The naturalistic explaination (I assume you are refering to natural selection and mutation) provides a number of constraints, wheras alternative explainations do not. One key constraint is that a new type of animal can only be derived from one existing type. So a new species of mammal cannot be built by taking parts from bats, birds and lizard for example. If an example of such a thing was found in the fossil record it would falsify the explaination.
The constraint also produces a tree of descent. If the fossil record did not match a tree of descent then that would falsify the explaination. For example finding a modern mammal fossil in the cambrian would falsify the mammal tree of descent, and through that falsify the explaination that mammals descended via the natural mechanisms of evolution.
Also the tree of descent implies a nested heirarchy of presnet day life. If genetic comparisons of living species do not fit a nested heirarchy then that would falsify the explaination.
There are many other ways that evolution can be tested, for example the naturalistic explaination puts the constraint that new types of animal must originate in the same location as the type they derived from. So the theory would not be compatible with indigenous elephants on hawaii.
"If an example of such a thing was found in the fossil record it would falsify the explaination."
You mean like a Duck-Billed Platypus?
"The constraint also produces a tree of descent. If the fossil record did not match a tree of descent then that would falsify the explaination."
Or they would just call it "convergent evolution". Oh wait, that's what is happening already.
"For example finding a modern mammal fossil in the cambrian would falsify the mammal tree of descent"
Or an ad-hoc explanation such as "reworking" would be invoked.
"and through that falsify the explaination that mammals descended via the natural mechanisms of evolution."
Or would you just reconstruct the tree?
"If genetic comparisons of living species do not fit a nested heirarchy then that would falsify the explaination."
That's interesting, because they don't.
"There are many other ways that evolution can be tested, for example the naturalistic explaination puts the constraint that new types of animal must originate in the same location as the type they derived from."
I'm pretty sure there are counterexamples of that, too, but I'll have to double-check.
Falsifying the tree of descent, not the theory of natural selection, is the key phrase above. Given that there are now competing claims as to whether dinosaurs were more reptilian or more avian, and that evolutionists are ready with explanations for either case, I am not confident that any fossil find would be accepted as falsifying Natural Evolution.
Nor does the fact that it could be falsified by a non-experimental observation make it an empirical science. There are many theories about the JFK assassination. A document found in the KGB file giving instructions and a post operation report complete with confirming film evidence would falsify the other competing theories. Prior to such conclusive evidence however the study is a forensic one, not an empirical one. Such is the case with Evolution.
My problem is not that supporters Evolution are presenting a theory but that they are insisting that it has a greater confidence of being true than it really does. It is also dishonest to suggest that competing theories must somehow be unscientific if they do not lead to a naturalistic conclusion. In science nothing should be presupposed.