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Definition of destructiveness : 1. The faculty supposed to impel to the commission of acts of destruction; propensity to destroy.
2. The quality of destroying or ruining.

Synonyms:

ferocity, insurrection, broil, vandalism, brutishness, frenzy, atrocity, outrage, brawl, wildness, abuse, fracas, attack, barbarity, vehemence, thuggery, fierceness, violence, inhumanity, savagery, fight, terrorism, fury, assault, commotion, brutality, torture, turmoil, rage, intensity, uproar

Usage examples:

• And never a sign of man or mark of man's destructiveness; nor axe nor fire had harmed a single tree. - "The So-called Human Race", Bert Leston Taylor.
• Many children see and hear the birds, but if they have not been brought into sympathetic relation with them, they never learn to appreciate them; on the contrary, their attitude becomes one of indifference or of destructiveness. - "Ontario Teachers' Manuals: Nature Study", Ontario Ministry of Education.
• But in the drawing- room one lays off his destructiveness with his hat and gloves, and the Young Person enjoys the same immunity that a sleepy mastiff grants to the worthless kitten campaigning against his nose. - "The Fiend's Delight", Dod Grile.