In other words, just because you might think some probabilities are “more accurate and reliable,” does not mean that everyone agrees with you. To assume that everyone agrees with you is to assume the very thing you are trying to prove. The burden is on you, after all, to prove that certain probabilities are “objective” in some sense, in spite of the glaring fact that not everyone believes this.

There is ample room for disagreement when we are dealing with uncertain events and phenomena. And this is just another way of saying that probability is a measure of subjective belief.

The question is whether in addition to this it is philosophically meaningful to talk of an “objective probability” of something happening.

If you believe that reality is non-deterministic, that God really does throw dice, then the probability of something happening is indeed a property of the universe.

But most of us tend to think that instead the universe is governed by deterministic laws of cause and effect. Under this hypothesis, probability is a function of our models of the universe and their adequacy (related to the size of the error term, the bit we can’t adequately explain). Such models can be written down and critiqued, judged to have or not have predictive value – they are one step more “objective” than the ideas in somebody’s head.

I’d argue that it is philosophically meaningful to say that one person’s subjective probability is more accurate (more reliable) than another’s subjective probability of the same event. Which tends to imply an objective something which is used as the yardstick to judge our subjective perceptions.

In a Heisenbergian universe, it may be impossible to know whether or not it will rain in Denver tomorrow. A probability may be the best we can do.

Or, in a more relaxed version, it may the best we can know with the computing power available to us – an information theory limit rather than a physical one.