 We have explored one argument against the joint truth of EXT and SK, namely, the reductio to armchair knowledge of the world. But there is a further group of arguments to the same incompatibilist end. Such arguments rest on a different thought experiment, the “slow switching” experiment, to bolster the incompatibility of EXT and SK. In brief, the new thought experiment suggests that under EXT, self-attributions of thought content are not sufficiently discriminating to vindicate SK.