Joyfully he retires to his cell confident that the hanging will not occur at all. — Manuel
Solution #2 — T Clark
Solution #3 — T Clark
Solution #1 - Given that he is confident he won't be hanged, he'll be surprised whichever day he actually is. — T Clark
Indeed, as the prisoner reasons, the prediction must turn out to be false because it is a contradictory speech act. Unfortunately, in this case his logic rescues the judge from her contradiction, because he concludes that the execution cannot take place, rather than that the judge is irrational. — unenlightened
his reasoning must be faulty — Manuel
If you look at it in a Bayesian sense, then the probability of getting hanged on any particular day is mildly surprising, since absent any other information it's a 1/7 chance. — RogueAI
It is. That the judge's words constrain reality is an unwarranted assumption. The judge could have said anything, true or false, sensical or not. Never believe a judge! — unenlightened
It's a good paradox. I'm terrible at solving these sorts of things. — RogueAI
Upon reconsideration: Friday can be eliminated. Thursday would be a surprise only if he lived past Wednesday. Monday, Tuesday, and Wednesday would all be a surprise. — Fooloso4
we only had a one day week and atwoone day weekend. — Manuel
The judge tells K on Sunday afternoon that he, K, will be hanged the following noon and will remain ignorant of the fact till the intervening morning. It would be like K to protest at this point that the judge was contradicting himself. And it would be like the hangman to intrude upon K's complacency at 11.55 next morning, thus showing that the judge had said nothing more self-contradictory than the simple truth. If K had reasoned correctly, Sunday afternoon, he would have reasoned as follows. "We must distinguish four cases: first, that I shall be hanged tomorrow noon and I know it now (but I do not); second, that I shall be unhanged tomorrow noon and know it now (but I do not); third, that I shall be unhanged tomorrow noon and do not know it now; and fourth, that I shall be hanged tomorrow noon and do not know it now. The latter two alternatives are the open possibilities, and the last of all would fulfil the decree. Rather than charging the judge with self-contradiction, therefore, let me suspend judgment and hope for the best." — Quine - On a so-called paradox
if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise [he'll know it already] if he's hanged on Friday. — Manuel/Wiki
to confuse two things; (i) a hypothesis, by K at t, that the decree will be fulfilled, and (ii) a hypothesis, by K at t, that K will know at t + n - 1 that the decree will be fulfilled. Actually hypothesis (i), even as a hypothesis made by K, admits of two sub-cases: K's hypothetical ignorance and K's hypothetical awareness of the hypothetical fact. — Quine - On a so-called paradox
that I shall be hanged tomorrow noon and do not know it now. — Quine - On a so-called paradox
But if the judge says you will be killed tomorrow, then how can he not know he's going to get killed, the judge said so now. — Manuel
It is notable that K acquiesces in the conclusion (wrong, according to the fable of the [eventual] hanging) that the decree will not be fulfilled. If this is a conclusion which he is prepared to accept (though wrongly) in the end as a certainty, it is an alternative which he should have been prepared to take into consideration from the beginning as a possibility. — Quine - On a so-called paradox
it is an alternative which he should have been prepared to take into consideration from the beginning as a possibility. — Quine - On a so-called paradox
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