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Author Topic: The Shipwreck Arcana and broken logic  (Read 5296 times)

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Re: The Shipwreck Arcana and broken logic
« Reply #25 on: May 14, 2021, 09:48:39 am »

If the judge means "at the time of this sentencing you don't know which day the hanging will be", then there is no contradiction; the hanging could be any day.
If the judge means "each evening you won't know if it'll be tomorrow or not", then logically that is the same as saying "it won't be Friday, it won't be Thursday, it won't be Wednesday, etc", which, taken alongside the statement "it'll be sometime next week", amounts to a sentence equivalent to "you will be hanged; you won't be hanged".

The way I've heard it worded is basically "you won't know until the moment I come for you in the morning that today's the day"; which is basically the second interpretation. You can also just simplify it by stripping out the extra days... it's Thursday evening, and the judge says "1 morning between now and tomorrow I will come to get you, but you won't know until the moment I do which day it is". It's more obviously a nonsensical sentence at that point.

Here's another paradox, similar to the hangman one, but with a flavour similar to the one in the OP:
Logicians A and B each choose a number, which they tell C in secret. C then tells them "each of you has chosen a different positive integer, but neither of you knows which of you chose the smaller number".

Neat, I hadn't heard that one. I had to think about it for a bit before I realized the paradox.
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