Suppose our untestable-in-principle hypothesis is that undetectable dragons in your garage cause cancer. Then X is “undetectable garage dragon.” As far as I can tell, there is no way to assign a probability to an undetectable dragon.
What’s wrong with zero? An indetectable something is redundant and can be eliminated without loss; it has no consequences that the negation of its existence doesn’t also imply. You might as well treat it as impossible—if you don’t like giving zero probabilities, assign it whatever value you use for things-that-can’t-occur.
Bayes’ Theorem never returns “undefined”. In the absence of any evidence it returns the prior.
Bayes’ Theorem is undefined if p(X) is undefined.
Suppose our untestable-in-principle hypothesis is that undetectable dragons in your garage cause cancer. Then X is “undetectable garage dragon.” As far as I can tell, there is no way to assign a probability to an undetectable dragon.
Please correct me if I’m wrong.
Solomonoff induction. Presumably you agree the probability is less than .1, and once you’ve granted that, we’re “just haggling over the price”.
What’s wrong with zero? An indetectable something is redundant and can be eliminated without loss; it has no consequences that the negation of its existence doesn’t also imply. You might as well treat it as impossible—if you don’t like giving zero probabilities, assign it whatever value you use for things-that-can’t-occur.