Suppose that your good friend, the police commissioner, tells you in strictest confidence that the crime kingpin of your city is Wulky Wilkinsen. As a rationalist, are you licensed to believe this statement? Put it this way: if you go ahead and mess around with Wulky's teenage daughter, I'd call you foolhardy. Since it is prudent to act as if Wulky has a substantially higher-than-default probability of being a crime boss, the police commissioner's statement must have been strong Bayesian evidence.
Our legal system will not imprison Wulky on the basis of the police commissioner's statement. It is not admissible as legal evidence. Maybe if you locked up every person accused of being a crime boss by a police commissioner, you'd initially catch a lot of crime bosses, plus some people that a police commissioner didn't like. Power tends to corrupt: over time, you'd catch fewer and fewer real crime bosses (who would go to greater lengths to ensure anonymity) and more and more innocent victims (unrestrained power attracts corruption like honey attracts flies).
This does not mean that the police commissioner's statement is not rational evidence. It still has a lopsided likelihood ratio, and you'd still be a fool to mess with Wulky's teenager daughter. But on a social level, in pursuit of a social goal, we deliberately define "legal evidence" to include only particular kinds of evidence, such as the police commissioner's own observations on the night of April 4th. All legal evidence should ideally be rational evidence, but not the other way around. We impose special, strong, additional standards before we anoint rational evidence as "legal evidence".
As I write this sentence at 8:33pm, Pacific time, on August 18th 2007, I am wearing white socks. As a rationalist, are you licensed to believe the previous statement? Yes. Could I testify to it in court? Yes. Is it a scientific statement? No, because there is no experiment you can perform yourself to verify it. Science is made up of generalizations which apply to many particular instances, so that you can run new real-world experiments which test the generalization, and thereby verify for yourself that the generalization is true, without having to trust anyone's authority. Science is the publicly reproducible knowledge of humankind.
Like a court system, science as a social process is made up of fallible humans. We want a protected pool of beliefs that are especially reliable. And we want social rules that encourage the generation of such knowledge. So we impose special, strong, additional standards before we canonize rational knowledge as "scientific knowledge", adding it to the protected belief pool.
Is a rationalist licensed to believe in the historical existence of Alexander the Great? Yes. We have a rough picture of ancient Greece, untrustworthy but better than maximum entropy. But we are dependent on authorities such as Plutarch; we cannot discard Plutarch and verify everything for ourselves. Historical knowledge is not scientific knowledge.
Is a rationalist licensed to believe that the Sun will rise on September 18th, 2007? Yes - not with absolute certainty, but that's the way to bet. (Pedants: interpret this as the Earth's rotation and orbit remaining roughly constant relative to the Sun.) Is this statement, as I write this essay on August 18th 2007, a scientific belief?
It may seem perverse to deny the adjective "scientific" to statements like "The Sun will rise on September 18th, 2007." If Science could not make predictions about future events - events which have not yet happened - then it would be useless; it could make no prediction in advance of experiment. The prediction that the Sun will rise is, definitely, an extrapolation from scientific generalizations. It is based upon models of the Solar System which you could test for yourself by experiment.
But imagine that you're constructing an experiment to verify prediction #27, in a new context, of an accepted theory Q. You may not have any concrete reason to suspect the belief is wrong; you just want to test it in a new context. It seems dangerous to say, before running the experiment, that there is a "scientific belief" about the result. There is a "conventional prediction" or "theory Q's prediction". But if you already know the "scientific belief" about the result, why bother to run the experiment?
You begin to see, I hope, why I identify Science with generalizations, rather than the history of any one experiment. A historical event happens once; generalizations apply over many events. History is not reproducible; scientific generalizations are.
Is my definition of "scientific knowledge" true? That is not a well-formed question. The special standards we impose upon science are pragmatic choices. Nowhere upon the stars or the mountains is it written that p<0.05 shall be the standard for scientific publication. Many now argue that 0.05 is too weak, and that it would be useful to lower it to 0.01 or 0.001.
Perhaps future generations, acting on the theory that science is the public, reproducible knowledge of humankind, will only label as "scientific" papers published in an open-access journal. If you charge for access to the knowledge, is it part of the knowledge of humankind? Can we trust a result if people must pay to criticize it? Is it really science?
The question "Is it really science?" is ill-formed. Is a $20,000/year closed-access journal really Bayesian evidence? As with the police commissioner's private assurance that Wulky is the kingpin, I think we must answer "Yes." But should the closed-access journal be further canonized as "science"? Should we allow it into the special, protected belief pool? For myself, I think science would be better served by the dictum that only open knowledge counts as the public, reproducible knowledge pool of humankind.