This is where things go wrong. The actual credence of seeing a hypercomputer is zero, because a computationally bounded observer can never observe such an object in such a way that differentiates it from a finite approximation. As such, you should indeed have a zero percent probability of ever moving into a state in which you have performed such a verification, it is a logical impossibility. Think about what it would mean for you, a computationally bounded approximate bayesian, to come into a state of belief that you are in possession of a hypercomputer (and not a finite approximation of a hypercomputer, which is just a normal computer. Remember arbitrarily large numbers are still infinitely far away from infinity!). What evidence would you have to observe for this belief? You would need to observe literally infinite bits, and your credence to observing infinite bits should be zero, because you are computationally bounded! If you yourself are not a hypercomputer, you can never move into the state of believing a hypercomputer exists.
Sorry, I previously assigned hypercomputers a non-zero credence, and you’re asking me to assign it zero credence. This requires an infinite amount of bits to update, which is impossible to collect in my computationally bounded state. Your case sounds sensible, but I literally can’t receive enough evidence over the course of a lifetime to be convinced by it.
Like, intuitively, it doesn’t feel literally impossible that humanity discovers a computationally unbounded process in our universe. If a convincing story is fed into my brain, with scientific consensus, personally verifying the math proof, concrete experiments indicating positive results, etc., I expect I would believe it. In my state of ignorance, I would not be surprised to find out there’s a calculation which requires a computationally unbounded process to calculate but a bounded process to verify.
To actually intuitively give something 0 (or 1) credence, though, to be so confident in a thesis that you literally can’t change your mind, that at the very least seems very weird. Self-referentially, I won’t actually assign that situation 0 credence, but even if I’m very confident that 0 credence is correct, my actual credence will be bounded by my uncertainty in my method of calculating credence.
Sorry, I previously assigned hypercomputers a non-zero credence, and you’re asking me to assign it zero credence. This requires an infinite amount of bits to update, which is impossible to collect in my computationally bounded state. Your case sounds sensible, but I literally can’t receive enough evidence over the course of a lifetime to be convinced by it.
Like, intuitively, it doesn’t feel literally impossible that humanity discovers a computationally unbounded process in our universe. If a convincing story is fed into my brain, with scientific consensus, personally verifying the math proof, concrete experiments indicating positive results, etc., I expect I would believe it. In my state of ignorance, I would not be surprised to find out there’s a calculation which requires a computationally unbounded process to calculate but a bounded process to verify.
To actually intuitively give something 0 (or 1) credence, though, to be so confident in a thesis that you literally can’t change your mind, that at the very least seems very weird. Self-referentially, I won’t actually assign that situation 0 credence, but even if I’m very confident that 0 credence is correct, my actual credence will be bounded by my uncertainty in my method of calculating credence.