This word is acceptable for play in the US & UK dictionaries that are being used in the following games:

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n. the state or quality of being destructive

n. The quality of destroying or ruining.

n. The faculty supposed to impel to the commission of acts of destruction; propensity to destroy.

n. The quality of being destructive; tendency to destroy or ruin.

n. In phrenology, the tendency to destroy or overthrow, supposed to be located in a special organ of the brain. See cut under phrenology.

n. the quality of causing destruction

"And Maud's, face brightened; for destructiveness is one of the earliest traits of childhood, and ripping was Maud's delight."

quality   

harmfulness    poison    injuriousness   

bloodthirstiness    inhumanity    wastefulness    unreason    sadism    rapacity    fundamentalism    militancy    bigamist    licentiousness