Bayesian probability works well when the specific values are known (they use the example of predicting the color of a ball to be drawn out of a container). In theology, the values are not known.
If you don’t allow exact probabilities for things, there are decisions it becomes impossible to make, such as whether or not to take a given bet. If you try to come up with a different method of choosing, you either end up with paradoxes, or you end up behaving exactly as if you were using Bayesian statistics.
If one wants to evaluate the probability that this world exists and there are infinitely many possibilities, n, then no matter how small a probability one assigns to each one, the sum will be infinite.
This is only true if we assign them all the same probability. We tend to weight them by their complexity. Also, if you didn’t, the more complex possibilities would tend to contain the simpler ones, which may approach a limit as the number of possibilities considered increases.
Also, if you didn’t, the more complex possibilities would tend to contain the simpler ones, which may approach a limit as the number of possibilities considered increases.
Loved that point. Well said and I hadn’t thought of that.
...or you end up behaving exactly as if you were using Bayesian statistics.
Which is what I think they’re doing here. Coming up with some new formulation that may be operating within the realm of Bayes anyway.
If you try to come up with a different method of choosing, you either end up with paradoxes...
I’d be interested in hearing more about this. Can you give an example of a paradox? Do you just mean that if your decision making method is not robust (when creating your own), you may end up with it telling you to both make the bet and not make the bet?
Either you would a) neither be willing to take a bet nor take the opposite bet, b) be willing to take a combination of bets such that you’d necessarily lose, or c) use Bayesian probability.
If you don’t allow exact probabilities for things, there are decisions it becomes impossible to make, such as whether or not to take a given bet. If you try to come up with a different method of choosing, you either end up with paradoxes, or you end up behaving exactly as if you were using Bayesian statistics.
This is only true if we assign them all the same probability. We tend to weight them by their complexity. Also, if you didn’t, the more complex possibilities would tend to contain the simpler ones, which may approach a limit as the number of possibilities considered increases.
Loved that point. Well said and I hadn’t thought of that.
Which is what I think they’re doing here. Coming up with some new formulation that may be operating within the realm of Bayes anyway.
I’d be interested in hearing more about this. Can you give an example of a paradox? Do you just mean that if your decision making method is not robust (when creating your own), you may end up with it telling you to both make the bet and not make the bet?
Either you would a) neither be willing to take a bet nor take the opposite bet, b) be willing to take a combination of bets such that you’d necessarily lose, or c) use Bayesian probability.
Thanks for the link and explanation.