In the 17th century, new discoveries in physics and mathematics made some philosophers seek for certainty in their field mainly through the epistemological approach. Rene Descartes (1596-1650), a French philosopher and the founder of the mathematical rationalism, was one of the prominent figures in the field of philosophy of the 17th century. He defended the idea of the omnipotence and infallibility of the mind.
Descartes recognized the existence of two substances: the matter and the spirit. The main attributes of spirit are thinking and consciousness. The philosopher saw the matter as the eternal universe comprised of the corpuscles that may be divided endlessly. Along with the longitude, the physical objects are characterized by the movement which Descartes had primarily reduced to the mechanical one.
In his Theory of Knowledge, Descartes introduced an important methodological technique – doubt. The method of doubt was founded on the principle of “cogito ergo sum” that is usually translated as “I think, therefore I am.” This principle is primarily idealistic, yet it is characterized by the epistemological approach. Descartes’ principle is meant to find the truth and natural reality, and it has played a significant role in the process of the modern science formation because it calls on to doubt everything and not to take anything on trust or faith.
While asserting the epistemological rationalism, Descartes formulated a set of rules of the rationalist method. First of all, one shouldn’t accept anything as truth until he/she cognized it with evidence. Secondly, it is important to avoid haste and the personal interest in the truth that could be used for the personal benefit. Each research question must be divided into as many parts and sections as it may be needed to cognize it with the patency. It is better to commence the research with the simplest objects that can be cognized more easily and then move towards those that may be harder to comprehend. Each question of the study must be illuminated extensively to make sure that all of its aspects are taken into consideration and are not neglected.
According to Descartes, only the being of thinking is authentic and reliable (cogitatio est). Thinking is the criterion that determines the reliability of objects. As Descartes claims, the real thing is the thing that is understood. In the external nature, only the mathematical elements can be comprehended, and these elements thus are real in their internal nature. Nature acts in the compliance with the rules of mathematics. Therefore, it is regular and cognizable, and, consequently, it is real.
While rightly emphasizing the qualitative distinction of the rational aspect of thinking from the sensory one, at the same time, Descartes exaggerated the rational thinking capacities and separated them from empirical and emotional experiences avoiding the fact that the rational thinking originates from these senses. In this way, Descartes inevitably came to idealism. He recognized the existence of a special and pure rational source of knowledge, innate concepts, to which he has primarily attributed the mathematical axioms. Overall, all the dimensions of the sensory knowledge were associated and transformed into the mathematical objects in the Descartes’ theory.