Is propositional logic present in all languages?

I wonder whether propositional logic could be formed in all languages. I can imagine some could have problems to construct phrases based on the rules of the logic (e.g. Quechua), but I wonder if there are some, where such "thinking" is not present.

• There appears to be a typo in either the title or the body of this question. Given that propositional logic is a common and standard term, whereas prepositional logic isn’t (as far as I can tell), I take it that the body is correct and the title is incorrect? If not, you’ll have to explain what you mean by ‘prepositional logic’. Mar 8 at 13:21
• Also, what do you mean with “have problems to construct phrases based on the rules of the logic”? That laws of logic could not be expressed in, say, Quechua? Or that the semantics of these languages cannot be expressed using propositional logic? Mar 8 at 13:27
• @Keelan I wonder that in agglutinative languages like Quechua formulaic templates, as mentioned below, are hard to form. Mar 10 at 7:54

Every natural language has the resources required for constructing a system of propositional calculus, and no language naturally encodes exactly some system of propositional calculus. One fundamental concept of logic corresponds to English "and", which is graphically symbolized in a variety of ways such as ∧ or &. The natural language use of "and" is broader than the formal logical use, which is one reason that logicians like to use separate symbols to keep clear that they are talking just about "∧".

While English has separate words "no, not" corresponding to "~, ¬, ^" etc, negation of a proposition may in natural language be signalled by a particular verb form (a negative inflection). Therefore, translation of a sentence of one natural language into some system of propositional calculus might be more complicated compared to a translation from English. The real difference between English and other languages (Quechua, Zulu, Navaho...) in terms of converting sentences into formal propositions is that there has been a huge amount of work done in discovering the logic-to-language relations of English where they even teach formulaic templates (such as "just in case") with conventional formal logic expressions. Quechua has benefited less from such efforts, but there is no intrinsic linguistic impediment to doing so.

• Logic is just a 'stick-figure' representation of language. It is not thought, and it is not language; it's a variety of mathematics that attempts to formalize certain kinds of talk. Mar 8 at 18:57
• @jlawler so what you are saying, is that it was created upon the language? But when using Euler diagrams to explain different concepts of logic, it is no longer about language. Moreover, I can imagine the situations in nature, which may follow concepts of this logic also. Mar 10 at 7:57
• Logic is mathematics. Language is hundreds of thousands of years old. Mathematics (and logic) is a practice of literacy, and only thousands of years old. Plus it's known only by a few. It's a mathematical tool, like calculus, and it's based on language like calculus is based on motion. Mar 10 at 17:18
• @jlawler, Aristotle disagrees with you, though Frege might. Mar 10 at 17:40
• Aristotle thought that talk in Greek was transparently thought. And he didn't know mathematics. Mar 10 at 17:44