So then, moving on to the argument that “because I might believe 2+2=3 tomorrow (albeit very unlikely), I can’t believe 2+2=4 100% today”.
If Omega tells you that tomorrow you will believe that 2+2=3, most of your probability mass is concentrated in the possibility that 2+2=4, but you’ll be somehow fooled, perhaps by hypnosis or nano-editing of your brain. Very little if any probability mass is for the theory that 2+2 really equals 3, and you’ll have the major revelation tomorrow. In order to use this thought experiment to show that I don’t have 100% confidence in 2+2=4, you need to assert that the second probability exists, however the thought experiment is also consistent with the first probability being high or one and the second being zero (you can’t assume I agree that zero is not a probability, or you’re begging the question).
So then, moving on to the argument that “because I might believe 2+2=3 tomorrow (albeit very unlikely), I can’t believe 2+2=4 100% today”.
If Omega tells you that tomorrow you will believe that 2+2=3, most of your probability mass is concentrated in the possibility that 2+2=4, but you’ll be somehow fooled, perhaps by hypnosis or nano-editing of your brain. Very little if any probability mass is for the theory that 2+2 really equals 3, and you’ll have the major revelation tomorrow. In order to use this thought experiment to show that I don’t have 100% confidence in 2+2=4, you need to assert that the second probability exists, however the thought experiment is also consistent with the first probability being high or one and the second being zero (you can’t assume I agree that zero is not a probability, or you’re begging the question).