Language is not algebra. Language is a correspondence between thoughts and their expression. Each language is an open continuum which is created by many people of different trades and in different cultural contexts. One of the most common ways to create something new is analogy. Being applied on various levels, it gives a nested recombination of known elements which correspond to known images related to perception and reasoning. Human brain has all the necessary power to learn any language from scratch, not using any grammar. A native language is learned as a set of patterns. And each pattern makes sense. Formal grammar does not make sense, it lacks in detail. That's why it is much easier to read 10000 pages of text and conversation and learn a lot from it than to drill oneself with cards and guess-the-word exercises. I managed to push my English to an advanced level by doing so.