Imprison, confine, enclose, as in The dog was shut up in the cellar for the night, or She shut up her memories and never talked about the past. [c. 1400]
Close completely, as in The windows were shut up tightly so no rain came in. [Early 1500s] This usage also occurs in shut up shop, meaning "close the premises of a business," as in It's late, let's shut up shop now. [Late 1500s] Also see close up, def. 3.
Cause someone to stop speaking, silence someone, as in It's time someone shut him up. [Early 1800s]
Stop speaking, as in I've told you what I think and now I'll shut up. This usage also occurs as a rather rude imperative, as in Shut up! You've said enough. [First half of 1800s]
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