Gherald says:

Theological discussions being clearer is no more to the point than the Terminatrix comic being clearer. A lot of things become clearer when you make arbitrary assumptions.

[Though theology does run into problems when it makes contradictory assumptions, such as a perfectly just God doling out infinite punishment for finite sins.]

Anthropic reasoning need not involve beliefs. For instance, the weak anthropic principle is a truism that dismantles teleology.

[Teleological arguments were considered by many to be the strongest case for the existence of god(s), and people unfamiliar with anthropic reasoning still accept them.]

> But what then happens to your beliefs if new discoveries are made, of if the old answers are found to be in error?

Belief is the wrong word to use here, it's too imprecise.

When new discoveries or explanations are made that provide better answers than old ones, they should obviously be embraced. It's the theists who have the biggest problem accepting new evidence (just ask Galileo and Darwin).

New science can cause old knowledge to be discarded when it reveals that the underlying data was faulty. But most often accepted data is not faulty, and new science merely extends our understanding of it. For instance Newton's laws of motion gave way to Einstein's relativity. But there's still an enormous amount of evidence in support of Newton's laws and they're still extremely useful. Einstein's discovery was that they're actually approximations for the behavior of matter at speeds much slower than light.

[Relativity says that as you get closer to the speed of light you need to subtract time from distance equations.]