What exactly IS a premise?

A premise is simply a proposition that serves as the basis for doing something.
For example:

• Science is based on the premise that we can understand the world without recourse to supernatural explanations.
• You smile and greet a co-worker on the premise that doing so will win goodwill and regard in return.
  

Notice that a premise serves as a mission statement, a statement of purpose, an end:

• The mission of science is to understand the world without recourse to supernatural explanations.
• Your purpose in smiling and greeting your co-workers is to get friendliness back.
  

From another angle, a premise is just a path you take to get from Point A to Point B. For example, say you're standing in a field. That's Point A. You want to get to Chicago. That's Point B. You think, "If I walk due east, I'll get to Chicago." So, you head off, due east, on the premise that traveling due east will bring you to Chicago. If you get to Chicago, you will have proved your premise. If you get to Kansas City, you will have disproved it.

Science proves its premise every day, by successfully explaining the world without recourse to anything supernatural. In other words, it proves (demonstrates) that Scientific Method works. Theoretically, science could someday encounter a fact that cannot be so explained. That would disprove the premise on which science is founded. It would mean that science isn't a valid way of knowing.

Similarly, you prove your premise every day when you smile and greet your co-workers and they respond according to the Golden Rule. Theoretically, someday you might encounter a co-worker who reacts hostilely instead, frowning and pretending he doesn't see you. That would disprove your premise, the premise on which the Golden Rule is founded. It would mean that being nice to some people is counterproductive.

This result would suggest a revised premise — that you should give such people the opposite of what you want in return. You would have to test this revised premise to see whether it proves true.

So, keep in mind that, when we say you "prove your premise," we mean that you demonstrate it. That is, your story demonstrates it. But we don't mean that you prove it a universal truth. For example, traveling due east won't always bring you to Chicago. That premise proves true only if you're due west of Chicago.

If you prove a premise many times in many ways, we may be convinced that it's universally true. But you can never prove absolutely that a premise is universally true. That's because a premise is the product of inductive reasoning — reasoning from detailed facts to general principles. Only deductive reasoning (reasoning from general principles to detailed facts) can prove things universally true.