(The idea that what we see is filtered by the requirement that he have to exist in order to see it ...)
A scientific theory makes predictions, and it can be falsified by observing an event which is predicted to be impossible.
But in a quantum universe, nothing is certain, and even "impossible" things can happen, albeit with a very small probability.
So we have to rewrite the rules of prediction and falsification in terms of probabilities.
Probabilistic rewrite: A scientific theory makes predictions about the probabilities of events, and it can be falsified by observing an event which is predicted to have a very small probability.
(Exactly what constitutes "very small" is a matter of personal taste. Choose a number, and see if you feel confident that an event with that probability will never ever occur in the known lifetime of the universe in any part of the universe that you might be able to observe in any conceivable manner.)
Having rewritten the rule of falsification in probabilistic terms, the Anthropic Principle can then be applied:
All predicted probabilities must be conditioned upon the existence of the observer.
In some cases, this conditioning may turn a "very small" probability into one that is not so small.
What does this have to do with explaining things?
We consider an observed event to be "explained", if we can show that it does not falsify commonly accepted scientific theories relevant to predicting the probability of that event.
If we have a choice of theories, then any theory which is not falsified by the observation can be said to "explain" that observation.
The Anthropic Principle can "rescue" a theory which would have been falsified if we did not condition predicted probabilities on the existence of the observer.
In which case, we can say that the Anthropic Principle "explains" the observation, or more precisely, helps the theory to "explain" the observation.
Whether the Anthropic Principle is actually relevant to explaining anything significant about the universe, other than the obvious prerequisites to the evolution of Homo Sapiens (such as the fact that we exist on a planet which is a certain distance from a certain type of star), remains controversial.
But skepticism about the relevance of the Anthropic Principle to the explanation of any particular observation does not rule out its validity as a general principle which qualifies the rules of prediction and falsification as applied to scientific theories.
