In english, a 'complete sentence' seems to refer to having at least a single, complete clause — i.e. a subject (noun) and verb — e.g. "I run". This seems to be engrained in the concept of a complete idea or thought, basically a classical predicate — providing information about a subject.
The concept of a "complete" sentence (or complete idea) is definitely common in other languages (at least latin and germanic). Is it common to all languages and cultures?
At first it may seem like an arbitrary linguistic construct that need not be obeyed in unrelated languages, but at the same time --- as I tried to suggest above, it seems to be deeply rooted in our way of thinking.
Edit: I hoped it was obvious from the context I gave above, but I'm not interested in the pedantic question of what minimal requirements satisfy the purely-structural concept of a 'sentence'. E.g. perhaps, "I.", can be a complete sentence in response to a question, or "Go.", as an imperitive. This related, but different, topic is the basis for all of the discourse I've found online, and what I've seen discussed at length by scholars (e.g. Chomsky). Instead, I'm interested in the the concept of a 'complete sentence' in the context of 'a complete thought' per se, in the context of theory of mind/thought, compared in different cultes and languages.