>"The problem I have with the Bayesian definition of probability is that it isn't a definition, is it?"
You'll have to clarify what exactly your problem with the concept is here.
>"So what does the 1 in 1/6 actually mean? And the 6?"
It means there are six possible outcomes, one of which is of special interest and five others. You have no reason to think any one possibility is more likely than any other.
>"What does it mean that someone is 1/6 certain of something?"
You would take any bet on it with better than 6 to 1 odds. If you have to decide between a 1/6 opportunity and a 1/60th opportunity for the same reward you should choose the first. You can use such probabilities to perform a cost-benefit analysis amongst various possible actions with various costs and rewards.
>"How does one measure certainty?"
I assume you are using "certainty" as a synonym for "probability", in which case one way is to ask people to bet.
>"The more I think about it the more I'm convinced Bayesian probabilities are a flawed concept."
Ok, but your objections here don't seem to have much thought/experience behind them.
You'll have to clarify what exactly your problem with the concept is here.
>"So what does the 1 in 1/6 actually mean? And the 6?"
It means there are six possible outcomes, one of which is of special interest and five others. You have no reason to think any one possibility is more likely than any other.
>"What does it mean that someone is 1/6 certain of something?"
You would take any bet on it with better than 6 to 1 odds. If you have to decide between a 1/6 opportunity and a 1/60th opportunity for the same reward you should choose the first. You can use such probabilities to perform a cost-benefit analysis amongst various possible actions with various costs and rewards.
>"How does one measure certainty?"
I assume you are using "certainty" as a synonym for "probability", in which case one way is to ask people to bet.
>"The more I think about it the more I'm convinced Bayesian probabilities are a flawed concept."
Ok, but your objections here don't seem to have much thought/experience behind them.