It is a prediction of Newtonian physics that two isolated massive bodies will move relative to each other in a conic section. It is a presupposition of Newtonian physics that there is space. It is a prediction of perfect being theology that persons (or at least, good persons) live forever. It is a presupposition of perfect being theology that there are objective values.
The distinction matters epistemologically. Suppose you have significant but non-overwhelming evidence for Newtonian theory but don't notice that the theory presupposes that there is space. And then you learn that there is this presupposition. This should make you both (a) more suspicious of Newtonian theory (after all, the presupposition might be false) and (b) more friendly to the idea that there is space (after all, the inference to best explanation argument for Newtonian physics now extends to the existence of space).
On the other hand, if you don't realize that Newtonian physics implies that two bodies will move in a conic section, and then you come to realize it, that will make you want to run to the observatory to see if the prediction is true. But while you're running to the observatory, your credence in the theory will not have gone down. It will only go down if the prediction is not borne out.
Likewise, suppose that you have significant but non-overwhelming evidence for perfect being theology, and then you realize—somehow you missed it before—that this theology presupposes objective values. If your evidence for objective values is non-overwhelming (I think it's overwhelming) then this realization will make you more suspicious of perfect being theology. On the other hand, if you realize that the theory predicts that persons live forever, that by itself shouldn't make you more suspicious of the theory, just make you look for evidence for and against this prediction.
Yet, you might think this: "Both the prediction and the presupposition is something you get committed to by the theory. Learning that you're committed to more things by a theory makes the theory more top-heavy, and so it should make you more suspicious of the theory."
That's a mistake. Discovering that a scientific theory has predictions you didn't see before doesn't by itself make us more suspicious of the theory (of course, if we have evidence against the predictions, that's a different thing). But the thought highlights a crucial question: What is the difference between the presupposition and the prediction? Both are implied (entailed, or maybe just significantly probabilified) by the theory. The difference isn't logical, but I think explanatory:
- A prediction of a theory is an implication that the theory explains.
- A presupposition of a theory is an implication that the theory does not explain.
From a Bayesian point of view, we can now say a little bit more about what happens when we discover a new prediction or presupposition. In general, when we discover an implication of a theory, we realize that we were mistaken in regard to logical interconnections. When that happens, we need to go back to the drawing board, and re-do our relevant priors.
Now when we learn of a new prediction of a theory, that doesn't affect the complexity of the theory, because only the explanatorily fundamental parts of a theory enter into the complexity of the theory (see this post), and while perhaps complexity isn't the only determinant of priors, I do not see any other relevant one here that would raise the probability. So our priors for the theory stay the same, but now the prediction gets tied to the theory, so that the evidence for the theory ends up typically being evidence for the prediction as well.
On the other hand, when we discover a new presupposition, that makes the explanatorily fundamental parts of the theory more complicated, and so the prior for the theory should go down a little. But at the same time, once we factor in the posterior evidence, then typically the evidence for the theory will transfer to the presupposition. As a result, our prior for the theory goes down, and hence so does the posterior, but the posterior for the presupposition is apt to go up.