Step 3 doesn't quite work. If not being a Boltzmann brain implies that you are a Boltzmann brain, then it is irrelevant that this logic no longer works under th

Step 3 doesn't quite work. If not being a Boltzmann brain implies that you are a Boltzmann brain, then it is irrelevant that this logic no longer works under the assumption that you are a Boltzmann brain. The first is enough to show that not being a Boltzmann brain is impossible, the second is not enough to cause a paradox.