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I'm looking for a phrase or type of argument for the line of thinking that goes like this:

"The remote control is lost. Since I have not (literally) checked every inch of the living room, I don't know for sure that the remote is not in the living room."

In this case, I'm trying to express the absurdity of this type of thinking when compared to other problems, for example, "I have not literally checked every inch of the world so I don't know for sure that there are no unicorns."

and also the opposite:

"The remote control is lost. I've checked three places in the living room, so I know it is not in the living room."

Again, I'm trying to express the absurdity of this type of thinking when compared to other problems, for example, "A tiger was not in any of the places that I checked, so tigers must not exist."

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Both are logical fallacies. The first is Argument from Ignorance.

Description: The assumption of a conclusion or fact based primarily on lack of evidence to the contrary. Usually best described by, “absence of evidence is not evidence of absence.”

Explanation: There is an infinity of things we cannot prove -- the moon being filled with spare ribs is one of them. Now you might expect that any “reasonable” person would know that the moon can’t be filled with spare ribs, but you would be expecting too much. People make wild claims, and get away with them, simply on the fact that the converse cannot otherwise be proven.

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The second is perhaps Hasty Generalisation

Description: Drawing a conclusion based on a small sample size, rather than looking at statistics that are much more in line with the typical or average situation.

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The second is Hasty Generalization. The first is not a logical fallacy at all. It is perfectly correct and logical to say that, if you haven't done an exhaustive search for unicorns, you can't state with certainty that there are no unicorns in the world. This type of reasoning is important in science.

However, if you take this uncertainty very seriously, you tend to get into a philosophical viewpoint called radical skepticism.

Usually, though, uncertainty tends to go hand in hand with inductive reasoning, which says that, if you have examined 2000 crows and every one of them is black, it is likely that all crows are black, and this becomes the prevailing theory until a counterexample appears. It becomes about what is probably true rather than what is certainly true.

Incidentally, it might be argued that there are indeed unicorns in the world. The animal was first described, in some detail, by a number of Greek writers—a large, one-horned animal, with legs like an elephant and a body like a horse. They were probably talking about the rhinoceros, but the "body of a horse" part seems to have been misinterpreted.

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