The British spelling of apostrophize: to address someone absent or something non-human directly in speech or writing; to use apostrophes in text.
From apostrophe plus the verb-forming suffix -ise (British convention, versus American -ize). Both spellings emerged from the rhetorical practice and punctuation convention.
British and American English literally can't agree on how to spell their verbs—it's apostrophise vs. apostrophize, and somehow both are 'correct' depending on which side of the Atlantic you're on!
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