The quality or state of not being defensible.(noun)
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Use "indefensibility" in a sentence
"Secondly, the argument about the indefensibility of the 1967 borders completely ignores the conventional military and nuclear superiority of Israel."
"This idiot move of Huckabee's -- probably the best he can come up with given the craven indefensibility of his actions in the Dumond case -- simply highlights what his "compassion" caused: the needless brutal murder of one and perhaps two women."
"The justness of the cause, the moral bankruptcy of segregation and the indefensibility of the system had a lot more to do with it."