 In the standard terminology, the dispute is between incompatibilists who affirm the conflict between EXT and SK, and compatibilists who deny it. Incompatibilists have pressed the conflict mainly in two ways. The first way, discussed in section 2, is by a reductio ad absurdum: Incompatibilists argue that EXT plus SK entail the absurdity that one can know just from the armchair contingent facts about the external world. The second way, discussed in section 3, features a thought experiment about “slow switching” between two environments. Incompatibilists argue that such thought experiments show that EXT precludes SK. In section 4, we will end with some lesser-known issues for externalist self-knowledge.