formally argue, in such a way that one does not have to know the meaning of the characters and character strings, which one changes, generates or removes there according to certain rules. At the syntactic level, therefore, we are only dealing with strings of different complexity, without these having already been assigned a meaning.Įven a rudimentary knowledge of mathematics gives us an indication of the usefulness of a formal language. The syntax specifies exactly what should be allowed with regard to the formation of character strings. In formal languages, the distinction between syntax and semantics becomes even clearer. Semantics, on the other hand, deals with the meaning of words and sentences. The syntax or grammar thus regulates the formal structure of a language. It shows, for example, how words are declined or conjugated in a sentence regardless of their meaning, depending on their function and position, and in which order they can occur in a sentence. Syntax is what is called grammar in natural languages. Here the important difference between syntax and semantics has to be discussed. So you learn to write the letters first, then the words and then the sentences.
In colloquial language this set represents the usual alphabet, strings are words and several strings represent sentences. In all three languages there is a certain set of characters with which you can form strings. Thus, we now look at three languages: logic, mathematics and our colloquial language. The language of mathematics may serve as an intermediate station between the formal language of logic and our colloquial language, because it is already formal and the contemporary has at least some experience with it. It’s just all so much easier, and so simple, that at first you feel yourself as a stranger. The best thing to do is to look at the structure of a formal language in analogy to the structure of our mother tongue and to demonstrate the similarity of a formal language with our colloquial language.
Since one experiences again and again, which shyness most contemporaries have at mathematical formulas, one has to exercise great caution with the representation of a formal language for the logic. Its mathematical form made it possible to transfer logical reasoning rules to machines, which has led, among other things, to the now flourishing field of “artificial intelligence” research. The “term logic”, as the philosophers had always practiced until then, was soon replaced by this propositional logic logic developed into a predominantly mathematical discipline. The final form of a “propositional logic” was then created somewhat later by Alfred North Whitehead (1981 to 1947) and Bertrand Russell (1872 to 1970). And again one can see how formalization leads to an accelerated development of a field of knowledge, then “emigrating” from philosophy. He thus discovered a “new science” for logic, as Galileo had done for natural research. So Frege probably knew the power of a formal language with such a language he then raised logic to a new level, on which one could lead proofs as in mathematics. Gottlob Frege was a philosopher and mathematician, his father had written a New High German grammar (Wikipedia: Gottlob Frege). Leibniz is thus the godfather of the modern formal logic (Wille, 2018, p. The foreword says: In this “small script I have now tried a rapprochement with the Leibniz thought of a lingua characteristicistica”. The mathematician and philosopher Gottlob Frege (1848-1925) founded modern logic with a book entitled “Begriffsschrift – Eine der arithmetischen nachgebildete Formelsprache des reinen Denkens” (“Conceptual writing – one of the arithmetic formula languages of pure thought”). Therefore, I want to skip this and talk about modern logic. But this and other developments in this direction can be better assessed in retrospect. For this purpose Leibniz wanted to develop a “lingua characteristica” with suitable characters (characteristica universalis). It would also be his great project to describe a “Scientia generalis” based on the model of mathematics, in order to “bring about in all scients what Cartesius and others did by algebra and analysis in Arithmetica et Geometria”. In particular, the work of Gottfried Wilhelm Leibniz (1646 to 1716), in which important approaches to modern logic can already be found, should be honoured. After briefly introducing Aristotle’s syllogistics in the last blog post, I should now actually explain how it were received and elaborated in antiquity, the Middle Ages and into modern times.
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