The inherent problem of scientific theories is that there exists an infinite equally valid explanations. Why? Because in science, we never have perfect information. First, some background on Bayes’ theorem. Bayes’ theorem is used to judge how likely an event caused an observation, like how likely a test result means cancer. Yet, Bayes Theorem produces probabilities, not axioms. There is always a chance that our belief is wrong.
Statement of Bayes’ theorem. This says: the probability of A given B is the product of the probability of B given A and the ratio of the probability of A to the probability of B.
In science, Bayes theorem determines probabilistically if observations support a theory. However, an infinite number of theories can explain the observations. We can eliminate theories by testing, and we can judge how likely a theory explains observations, but Bayes Theorem is probabilistic, and we can never certain. For example, in physics, many theories successfully explain observations, like String Theory and the Standard Model. Yet an infinite number of other theories exist that explain all our observations, even though we haven’t thought of them yet.
OK, so our world understanding improves as we verify models, like if the Large Hadron Collider finds the Higgs… right? Theoretically, no. An infinite number of theories that are just as “probable” as the others still exist to be tested. All that was done was eliminate some of the theories. Subtracting anything from infinity is still infinity.
An infinite number of theories exist because we can never have perfect information about everything, both practically (we can’t be everywhere and observe everything) and theoretically. For example, the Heisenberg Uncertainty Principle states that the more one knows about a particle’s momentum, the less one may know about its position and vice versa. Even if one was momentarily omniscient, it’s theoretically impossible to know the prior state of every particle in the universe.
A simpler example: say my entire life, every swan I see is white. With reasonable confidence, I can assume that all swans are white. However, somewhere in the universe, there may be a black swan, disproving my theory. So then I could reasonably adjust my theory to say almost all swans are white. However, suppose I live in a region predominantly occupied by white swans, but really, black swans are the predominant type of bird. Or maybe black swans simply avoid me and my colleagues. How would I know?
In essence, while science finds theories that explain the observations that we see, we have no way of proving if it is the one correct theory. It’s probably wrong —all refuted theories in the past have been. We can never know the truth, and we can never have the real model of anything we don’t define ourselves. The best we can do is agree to use a model that works for humanity’s tiny set of observations.
For further reading on this topic: