Consider this valid argument:
- (Premise) Intelligent Design is irrefutable.
- (Premise) Intelligent Design is incompatible with evolution.
- (Premise) If p is incompatible with q, and p is established, then q can be refuted.
- So, evolution is not established.
Premise 3 will be taken to be false by many if "refute" and "establish" are understood in the knowledge sense or even in the sense of knowledge-type justification, since knowledge and knowledge-type justification is not closed under entailment. Some will say that although it is established that I have two hands, and that I am a brain in a vat is incompatible with that, that I am a brain in a vat cannot be refuted. I think this response is mistaken—I know I am not a brain in a vat—but I won't insist on it.
On the other hand, if "refute" and "establish" are taken in the sense of assigning low and high rational probability, respectively, then 3 is surely true: if p and q are incompatible, and one has high probability, the other has low probability. Thus, it seems, that those who claim that evolution is established should either hold that Intelligent Design is compatible with evolution or stop arguing that it is irrefutable.
But perhaps what I just said isn't right. Maybe to refute q is both to get to assigning a low probability to q and to obtain significant incremental disconfirmation. Then 3 is false. For suppose that q has very low rational priors. Then we can establish p without getting any incremental disconfirmation for q—we get incremental confirmation for q, and q ends up with high probability, but p's probability is basically unchanged from the priors. Maybe it is empirically established that I have two hands, but the brain in a vat scenario continues to be ruled out by low priors.
If this response is right, then the evolutionary theorist who wants to claim that evolution is established while yet accepting 1 and 2 needs to hold that the rational priors of intelligent design are low. But are they?