The quality or state of being four; the abstract property of having four units or components.
From Middle English, combining the cardinal number 'four' with the abstract noun suffix -ness. This suffix creates abstract nouns from adjectives and numbers, similar to how 'happiness' comes from 'happy' or 'sameness' from 'same'.
While we don't use 'fourness' much anymore, medieval and ancient mathematicians and philosophers used it to describe the essential abstract property of the number four, which was philosophically important because four represented stability in many cultures (four directions, four seasons, four elements).
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