From Leibniz to artificial intelligence: A logical and epistemological study on formal languages

The search for the perfect language, ideal language or universal language has continued in various forms over the centuries. As a result of this search, a posteriori languages, which include a synthesis of natural languages have emerged, as well as a priori languages as a result of completely arbitrary choices. While a posteriori languages are talkable languages, a priori languages are usually formal languages. The aim of our thesis is to discuss the universality of programming languages, which are a reflection of a priori philosophical languages that base concept classification on logical foundations. The basis of our discussion is Leibniz's characteristic language, characteristica universalis, which is an a priori philosophical language, and calculus ratiocinator, which he proposed for calculating judgments in this language. The features of Leibniz's universal language that distinguish it from all other universal language studies are the starting points set for our thesis to move on the right path. Leibniz not only imagines or proposes a universal language, but proposes to give a characteristic number to the primary form of each concept. He also emphasizes that as a result of four simple operations with these characteristic numbers, the truth or falsity of our arguments can be judged. Leibniz's work for the universal language did not end up with a universal language, but it did yield quite rich by-products: "Logic as language" and "logic as calculus". These two separate areas of logic contain very important points that will lead us to question the universality of programming languages. In this study, we will handle the universality of programming languages, which have an important place in today's information technologies, starting from Leibniz's dream of a universal language. For this, first of all, we will try to reveal the logical and mathematical structure of Leibniz's universal language. As a result of Frege's Begriffsschrift (Concept-Script), another example of a priori philosophical language designed in the context of Leibniz since the end of the nineteenth century, we will follow the development of the precise syntax of today's notation and formal language of mathematics through various logics. In order not to lose the trace of Leibniz's universal language, it is clear that we can not carry out a question of universality in programming languages without the transfer of these developments in the fields of mathematics and logic. Because in order to reach programming languages from Leibniz, it is clearly necessary to use the bridge of mathematics and logic in the nineteenth century. While programming languages perform their commands and loops in expressions with English-like imperative moods, their syntax consists entirely of logical and mathematical notations. As such, it is clear that they are genuine a priori philosophical languages. For this reason, claims have emerged that these language structures have the feature of being universal. In addition, another point that should be mentioned is that programming languages, which are a priori philosophical language, are used to write programs that are developed entirely on mathematical operations and calculations. Thanks to these languages, we can make a computer do the work what we want. The process that takes place for this to happen is computational. Thus, we face with the criterion of universality in the context of computational theory. In this sense, our thesis will follow Leibniz's dream of a universal language through programming languages on the one hand, on the other hand through context of computational theory and artificial intelligence. As a result, we can state that such a universal language is not possible through the basic theories of mathematical logic, but we will continue to keep the necessity of a universal language alive.