An orthodox sceptical hypothesis claims that one's belief that "I am not a brain-in-a-vat (BIV)" (or any other ordinary anti-sceptical belief) is insensitive.A form of sensitivity-based scepticism,can thus be constructed by combining this orthodox hypothesis with the sensitivity principle and the closure principle.Unlike traditional solutions to the sensitivity-based sceptical problem,this paper will propose a new solution——one which does not reject either closure or sensitivity.Instead,I argue that sceptics' assumption that one's ordinary anti-sceptical beliefs are insensitive will give rise to self-contradiction.The orthodox sceptical hypothesis is thus revealed to be incoherent and arbitrary.Given that there is no coherent reason to presuppose our ordinary anti-sceptical beliefs to be insensitive,the argument for sensitivity-based scepticism can thus be blocked at a lower epistemological cost.