Affirming the consequent and predictive value
In the hard sciences, the ability of a theory to make accurate predictions is taken to count in favour of that theory. Let's use gravity as an example. Although on earth, nobody had ever dropped a feather at the same time they dropped a heavy dense object and observed them falling at the same rate, the theory of gravity predicted that they should fall at the same rate if you eliminate all the forces (especially air friction) and drop them in a vacuum. Since then, the theory has been tested by dropping feathers and bowling balls together in vacuums and found to be true. The feather and the bowling ball do drop at the same rate in a vacuum where there is no air resistance. That counts in favour of the theory of gravity.
Criminal investigators use this kind of reasoning, too. For example, when somebody flees, that's taken as evidence of their guilt because fleeing is exactly what we'd expect from somebody who's guilty.
Historians also use this kind of reasoning. I can't think of an example off the top of my head, but if I did, the scenario would be pretty much just like the criminal investigator scenario above.
This type of reasoning appears to commit one of the most basic formal fallacies called "affirming the consequent." It takes this form:
1. If P, then Q.
3. Therefore, P.
In the case of gravity, the reasoning would look like this:
1. If the theory of gravity is true, then a feather and a bowling ball should drop at the same rate in a vacuum.
2. A feather and a bowling ball DO drop at the same rate in a vacuum.
3. Therefore, the theory of gravity is true.
This whole principle of predictive value seems to depend on this fallacy:
1. If theory X is true, then effect Y should be observed.
2. Effect Y is observed.
3. Therefore, theory X is true.
Don't get me wrong, though. I'm not trying to argue that the predictive value of a theory does not count in its favour. What I suspect, instead, is that it's not a deductive argument, and it's a mistake to characterize it as such.