John and Mary were watching TV when they received a phone call from their neighbour, inviting them to join her for a few drinks.
Mary turned the TV off, and they both left the house shortly after.
When they came back a couple of hours later, they were surprised to find the TV on.
Mary said that she was certain the TV was off before they left the house. She then claimed that someone must have broken into the house and turned it on. However, when they carefully looked around the house, they could not find any evidence that anyone had entered the house.
John, an electronics engineer by trade, also believed that the TV was off when they left the house. However, he claimed that in certain situations — rather unlikely, but possible nonetheless — the TV could be turned on as the result of a random electrical discharge of its internal components. Therefore, the TV could have turned on by itself and as the result of an unprovoked, random event.
Mary cannot prove that someone was in the house and turned the TV on, nor can she disprove that the TV was turned on by itself, according to John’s explanation.
John cannot prove that the TV was turned on by itself, nor can he disprove that someone else was responsible for turning the TV on.
Who is right?
The “TV Problem,” as I describe it here, is best read as an instance of epistemic underdetermination — one I will return to in several future notes.