If one thing (B) follows from something (A) that is sufficient, then that which follows (B) is a necessity for the something (A). (If that is confusing just keep reading it will be blatantly clear at the end.) A hidden assumption is a necessary condition that was not stated. If it is claimed that something is sufficient but it is not, this must lead to a logical contradiction once a rule is applied that is only applicable if the statement is indeed sufficient. If indeed B follows from A alone, then A can not be without B. But if in reality there is a side condition for B other than A, then A can be without B. This thinking can be used to check the completeness of assumptions. In a world were “(C and D) → E”, I might make the (false) claim: “C → E” But from that follows that C can never be true if E is false. Knowing the world you might come up with a case were C can be true without E being true, then you found the counter argument and likely the side condition D that was not met in your counter case. Aside from checking arguments this is useful in checking technical requirements. “In the event of a crash the passenger air bag deploys.” Therefore “If the airbag is undeployed there can not have been a crash.” Now that is clearly wrong, thus the first statement must have been wrong.
This sometimes helps to expose assumptions
If one thing (B) follows from something (A) that is sufficient, then that which follows (B) is a necessity for the something (A). (If that is confusing just keep reading it will be blatantly clear at the end.) A hidden assumption is a necessary condition that was not stated. If it is claimed that something is sufficient but it is not, this must lead to a logical contradiction once a rule is applied that is only applicable if the statement is indeed sufficient. If indeed B follows from A alone, then A can not be without B. But if in reality there is a side condition for B other than A, then A can be without B. This thinking can be used to check the completeness of assumptions. In a world were “(C and D) → E”, I might make the (false) claim: “C → E” But from that follows that C can never be true if E is false. Knowing the world you might come up with a case were C can be true without E being true, then you found the counter argument and likely the side condition D that was not met in your counter case. Aside from checking arguments this is useful in checking technical requirements. “In the event of a crash the passenger air bag deploys.” Therefore “If the airbag is undeployed there can not have been a crash.” Now that is clearly wrong, thus the first statement must have been wrong.