Proof, logic, reason, thinking, knowledge pertain to and deal only with that which exists. They cannot be applied to that which does not exist. Nothing can be relevant or applicable to the non-existent. The non-existent is nothing. A positive statement, based on facts that have been erroneously interpreted, can be refuted - by means of exposing the errors in the interpretation of the facts.
Rational demonstration is necessary to support even the claim that a thing is possible.
It is a breach of logic to assert that that which has not been proven to be impossible is, therefore, possible. An absence does not constitute proof of anything. Nothing can be derived from nothing. Doubt must always be specific, and can only exist in contrast to things which cannot properly be doubted. There isn t.