ABSTRACT
It is not possible to prove definitively that a hypothesis about nature is correct. One reason for this state of affairs is that theories are underdetermined by observations. The underdetermination of theory by observation means a myriad of hypotheses can always be identified that can account for whatever data are available. In addition, it might appear at first glance that a hypothesis about nature can be proven to be true by logical argument. But the argument fails because it is shown to be an example of a logical fallacy called affirming the consequent rather than an argument that is valid. Mathematics can prove propositions are correct but they are not capable of proving propositions about nature are true. A mathematical proof accomplishes no more and no less than deriving consequences from premises that are assumed to be true. If the premises do not accurately represent nature (i.e., if the assumptions are not true), the derived consequences have not been proven to represent nature. And there is no way to know definitively if the assumptions are true.
