Saussure, Gödel, Popper in relation to linguistic and mathematics

Mathematics which is the common language of scientific world has witnessed internal crisis for many times in its own historical development. By bypassing these crises with a series of transformations, it was reborn like a phoenix from its own ashes. While getting a more steady appearance it had a unique intellectual technique and language. Its language based on mathematical thinking turned out to be the common language of science, too, due to the ability of explaining the concrete reality. This language ,which has been tried to be fully formalized with a logic-based approach, has been irrepressibly wounded by the logical breaks created by Godel. As cleary understood from the history of science, the language of mathematical thinking which has turned to be a common language for almost all disciplines, while taken with a Saussurean approach, apparently is not a language which can be easily left. We now know that a language used for a common purpose and possesing signs is not abandonable. So how can the language of mathematical thinking, which still lacks the ability to express its own completeness in the systematic language, continue to be a representation language for the visual and physical world? The purpose of this thesis is to show that while the language of mathematical thinking expresses its place and value in the scientific world with a Saussurean approach, the falsibility theory widely accepted in Popper's philosophy of science can be used for mathematics as well. In this way, although Gödel's contribution to mathematical thinking is relative, it will try to achieve the result that the use of this language can continue as long as it is useful. Keywords: Saussure, Gödel, Popper, Linguistic, Semiology, Logic, Mathematics, Falsibility