too many ideas

What if we're trying to refute ideas with criticism, but several contradictory ideas are left and we don't see flaws in any of them? How should we handle having several non-refuted ideas?

Let's label the ideas A and B. Let's focus on A first. A is contradicted by B. A does not offer a clear explanation of why it's right and B is wrong (or we would see a flaw in B, criticize it, and refute it). Therefore, A isn't very good. It doesn't do a good job of explaining why it's right and alternatives are mistaken. And by the identical argument, B isn't very good either.

What I've just offered is a criticism of A (and of B too). So what does that mean? Both A and B are refuted. They both aren't good enough and need to be improved. They're incomplete; maybe idea A2 will be better, but A itself does not solve our problem and tell us everything we need to know. We need to reject both A and B, and adopt a different idea that isn't flawed.

If we're just satisfying our curiosity, then try to think of a better idea, and if you can't, try again later. Do what we talked about on the previous page.

But what if we need to make a decision right now? Then we need a speedy resolution and we can't wait until we come up with a way better idea. In that case, ask the question, "Given that I don't know the answer, but A and B seem sort of halfway reasonable, and I have no reason to prefer one of the other, what should I do?" This question isn't so hard to answer. You could answer it by flipping a coin, or picking whatever you feel like (no harm done, right?), or finding a way to delay the issue, or finding a way to avoid the issue, or just coming up with some criterion that seems mildly useful (like, "Which one is more fun?"). In this way, you can come up with a decision for what to do next that isn't refuted by any criticism.