VS + 게
From Jonathan Gardner's Korean Notebook
Verb Stem + 게: "in a ~ way"; "to allow ~ to occur"
This special form converts a verb or an adjective into an adverb. The result has one of two meanings:
With adjectives, it means "in a ~ way."
With action verbs, it means, "to allow ~ to happen".
- 내가 읽게 나가줘: "Leave so I can read."
This leads to the following special verb endings:
There is one special, very common abbreviation:
- 하게 -> 히
It is so common that you will only rarely hear "하게", and then only in older speech.
My personal theory: VS + 겠다 is really an abbreviation of VS + 게 and 있다. That's why it has such a weird meaning, ranging from "will ~" (or rather, "to exist such that ~ occurs"), to "might be ~" (or rather, "to exist in a ~ way".) Obviously, native Koreans don't think this makes any sense.