 This enables Stalnaker to avoid the argument against non-truth-functional truth conditions given in §2.2. The argument was as follows. There are six incompatible logically possible combinations of truth values for \(A, B\) and \({\sim}A\gt B\). We start off with no firm beliefs about which obtains. Now we eliminate just \({\sim}A \amp{\sim}B\), i.e. establish \(A\) or \(B\). That leaves five remaining possibilities, including two in which “\({\sim}A\gt B\)” is false. So we can’t be certain that \({\sim}A\gt B\) (whereas, intuitively, one can be certain of the conditional in these circumstances). Stalnaker replies: we can’t, indeed, be certain that the proposition we were wondering about earlier is true. But we are now in a new context: \({\sim}A \amp{\sim}B\)-worlds have been ruled out (but \({\sim}A \amp B\)-worlds remain). We now express a different proposition by “\({\sim}A\gt B\)”, with different truth conditions, governed by a new nearness relation. As all our live \({\sim}A\)-worlds are \(B\)-worlds (none are \({\sim}B\)-worlds), we know that the new proposition is true.