Probability as Degrees of Logical Support
- is actually very similar to Probability as Degrees of Belief. The main difference is that, instead of degrees of belief, here you talk about the degree of logical support for a particular hypothesis. In this view, probabilities are a generalization of classical logic
In the most general sense, a probability is a number attached to a statement. That number specifies how likely it is that the statement is true. Examples of such statements are:
- A coin will land on its “tails” side.
- It will rain tomorrow.
- Your girlfriend is pregnant.
- The cat trashed the house.
Each of these statements is true with some probability. If it’s 0, the statement is definitely false, and if it’s 1, the statement is definitely true. So far, this is really just good old logic.
What logical probabilities introduce is a way to handle uncertainty. If a probability is any number other than 0 or 1, then there is some level of uncertainty about the truth of the statement. The uncertainty grows as the probability gets further away from 0 and 1 (and closer to 0.5). Uncertainty is greatest when the probability is exactly 0.5 because then the evidence is equally undecided about the truth of the statement.
With this definition, you still update probabilities with Bayes’ theorem. The difference is that you are more constrained in your initial assignment of priors. You can’t appeal to vague things like your gut feeling. However, there’s still some disagreement among theoreticians on this point.