Of course you don’t have to make use of it, you can use any numbers you want, but you can’t assign a prior of 0.5 to any proposition without ending up with inconsistency. To take an example that is more detached from reality—there is a natural number N you know nothing about. You can construct whatever prior probability distribution you want for it. However, you can’t just assign 0.5 for any possible property of N (for example, P(N10)=0.5).
There can also be problems with using priors based on complexity; for example the predicates “the number, executed as a computer program, will halt” and “the number, executed as a computer program, will not halt” are both quite complex, but are mutually exclusive, so priors of 50% for each seems reasonable.
Assigning 0.5 for any possible property of N is reasonable as long as you don’t know anything else about those properties—if in addition you know some are mutually exclusive (like in your example), you can update your probabilities in consequence. But in any case, the complexity of the description of the property can’t help us choose a prior.
I was refering to the idea that complex propositions should have lower prior probability.
Of course you don’t have to make use of it, you can use any numbers you want, but you can’t assign a prior of 0.5 to any proposition without ending up with inconsistency. To take an example that is more detached from reality—there is a natural number N you know nothing about. You can construct whatever prior probability distribution you want for it. However, you can’t just assign 0.5 for any possible property of N (for example, P(N10)=0.5).
On the other hand it has been argued that the prior of a hypothesis does not depend on its complexity.
There can also be problems with using priors based on complexity; for example the predicates “the number, executed as a computer program, will halt” and “the number, executed as a computer program, will not halt” are both quite complex, but are mutually exclusive, so priors of 50% for each seems reasonable.
Assigning 0.5 for any possible property of N is reasonable as long as you don’t know anything else about those properties—if in addition you know some are mutually exclusive (like in your example), you can update your probabilities in consequence. But in any case, the complexity of the description of the property can’t help us choose a prior.