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.