Probability

Let's say that we need reasons to attribute a probability p to an event e.  Without the possibility of reasons, attribution of probability is unintelligible.  This might be taken to be a way of saying that there are no 'real' probabilities, but since 'real' and 'can talk as if real' work in the same way in all discourse, we don't need to worry about this.

If I say 'e is more probable than ~e', I am saying that p > 1/2.  All probability attributions are at least strict inequalities, if not specific values.

My reasons for attributing probability p to event e must, then, include a computation that demonstrates the vailidity of the strict inequality.  In Baysian computations, we show how some probabilties are derived from others - the results of statistical tests are an example.  At the basis of these are appeals to theories (e.g. combinatorial considerations, engineering descriptions, or wave and field equations) from which basic probabilities can be directly derived.

These computations, and the theories which provide the primitive probabilities, must be articulated in a shared language.  There is no way of attaching a meaning to questions (in the same language) about the probability that the way we speak the language, or the language itself, may be unreliable here (whether or not we can attach a meaning to the possibility of this).  We cannot say 'it is more likely than not that our language works' because no conceivable computation could validate the relevant inequality.

(Equally, we cannot say 'It is quite certain that our language works' if we read this in the sense of the probability of its not working being zero.  Our ability to attribute probabilities depends upon our ability to speak, so attributing a probability to our ability to speak is circular.)

We can make the classical distinction between risk and uncertainty by saying that we can attribute probabilities to risky outcomes, but uncertain ones may only be partly tabulatable.  We can make a list of some of them, but neither attribute probabilities to them nor be sure that the list is exhaustive.

To say that there is a definite, but unknown p of e is to promise a computation that produces p.  The Born rule can be accepted in the 'world' in which we speak, because - in that world - it is a testable empirical theory.  Maybe if we want to talk about many worlds then we cannot talk - and we do not need to talk - about Born probabilties.  Only the illusion of 'real' probability makes this seem puzzling.