# Can Misinformation Be Informative?

Can misinformation be informative and if so, how? Here are some thoughts on the matter, with three ways in which misinformation can be considered informative. The first two are simply rehashes of standard facts about truth, falsity and logic explicated in informational parlance. The third is a novel point.

1. In an actual world where A is true and B is false, the statement A & B is false. Yet, it still contains some true constituents, some information, namely A
2. Valid reasoning with false or misinformative premises can still lead to true or informative conclusions. Take for example, a case where A -> B is true, A is false and B is true. One can still validly infer the true B from the presumed truth of A -> B and A. Although, it must be pointed out that although B is true, it is arguably not genuine information because it was derived from false premises.
3. The third way is as follows. Take an example where three people, Bob, John and Harry, are in a room and are looking to find out what time it is. John asks Bob to head out into the hallway, where there is a clock, to find out what the time is. John knows that the clock in the hall is 15 minutes fast, but he does not know whether or not Bob is aware of this fact. He will assume though that Bob is not aware of this fact. Also, Harry is not aware of this fact.

Now, imagine two possible scenarios. In the first scenario, Bob is indeed not aware of the clock being 15 minutes fast. He looks at the clock, which reads 6:15 and forms the belief that it is 6:15. This means that the actual time is 6:00. So the belief that Bob holds is misinformation. When Bob returns to the room to tell John and Harry the time, what happens? Although Bob is misinforming Harry that the time is 6:15, his misinformation is informative for John, who decodes Bob’s misinformation and translates 6:15 to 6:00.

In the second scenario, Bob is aware of the clock being 15 minutes fast. He looks at the clock, which reads 6:15 and forms the belief that it is 6:00. So Bob is informed that it is 6:00. When Bob returns to the room to tell John and Harry the time, the outcome is reversed. Bob informs Harry that it is 6:00, but John incorrectly decodes Bob’s information and ends up forming the false belief (holding the misinformation) that it is 5:15.