The quality or state of being faint; weakness, timidity, indistinctness, or lack of strength or courage.
From 'faint' (adjective) plus the noun suffix '-ness,' which creates abstract nouns from adjectives. The word has been in English since the 13th century with this meaning.
The word 'faintness' can refer to physical weakness (like the faintness of a voice) or moral weakness (like the faintness of character)—so English uses the same word for both physical and psychological pallor, suggesting ancient people saw a connection between them.
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