A theory cannot be scientific if it does not admit consideration of the possibility of its being false

I see the word falsifiability appear often in debates, usually when pseudo-science and creationism are involved.

Searching Wikipedia I get this:

Falsifiability is an important concept in the philosophy of science that amounts to the apparently paradoxical idea that a proposition or theory cannot be scientific if it does not admit consideration of the possibility of its being false. "Falsifiable" does not mean "false". For a proposition to be falsifiable, it must be possible in principle to make an observation that would show the proposition to be false, even if that observation has not been made. For example, the proposition "All crows are black" would be falsified by observing one white crow.

What if there was a hypothesis (not a theory) that some very useful phenomenon may be possible, but nobody could think of any experiment that would potentially falsify it?

If the experiment cannot falsify the hypothesis, then this means that any result the experiment gives is consistent with the hypothesis. So we would have no more reason to think the hypothesis is true after doing the experiment than we did before.

A negative result leaves several possible explanations. That means several possible hypotheses. You have stated that a positive result will rule out all but two of these hypotheses, namely the one that says the device should work, and one other. That means that a positive result falsifies some of the other alternative hypotheses.

What if your experiment did not test your hypothesis, but instead some set of alternative hypotheses. You are still making use of the falsification principle, though. The appropriate interpretation of a positive result will depend on whether you are really justified in claiming that only two possibilities remain, or on whether those two possibilities are just the only two which you have considered.

Another way to look at it is that the point is not really to confirm or reject hypotheses, but rather to acquire new knowledge. In order for an observation to provide us with new information about something, it must be possible for that observation to rule out one or more of the current possible explanations. This narrows down the list of possible explanations, bringing us closer to the correct one. In those cases we are not trying to falsify a particular hypothesis, but nevertheless every new piece of information we gather narrows down the set of possible explanations.

Formulating and testing hypotheses is just a useful methodology. The falsification principle goes much deeper than this simple methodology, though. The central point of the falsification principle is that our observations must provide us with new information to be useful, and the only way they can provide new information is if they could potentially rule out one or more possibilities.

Intelligent Design

I have seen the claim that the universe was intelligently designed can be falsified by demonstrating how the universe can come to be in the absence of a designer. The problem here is that you have to have some type of phenomenon to falsify the hypothesis, not just a rival theory. That would be like saying that Natural Selection can be falsified by demonstrating how a divine being could have directed evolution.

Creationism

Creationism cannot be falsified, so it is pointless using it as a theory. No matter how much you try, you can never prove that an all-powerful being did create the entire world. Creationists are constantly presenting the false dichotomy that if evolution is wrong, then their beliefs must be right. Creation can never be tested, it is a faith, not science.

Astrology

The key to astrology is the idea that the positions of the planets and constellations in the sky when a person is born can influence their personality. But astrologers can not make predictions which if unfulfilled would lead them to give up their theory, because they can't prove wrong. There is no evidence to support the claim. Concluding astrology isn't falsifiable, astrology is unscientific.

You can read more here:

Karl Popper's Falsification Principle

Karl Popper.