It happens all the time. Someone says, "Pray to God and he will answer your prayer." One may take that advice, try it, and see what happens. The outcome, whatever it is, would not qualify as scientific evidence. But it would be observational evidence.
Science can certainly show that said hypothetical being is superfluous to the complete explanations of large classes of phenomena. It can rule out specific claimed interventions of that being. So it while it certainly can't address a completely hidden variable, it can delineate under which circumstances said hidden variable can and cannot be observed.
I am afraid we will have to agree to disagree on this one. I do not believe that science can ever offer a "complete explanation" of anything. Scientific models, to be useful, are generally simplifications of reality. They are continually undergoing modification and refinement to make them more useful.
More important, science cannot "rule out specific claimed interventions" of God. Just the opposite: Science can state that in general God does not appear to intervene or contravene natural law; but science cannot rule out the occasional miracle.
For example, it is generally true that dead people are not observed to come back to life. (Scientists and non-scientists can agree on that.) But many people believe that Jesus Christ came back from the dead. I know of no scientific test that can disprove that claim. It is a miracle, and therefore outside the realm of science.
Finally, you dismiss as nonsense my statement that science depends on a faith. Yet one of the definitions of faith is "firm belief or trust in something for which there is not proof." Science depends on a number of propositions which cannot be proved. One of these is that the laws of physics (and not just our understanding of them) are the same yesterday, today, and tomorrow.
Now, I happen to believe that the laws of physics do not change. But I cannot prove it. Science—indeed any human activity—would be impossible if it required absolute proof of every proposition. Some faith is always required.
You are using the term "faith" in two different ways, which causes confusion. In theology, "faith" means accepting a proposition that is not supported by verifiable evidence or logical proof. Thus, the Resurrection is accepted on faith.
In the scientific context, however, the laws of physics are not accepted in the same way. They are supported by millions of observations and verifiable predictions. An appropriate word to use for accepting the laws of physics is "confidence." It's confidence that is justified by observations of objective reality.
Scientific laws can be discredited by newly-observed evidence, of course, but that's how it goes in the real world. Anyway, it's the factor of evidence that distinguishes theological faith in various ideas from the confidence exhibited by science in its findings.
If we keep our vocabulary straight, we'll communicate better.
Only within a very loose description of 'observational evidence'. Evidence is usually defined as a body of facts or information bearing on the truth of a proposition. If you collected a series of instances, you might have a body of information. But then, if you analysed that information properly, you'd be doing science; as was seen recently, when they analysed the effect of prayer on medical recovery.
So it appears your your test of other explanations seems to be concerned with cases where the evidence is scanty or not analyzed by scientifically adequate means. It's not so much that they are other than scientific; they are less than scientific.
More important, science cannot "rule out specific claimed interventions" of God. Just the opposite: Science can state that in general God does not appear to intervene or contravene natural law; but science cannot rule out the occasional miracle.
Sure it can. If you claim specific instance of a phenomenon A is an example of supernatural intervention, we can examine it to see if it followed deterministically from natural law, or if in fact supernatural intervention is a plausible explanation. So, for example, disease used to be attributed to supernatural action. We now know that it is caused by specific etiological agents. We have ruled out divine or Satanic action as a general cause of disease.
But many people believe that Jesus Christ came back from the dead. I know of no scientific test that can disprove that claim. It is a miracle, and therefore outside the realm of science.
We know that when people die, irreversible processes proceed that rapidly make resuscitation impossible. We can't rule out that some specific instance in time a miracle happened; but then we can't rule out any miracle, or any supernatural explanation. The world could have been created yesterday, with all our memories intact. So specific instances of 'miracles' are really inseparable from the general category of 'omphalism', and by adopting naturalism - and we are all naturalists in practice - we have discarded this category of explanations.
Miraculous explanations are nothing more than examples of spasmodic omphalism. If you adopt naturalism as a useful general policy, why would you abandon it in special instances, those instances remarkable only because they are the ones that survived from an earlier, less naturalistic age, by being more difficult to challenge?
I'm pinging thatcherite because he introduced me this morning to this magnificent and useful new word.