Dispatches from the War on Cliches

"There is no smoke without fire." This is a proverb that's been around for ages, but apparently is more often than not misunderstood and abused by its users.

This proverb is generally understood to express the real-life observation that "wherever there is smoke, there is fire". In predicate logic, the relationship is transcribed as "Fire only if smoke", or in more mathematical terms, (Fire → Smoke).

In logical terms, a necessary condition can happen on its own. So while you can't have fire without smoke, you can have smoke without fire.

However, the standard understanding of the proverb precisely believes that you can't have smoke without fire.
How is this a 'misunderstanding' and an 'abuse'? That's adequately illustrated by how people apply this proverb in real life.

"There can't be Rumours without Some Truth"

This new proposition is phrased in parallel with the original proverb. From predicate logic, again we note that while you cann't have Truth without some Rumours of it, it's entirely possible to have Rumours without any Truth.

But try convincing that to any idiot who spouts that proverb (in either form) to you.

And if you sincerely believe there can't be Rumours without Some Truth, or there can't be Smoke without Fire...

Tell that to the innocents who died in witch-hunts.

Tell that to Joseph MacCarthy and the victims of his hunt for Communists in America.

Tell that to victims of slander and character assasination.

Tell that to the millions of Americans who believe that Iraq was involved in the 9/11 bombings because their leaders kept insinuating and suggesting it, even without any proof, and indeed are now known to have LIED about it.

Tell that to the thousands of prisoners the coalition forces arrested and detained in Abu Ghraib on grounds that they could "possibly be dangerous", and the US Senator who claimed that those prisoners are all thieves, murderers, rapists, who deserved it, and the Red Cross, who says that the majority of the prisoners were actually innocent, and were detained without even knowing their charges.

There isn't any rumour so false and baseless that people won't believe eventually, because they believe that "there can't be smoke without fire".