The problem of mutual defeat in Strong Phenomenal Conservatism

Strong Phenomenal Conservatism, as defended by Michael Huemer, says that having an appearance that p is a necessary and sufficient condition for having a justified belief that p in the absence of defeaters. I argue that the no-defeater condition is problematic in Strong Phenomenal Conservatism because it leads to the problem of mutual defeat due to conflicting appearances, a problem that becomes especially clear with optical illusions. I show that the problem of mutual defeat cannot be avoided by looking at differences in strengths of appearances, differences in quantity and quality of appearances, higher-order appearances, or unjustified beliefs. The only way the mutual defeat problem can be avoided is by relying on justified beliefs that are not ultimately based on appearances, but this means that Strong Phenomenal Conservatism is false. Therefore, phenomenal conservatives should opt for a weaker version of it.