Lets see if I can sum up the entire knot of this thread:
Science seemingly operates on the logical fallacy of induction, by observing a subset of events and extrapolating that behavior to other events; even future events. However, inductive reasoning demonstrates great success given a sufficiently large sample size and duration of observation.
How do we reconcile these things? Simple; science does not claim absolute certainty and thus does not commit the fallacy of induction. If science shows that 999 times an object falls down due to gravity it would be a logical fallacy to conclude that the 1000th time the object is dropped it will, with absolute certainty, fall down. Instead science concludes that it is reasonable to assume that the 1000th time the object is dropped it will fall down, but that if it does not the theory will need to be modified or scrapped entirely.
This is the crux of the matter, centering around observation of future events and their comparison with our previous models. Science doesn't render conclusions about the absolute nature of reality, it renders expectations of the behavior of reality.
Religion suffers from the unwillingness to tentative conclusions, and thus necessarily commits the inductive fallacy. A Christian for instance does not read about prayer in the Bible and conclude that they can expect their prayers to come true, and then compare future observations against this expectation and modify it as indicated. They instead conclude from accounts in the Bible or anecdotally from friends that prayers come true, period. And in doing so commit inductive fallacy.
To sum things up:
"Everything seems to happen this way according to historical data set."
Inductive Reasoning (scientific, and A-OK): "We can reasonably expect other things in the future to happen that way. If they don't, modify or discard this expectation."
Inductive Fallacy (religious, unsound thinking): "Things in the future will always happen this way."
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