In Latin onus means “burden.” In English it came to mean “responsibility”: “the onus is on the defense attorney to convince the jury of the defendant’s innocence.” It is often used to mean “blame”: “he bears the onus of having lost the key to the vacation house.”
People sometimes mishear this word and turn it into “owness.” This form is also used by some to refer to the opposite of otherness, but that would be “ownness,” with two N’s.
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