The Discourse on Method is a philosophical and mathematical treatise published by René Descartes in 1637. Its full name is Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences (French title: Discours de la méthode pour bien conduire sa raison, et chercher la verité dans les sciences).
The Discourse on Method is best known as the source of the famous quotation "cogito ergo sum," "I think, therefore I am." In addition, it contains Descartes' first introduction of the Cartesian coordinate system.
This is one of the most influential works in history. It is a method which gives a solid platform from which all modern natural sciences could evolve. With this work, the idea of skepticism was born. Descartes started his line of reasoning by doubting everything, so as to assess the world from a fresh perspective, clear of any preconcieved notions.
The following quote from Discourse on Method presents the four precepts that characterise the Method itself:
"The first was never to accept anything for true which I did not clearly know
to be such; that is to say, carefully to avoid precipitancy and prejudice, and
to comprise nothing more in my judgement than what was presented to my mind so
clearly and distinctly as to exclude all ground of doubt.
The second, to divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.
The third, to conduct my thoughts in such order that, by commencing with objects the simplest and easiest to know, I might ascend by little and little, and, as it were, step by step, to the knowledge of the more complex; assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence.
And the last, in every case to make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted."
Descartes uses the analogy of tearing down the house to its foundation in order to build a secure edifice (He even extends the analogy to move next door into a house of morality, while his own house is being rebuilt). The foundation he reveals appears to have three parts.
Applying the method to itself, Descartes challenges his own reasoning and reason itself. But Descartes believes three things are not susceptible to doubt and the three support each other to form a stable foundation for the method. He cannot doubt that something has to be there to do the doubting (I think, therefore I am). The method of doubt cannot doubt reason as it is based on reason itself. By reason there exists a God and God is the guarantor that reason is not misguided.
Perhaps the most strained part of the argument is the reasoned proof of the existence of God and indeed Descartes seems to realise this as he supplies three different 'proofs' including what is now referred to as the ontological proof of the existence of God (some argue that Descartes inserted his statment on the existence of God in the Discourse on Method to appease censors of the time; a very serious concern, as within Discourse Descartes points out that he was at first reluctant to publish the work because of the recent show trial of Galileo by the Catholic Church in 1633, only four years earlier) .
Secure on these foundation stones, Descartes shows the practical application of 'The Method' in Mathematics and the Sciences.
One of the practical methods was to order the objects in different ways on paper to make them easy to see clearly. This became the basis of the Cartesian coordinate system, the Histogram and Analytic geometry. These ideas, among other methods of science, influenced Isaac Newton and Gottfried Leibniz in their development of calculus. The most important influence, however, was the first precept, which states, in Descartes words, to "never to accept anything for true which I did not clearly know to be such." This new idea of skepticism influenced many to start finding out things for themselves rather than relying solely on authority. The idea as such may have been the starting point for the development of modern science.