 That is, Joyce’s motivation rules out situations in which inaccuracy increases from \(c\) to \(m\) and then decreases from \(m\) to \(c'\). And this is what Weak Convexity also rules out. But Strong Convexity furthermore rules out situations in which inaccuracy remains the same from \(c\) to \(m\) and then from \(m\) to \(c'\). And Joyce has given no reason to think that such changes are problematic. What’s more, as Maher proves, the stronger convexity condition is crucial for Joyce’s proof. With only the weaker condition, the theorem is false.