Question: Isn't It Impossible to Prove Universal Negatives?
Answer: It is not impossible to prove a universal negative. Certainly there are some universal negatives which cannot be proven absolutely and so can only be held based upon the weight of omniscience — for example, the claim “No swans are orange.” We would have to know the contents of the entire universe in order to make such an assertion with certainty.
However, such knowledge is not necessary in order to make other negative statements. Examples of this latter type include “no married bachelors exist” or “no round squares exist.” We can prove each of them with logic, primarily based upon the definitions of the terms involved.
To assert the opposite of either statement entails asserting something which is incoherent — and we are rationally justified in denying something incoherent. If an atheist believes that the statement “God exists” is similarly incoherent, then that atheist can say “no god exists” with certainty and without being omniscient.
