bomb was excavated from beneath a gas station.

Subscribe to the Weekly Review newsletter. Don’t worry, we won’t sell your email address!

HARPER’S FINEST

Who Goes Nazi?

= Subscribers only.
Sign in here.
Subscribe here.

By

"It is an interesting and somewhat macabre parlor game to play at a large gathering of one’s acquaintances: to speculate who in a showdown would go Nazi. By now, I think I know. I have gone through the experience many times—in Germany, in Austria, and in France. I have come to know the types: the born Nazis, the Nazis whom democracy itself has created, the certain-to-be fellow-travelers. And I also know those who never, under any conceivable circumstances, would become Nazis."

Subscribe Today