# Gottfried Leibniz Concept of Method

June 27, 2021According to Leibniz, like Descartes and Spinoza, the only method leading to reliable knowledge should be in the mathematical structure, because information in mathematics is information that has absolute truth value, in which all its constituent elements are compatible with each other.

Everything is precise, clear and clear in mathematics. For this reason, if a method that leads to a mathematical structure can be applied, other sciences can become self-evident knowledge systems like mathematics, and a universal science system or encyclopedia can be created by harmonizing them with each other.

Therefore, Leibniz, in his De arte Combinatoria (1666), proposed a method first mentioned by a medieval thinker, Raymond Lulle, and also mentioned by Galileo and Descartes. Accordingly, terms with complex structures had to be resolved into simple terms: The term considered would be formally taken back to its constituent parts, so that the term would be defined, and then the available parts would be divided into their own parts and they would also be defined. With such an analysis, definitions of the terms of the first definition will be given, and the process will continue until the elements that cannot be defined any more.

These indefinable elements or terms will form the alphabet of human thought; just as all words are combinations of the indefinable letters of the alphabet in one way or another. In the second step, these indefinable terms will be represented by mathematical symbols. If the right way to combine these symbols can be found, an inventive logic will be created to draw new conclusions. In addition, this method will also serve to prove what is already known – to show their accuracy. Leibniz calls these undefined terms primae possibilitates because they form the basis of all propositions to be derived from them. This method reveals an art of new propositions and of reaching new propositions by combining them – the art of combining (ars combinatoria). As can be seen, this method demonstrates an effort to create a deductive-formal and mathematical logic. It can be said that this is a work that precedes the mathematical logic created by Bertrand Russell in the 20th century.

Leibniz certainly did not think that all truths could be deduced a priori in this way. For example, the facts that Paris is the capital of France, that Napoleon is the emperor of France, are those that are known through research on historical facts. Or realities, such as cats meowing and dogs barking, are realities known through empirical experience. But Leibniz thought that he could use the deductive mathematical structured combination art he proposed to derive correct propositions in fields such as metaphysics, physics, and law, apart from logic and mathematics. “The discovery of true mathematical symbolism would provide a universal language, a characteristica universalis, and with the use of this language in various branches of study, human knowledge could be developed without limit in such a way that there would be no more room for counter-theories than in pure mathematics” (Copleston, 1996: 11).

In this way, Leibniz dreamed of a universal science in which logic and mathematics were also part. Because he predicted that there are essential connections between all fields of existence in the universe. According to him, a deductive logic or mathematical system is an indication that the universe is a harmonious system. Thus, a deductive metaphysical science could become a general ontology. The establishment of this general universal science also led him to develop the idea of creating a comprehensive encyclopedia of human knowledge. In this system, all branches of knowledge could be seen and handled in relation to each other, starting from the basic lean elements. This system even made room for theological orders. However, Leibniz was unable to realize neither the ars combinatoria nor the design of the universal encyclopedia of knowledge. The results of such an understanding of method came to life in the following centuries by different attempts.

Prepared by: Sociologist Ömer YILDIRIM

Source: Omer YILDIRIM’s Personal Lecture Notes. Atatürk University Sociology Department 1st Year “Introduction to Philosophy” and 2nd, 3rd, 4th Grade “History of Philosophy” Lecture Notes (Ömer YILDIRIM); Open Education Philosophy Textbook