Plural of 'circularity': instances or qualities of being circular in shape, form, reasoning, or meaning.
From 'circular' plus '-ity' (from Latin '-itas'), a suffix that makes abstract nouns from adjectives, plus the plural '-ies.' The root 'circulus' (Latin for circle) is ancient.
When people say 'that's circular reasoning,' they're using a logic term that reveals a fundamental problem: if your proof depends on your conclusion, you've gone in a loop and proven nothing!
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