Use of Mathematics in Descartes's Philosophy

Influence of Mathematics on Descartes

Descartes and Mathematics

René Descartes, the father and originator of modern philosophy, puts great emphasis on mathematics. Of the many men who have been famous as mathematicians and as philosophers, Descartes was perhaps the most outstanding. Living in the first half of the 17^th century, he was the father of analytic geometry and of modern philosophy.  Descartes, like all other previous rationalists, holds the idea that reason is universal in human beings; that reason is the most important element in human nature; that reason is the only way to determine what is morally right and good and what constitutes a good society.  But unlike all other rationalists, Descartes gives more emphasis on mathematics and believes that mathematics will help him establish his rationalistic philosophy. This idea became the foundation for his way of thinking, and was to form the basis for all his works.

Descartes makes mathematics his model for the use of his reason. In his Discourse on Method, Descartes says: ’Of all who have sought for the truth in the sciences , it has been the mathematicians alone who have been able to succeed in producing reasons which are evident and certain.’’ And it was the method of mathematics , using reason alone , Descartes believes , which enabled the Polish astronomer Copernicus in the sixteenth century to revolutionize astronomy with his new heliocentric theory of the universe, and enabled the Italian astronomer Galilio in the seventeenth century to provide the proof of the Copernican theory. 

Mathematics is the method which Descartes the mathematician, himself the inventor of analytical geometry, wants to use for philosophy. Mathematics, he thinks, can clear up the confusions and uncertainties of philosophy. The method of mathematics will gain the same clarity and certainty for philosophy  as for geometry and as the scientists have gained for physics and astronomy. By using the method of mathematics, philosophy could achieve absolute certainty and could prove itself, as mathematics does, to my reason, to all human reason, and be acknowledged as universally true. Philosophy could then reach   final and certain truth which would decisively end the disputes among the philosophers and the bitter controversy raging between the Church and the scientists. Philosophic certainty would also bring about an end to the fear of the Inquisition under which scientists lived, the fear of being sentenced to imprisonment or torture, the fear that Descartes himself had that he might suffer the same fate as Galileo.  

Descartes talks about two mental operations namely intuition and deduction in his Rules for the Direction of the Mind. According to him true knowledge can be achieved by intuition and deduction.

Intuition: By intuition he means our understanding of self-evident principles, such as the axioms of geometry ( a straight line is the shortest distance between two points ; or things equal to the same thing are equal to each other) or such as an arithmetic equation (3+2=5). These statements are self-evident in that they prove themselves to reason: To understand them is to know that they are absolutely true; no rational mind can doubt them. 

Deduction: By deduction he means orderly, logical reasoning or inference from self-evident propositions , as all of geometry is reasoned in strict order by deduction from its self-evident axioms and postulates. The chief secret of method, says Descartes, is to arrange all facts into a deductive, logical system. 

Thus, Descartes’s goal as a philosopher is to build a system of philosophy based upon intuition and deduction which will remain as certain and as imperishable as geometry. No philosopher has ever made a bolder attempt to arrive at a philosophy of absolute truth. The entire series of the six meditations , day after day, is a single sustained effort to reconstruct philosophy, to find for philosophy the certainty of a mathematical proof.