No matter how open-minded you think you are, you could probably be twice as open-minded.
In Tai Chi, a teacher might tell you: "No matter how little tension you're holding in your body, try to hold only half as much tension". This is often said to students engaged in deeply sunken (in kind of a deep knee bend) postures that are difficult to hold for long. This image comes to mind when I think about being open intellectually to almost all possibilities. Most of us think we are somewhat open-minded, but could we be more so?
I consider open-mindedness to be the crucial foundation of human intelligence. Most great breakthroughs seem to result from breaking out of preconditioning. Being open does not require abandoning critical thought. In a sense, it means setting your sights on MORE aspects of reality. You must first view or consider a subject, before you can apply thought and intuition to it. The universe is a big place. Any reference frame you overlay REALITY with, will come up lacking.
Whenever you intellectually debate or argue with someone, imagine how you'd argue your opponent's position most effectively. This practice makes you search for the truth in the other person's position, thereby causing you to evolve. I often, when debating someone, have the thought, HERE's the weak link in my argument, you should attack me on THIS point. Also, with evolution, our views should evolve. For example, I have some anti-government leanings in my political views, but have learned to see that government evolution partly follows consciousness evolution, and that it now makes sense to me that medical service is a major part of most first world governments.
Note how society continually changes as regards what is considered absurd by the masses. Less than a lifetime ago, yoga, eastern philosophy, running a lot for exercise, avoiding doctor recommended surgery, acupuncture, healing through mind power, and a host of other things were regarded by 99% of Americans as absurd. You, as an individual, have the ability to rise above this tunnel-vision automatism.
What have you written off as being impossible? Is it out-of-body experience? Read the books of Robert Monroe. Is it UFO abduction? Read "Alien Dawn" by Colin Wilson (I'm not necessarily saying that UFO abduction is what its "victims" claim it to be, but that some real (read conscious/experiential) phenomenon is behind it).
How do you limit your world view? Are you certain that there could not have been advanced civilizations before Sumer or Indus? Are you certain that awareness (consciousness) does not create so-called material reality?
Another way of expressing my point here is that you should have NOTHING TO DEFEND. This means you try to have no preconceptions or ideas that go unquestioned. Here too, a martial arts analogy helps out. The opponent cannot defeat you if you have nothing to defend.
I in no way suggest that you believe ANYTHING you hear, just the opposite. Most of what you hear you probably DO believe in ways you may not suspect. Use your own laboratory of experience, critical thought, and intuition to judge everything for yourself!
Remember that (intuitive) wisdom is the higher octave of intelligence.