Theory (I'll be using this to strictly refer to hypothesis deduced from theory throughout)
Event/Fact
Event/Fact
Fact 3
Observation (Outcome)
The more natural form (But less clean form) is:
Theory&Fact&Fact => Observation
Religion, Science, and so forth occupy the 'Theory' slot. I'm going to clarify the 'event/fact' part since that's different from conventional usage. By 'facts', we're talking about how the universe/world is (Not necessarily Earth, but this 'realm' in general). So if the theory says the planet is 5000 yrs old (Or w/e the bible says) and it is a fact that the Earth is actually older, then you have a contradiction. If a theory and a set of facts demands an observation (Outcome), then in order to be a valid, there is no case in which the observation is false (Consequent) and the theory+facts (Antecedent) are true. Remember that 'valid' is hypothetical. Consequently, "If you watch and like Glee, thunder will strike you" + "You watch and like Glee" + "Therefore, thunder will strike you" is a valid claim. Laymen tend to confuse 'valid' with 'sound' and it is this latter term that people want to look at when they make the religion v science debate. Soundness is the question of whether the premise/conclusion
actually are true. So the above claim may be valid, but if one of those claims is false (ex: I've never watched Glee), then the claim won't be sound.
So how does this operate when the observation does not happen? If the premises, when all true, force the outcome, and the outcome does not happen, then you know one or more of those premises is false. The question is which one?
1. Denying the theory: This is what most atheists accuse religious people of failing to do. So allow me to demonstrate ignorance of Christian values. Lets assume the bible says "All people that pray will get money in X minutes." If you pray and X minutes passes, you damn well better get money! If it is not, then you can just deny that the theory (The bible's claim). What most atheists fail to realize (Because our revisionist history trims away these oddities) is that there are instances where science will fail to deny the theory as well. A classic example given by Putnam in "The corroboration of theories" is the discovery of Neptune where scientists did not reject the universal gravitation theory because an observation did not align. Other convenient examples include classroom experiments where your results may not perfectly align with the math.
2. Denying the 'fact': This is a common one for both religion and science. One of the versions of Buddhism roughly says that if you sincerely say Buddha's name, you will be enlightened. So if enlightenment fails to happen, it's common to maintain the doctrine but then say that the person never
sincerely said his name. Using the classroom experiment again, we can see that this route applies to science when we 'roughly measure' using instruments. So if you're conducting an experiment that requires you to heat an object to a certain temperature, the object may not be the exact temperature you want. Another example is the Neutrino incident.
3. Denying the observation: This is also one that people use to complain about religion. Since religion deals with blurry and imprecise terms such as 'good' and 'evil', it's quite possible for you to interpret results so that they 'fit' the observation you want. I've read of examples where natural science does this, but I cannot recall any common ones at this time.
The kicker is that you're not forced to deny any
specific one, logically. Since you're not logically compelled to deny any specific one, you're not "right" or "wrong" if you decide to deny the fact each time. You're not even compelled if the same premise appears in multiple instances where this problem arises.
Code:
Theory1 Theory1
Fact1 Fact2
Fact1' Fact2'
O1 O2
Even though Theory1 appears in both situations, you can reject Fact1 and Fact2 to explain both cases. There's no logical problem with that until begin maintaining that certain observations/facts
must be true. Yet, doing so with a posteriori facts is only possible if you do so
in faith.
So why science? I'm adding this at a last moment, so I don't have a precise or thoroughly checked answer, but I would say because science is more precise as to the outcome. If all you can predict are 'good' and 'bad' outcomes, then you don't have a very useful idea. There are a lot of outcomes that qualify as 'good' and 'bad', so predicting one or the other doesn't have much utility. And utility is the real benefit of science. Without said utility, I'm guessing society would have abandoned the idea many years ago.