The verb censor first developed in 1833 from the noun censor, which today means "one who censors" but at the time had a very specific definition referring to a Roman magistrate who administered censuses and oversaw public morals. Obviously, that latter function is what stuck, but the entire meaning is important as we go through Middle French (the term was borrowed sometime in the 1530s) and back to the Latin verb censere, which could mean "judge", "appraise", or "value" - three things Roman censors did. That, through Proto-Italic kenseo, derives from the Proto-Indo-European root kens, which meant "proclaim". And, for those of you who were wondering, censor is indeed related to the word census through the Roman role, because the person in question did both things.
Adam Aleksic, a freshman studying linguistics at Harvard University, has been described as the internet's sixth most famous etymologist. He has disturbing interests in words, vexillology, geography, board games, limericks, and law, and he loves writing about himself in the third person.
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