Some people object to asking about the probability that Shakespeare wrote this or that play. One objection is that someone has already written the play, either Shakespeare or someone else. If Shakespeare wrote it, then the probability is one that he did. Otherwise the probability is zero. By this reasoning, no one can make probability statements about anything that has already happened. Another objection is that probability only applies to random processes. We cannot apply probability to questions about document authorship because documents are not random.
I just ran across a blog post by Ted Dunning that weighs in on this question. He writes
The statement “It cannot be probability …” is essentially a tautology. It should read, “We cannot use the word probability to describe our state of knowledge because we have implicitly accepted the assumption that probability cannot be used to describe our state of knowledge”.
He goes on to explain that if we think about statements of knowledge in terms of probabilities, we get a consistent system, so we might as well reason as if it’s OK to use probability theory.
The uncertainty about the authorship of the play does not exist in history — an omniscient historian would know who wrote it. Nor does it exist in nature — the play was not created by a random process. The uncertainty is in our heads. We don’t know who wrote it. But if we use numbers to represent our uncertainty, and we agree to certain common-sense axioms about how this should be done, we inevitably get probability theory.
As E. T. Jaynes once put it, “probabilities do not describe reality — only our information about reality.”
This is interesting and, in fact, should be more widely known. It not only informs questions like that treated elsewhere on Endeavor (“Ignorance Doesn’t Change Reality”), I think it would help people in business, finance, and the general public to understand this kind of thing, especially when it comes to discussions of risk: http://www.haaretz.com/hasen/spages/1077151.html