To think like a linguist

Linguistics is the scientific study of natural language. Semiotics, by contrast, is the scientific study of anything symbolic, whether natural language or not. For example, linguistics doesn’t study the artificial languages of logic and mathematics, but semiotics does.
What’s the significance of the distinction in linguistics between “natural language” and “artificial language?” What about the related distinctions between “children” and “adults,” “natives” and “foreigners”?
To think like a linguist is to bring a logical or mathematical mind to the analysis of “intuition,” the structure of natural language being isomorphic to the structure of “intuition.”
In practice, linguistics is often the scientific study of folk physics, folk psychology, etc.

Ian Ryan