 It is a matter of ongoing debate what the conditions are under which it is rational to accept something. Nevertheless, it is commonly agreed that, as Hume put it, the wise person “proportions his beliefs to the evidence” (1955, p. 118). If this is right, then if a sufficient case can be made out for a contradiction, it will be rational to believe it. And sometimes this does seem possible. We have seen that a seemingly compelling argument can be made in favour of the truth of the strengthened Liar sentence, ‘This sentence is not true’. Whether or not one takes the argument in question to be completely persuasive, it suggests that there is nothing in principle impossible about the existence of good arguments for true contradictions. Of course, if there were conclusive evidence for the LNC, then no case for a contradiction could be strong enough. But conclusive evidence for any philosophical position is difficult to achieve.