Argument from silence (argumentum e silentio) – where the conclusion is based on silence of opponent, failing to give proof, based on "lack of evidence" - The argument from silence (also called argumentum e silentio in Latin) is generally a conclusion based on silence of opponent, failing to give evidence.
In the field of classical studies, it often refers to the deduction from the lack of references to a subject in the available writings of an author to the conclusion that he was ignorant of it. When used as a logical proof in pure reasoning, the argument is classed among the fallacies, but an argument from silence can be a convincing form of abductive reasoning.
Bobby: I know where Mary lives.Billy's conclusion may not be justified: perhaps Bobby doesn't want to tell him. Consider, however, the following type of argument:
Bobby: I'm not telling you!
Billy: You're just saying that because you don't know!
John: Do you know any Spanish?Afterwards, Jack continually refuses to give John the Spanish translation, either by ignoring John or by giving excuses. John then concludes, by argument from silence, that Jack does not in fact know Spanish or does not know it well. In other words, John believes that Jack's ignorance is the most plausible explanation for his silence. Use of argument from silence in this situation is reasonable given that the alternatives, that Jack either doesn't want or is afraid to translate, would be unreasonable without more information.......
Jack: Of course. I speak it like a native.
John: That's good, because I need to know the Spanish phrase for "Happy Birthday".
Jack: Sorry, I don't have time for that right now. Maybe tomorrow. Bye.