Discover the paradox of unexpected hanging and why it intrigues scientists

At a time when dozens of artificial intelligences always give us the right answers to the questions presented, an exercise in logic, which does not have a single answer and is universally accepted, has gone viral on social media: the so-called unexpected hanging paradox.

Publicized as a paradox by influential English philosopher Michael Scriven in the philosophy magazine Mind in 1951, the challenge was first proposed by Swedish mathematician Lennart Ekbom in the 1940s.

Designed to explore the limits of logical reasoning and our understanding of knowledge and predictability, the paradox continues today as a challenge to research and debate.

The concept challenges scientists to review their understandings of logic, knowledge and causality.

The unexpected hanging paradox

The story of the paradox begins on a Saturday. A judge known for keeping his word and sentences to the letter orders a prisoner to be hanged the following week.

“The hanging will take place at noon on one of the next seven days, but you will not know the date until you are informed on the morning of the day of execution,” the ruling says.

The paradox arises when the prisoner reasons together with his lawyer:

1. It cannot be on Saturday, because if Friday night arrives without being hanged, he would know that it could only be on Saturday, no longer a surprise .
2. Following the same line of reasoning, the execution cannot be on Friday, because, if Thursday night arrives without being hanged, he would be sure that it would be on Friday (since Saturday was eliminated).
3. The reasoning continues to go back to Sunday.
4. Happily, prisoner and lawyer conclude that hanging is impossible, as there is not a single day on which the necessary surprise of the sentence occurs.

Reassured by the lawyer’s logic, the prisoner says to himself: “This won’t come out until tomorrow. But they can’t hang me tomorrow because I know today!” — and slept peacefully, because he was sure that the judge’s decision could not be implemented in practice.

Until…

On Wednesday morning, the prisoner was surprised by the announcement, made by the executioner himself, that he would execute him at noon.

As, logically, he did not expect this, until he was informed at that very moment, the judge’s sentence was carried out, and the prisoner too as it was delivered.

What happened to logic?

Following all the lawyer’s perfectly logical arguments, the prisoner was awakened from his dream of impunity by the disconcerting visit of the executioner. What could have gone wrong?

A fan of paradox, English philosopher Michael Scriven thought the concept was (and is) so fascinating for its subtlety in the distinction between knowledge and belief, and how this affects our expectations and the very definition of surprise.

“The logician pathetically goes over the movements that always made the spell work, but, for some reason, the monster, reality, doesn’t understand the idea and moves on,” he said.

The fact is that, despite many discussions, a satisfactory resolution of the paradox has not yet been reached, and it continues to intrigue scientists.

Used to studying the principles of valid reasoning and the structure of arguments, logicians always try to expose flaws in the paradox, while epistemologists on duty go deeper and question the validity of knowledge.

At first, we could think that the only day on which the prisoner would not be surprised was just Saturday, as he would know in advance, on Friday, that this would happen.

Still, on Thursday night he would have two possible days, but not the knowledge, which he would only acquire after surviving Friday.

There are those who argue that the way the sentence was handed down was just a trap by the judge, so that the prisoner would reach that logical conclusion, and the surprise would be greater.

But even that wouldn’t work if the convict was considered a persistent pessimist.

In that case, he would reject the lawyer’s arguments and wake up every day with the certainty that he would be hanged. Impossible to be surprised, would he escape the gallows?

Conclusion (spoiler: none)

Perhaps what intrigues us all, laymen and scientists, is the way in which the paradox mocks our understanding of knowledge and prediction especially when technology gives us all the answers.

And it’s an example that a future event may be known to be true by one (powerful?) person, but not by another, until it happens.

In this sense, the unexpected hanging paradox resembles the thought experiment of the Austrian physicist Erwin Schrödinger who, by introducing his live-dead cat into a closed box with a vial of poison, broke classical logic.

Since this logical paradox is from 1935, perhaps Ekbom already knew that, after all, there is a third state to a proposition.

Thus, just like the cat, the prisoner was alive and dead in his cell, until he received the terrible news from the executioner.

But, in the case of the convict, things were even worse, as he used binary logic to discard all possible days, and, precisely by doing this, he was vulnerable to surprise and had to include them in a distressing way and then discard them. them in a loop that lasted until noon on Wednesday.

This content was originally published in Discover the unexpected hanging paradox and why it intrigues scientists on the CNN Brasil website.

Source: CNN Brasil