falsification is to prove that a theory is wrong. this is done in the following way: there is a set of statements (which are logically sound, and do not contradict each other) called theory. if a single logical statement can be found, which is also logically sound, and which contradicts one of the statements in the theory, then the theory is proven wrong. this can be done with observation, as in the example with the swans above. it can also be done using mathematical logic, using induction.