Have you ever wondered why Monaco Harbour has never been invaded by high-seas pirates? Legend has it that it nearly happened once, but the quick-thinking Monégasques took it all in their stride without lifting a finger. The tale goes something like this…
A long, long time ago, a fleet of villainous pirate ships approached Monaco’s coast below the Rock, towards what today would be known as Port Hercule. Standing on the bow of the lead ship was the fleet’s one-eyed, angry-looking captain, shouting across the water at the Monaco locals:
“I am a man of my word! At 1.00 pm, I shall send a ship into your harbour to destroy you all!”
The people of Monaco looked slightly concerned.
“Not until the first ship arrives at your shore will we begin our assault,” he continued, “but just to make certain of your destruction, as cover I’ll send another ship 15 minutes ahead of it, at 12.45 pm. That ship will start the attack and you shall have no escape. Oh, and just in case there are any issues with that ship, I’ll send another too, a few moments ahead of that, to begin the attack; and also another slightly ahead of that one. And one just ahead of that too; and another ahead of that. And so on… ad infinitum!”
At the words ad infinitum, the Monégasques suddenly relaxed.
They had spotted the flaw in the pirate’s plan. As the pirate was a man of his word, he seemed to have trapped himself in a paradox. Despite an infinite number of ships in his fleet on their way to invade, the Monégasques realised that none could ever possibly arrive first. Upon realising this, they relaxed, cracked open the pastis and enjoyed the peace of the harbour.
So why no threat?
Whatever ship the pirate intends to send first, he has also committed to sending another just in front of it to start the attack. So, the initially deployed ship can’t attack, as another has been sent ahead of it to begin the assault. And that ship can’t attack either, as the pirate keeps his word and sends another ahead of it. For every ship intended to begin the attack, there must always be another one preceding it. There is, therefore, never a first ship to arrive and begin the assault.
To get a clearer picture, the question to ask is which pirate ship from the infinite fleet would actually attack the harbour. It’s impossible to name one because, as soon as you do, the rebuttal comes that it can’t be that ship: another has been sent ahead of it as insurance. Point to that ship instead, and another has already been sent ahead of that one too… and so on, ad infinitum.
As the pirate has also proudly declared that he is a man of his word, he is far too stubborn to abandon his plan and is stuck with it. He is forever anchored off the coast of Monaco, scratching his beard with a puzzled look on his face, wondering why his infinite fleet of ships is having no effect whatsoever.
The long line of pirate ships coming to attack may be infinite, but as a result there can never be a first ship to begin the assault. Time to crack open the pastis indeed. There are no pirates attacking these shores any time soon and plenty of time to relax and enjoy the tranquillity of the harbour.
A se revede!
References
For further reading on similar phenomena:
Pruss, Alexander. “From the Grim Reaper Paradox to the Kalam Argument.” 2009.
Koons, Robert C. “A New Kalam Argument: Revenge of the Grim Reaper.” Noûs, 48, no. 2 (2014), pp. 256–267.